%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWW474^2 : 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 : n028.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 21.93s 4.57s
% Output : Refutation 21.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 318 ( 81 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 330 ( 47 ~; 36 |; 0 &; 226 @)
% ( 0 <=>; 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 : 192 ( 189 usr; 9 con; 0-6 aty)
% Number of variables : 58 ( 8 ^; 50 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
com: $tType ).
thf(type_def_7,type,
pname: $tType ).
thf(type_def_8,type,
option_com: $tType ).
thf(type_def_9,type,
state: $tType ).
thf(type_def_10,type,
hoare_1167836817_state: $tType ).
thf(type_def_11,type,
option_pname: $tType ).
thf(type_def_12,type,
option1574264306_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_1167836817_state: $tType ).
thf(func_def_4,type,
option_com: $tType ).
thf(func_def_5,type,
option_pname: $tType ).
thf(func_def_6,type,
option1574264306_state: $tType ).
thf(func_def_7,type,
wt: com > $o ).
thf(func_def_9,type,
body: pname > option_com ).
thf(func_def_10,type,
body_1: pname > com ).
thf(func_def_11,type,
skip: com ).
thf(func_def_12,type,
semi: com > com > com ).
thf(func_def_13,type,
while: ( state > $o ) > com > com ).
thf(func_def_14,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_15,type,
finite33115244te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > $o ).
thf(func_def_16,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_17,type,
finite1380128977tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
thf(func_def_18,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(func_def_19,type,
finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_20,type,
finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
thf(func_def_21,type,
finite979047547tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o ).
thf(func_def_22,type,
finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(func_def_23,type,
finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
thf(func_def_24,type,
finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
thf(func_def_25,type,
finite671847800tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o ).
thf(func_def_26,type,
finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(func_def_27,type,
finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
thf(func_def_28,type,
minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_29,type,
minus_1708687022te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_30,type,
minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_31,type,
minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_32,type,
the_pname: ( pname > $o ) > pname ).
thf(func_def_33,type,
the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_34,type,
hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
thf(func_def_35,type,
hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_36,type,
hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_38,type,
hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
thf(func_def_39,type,
if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ).
thf(func_def_40,type,
if_option_com: $o > option_com > option_com > option_com ).
thf(func_def_41,type,
semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_42,type,
semila1758709489te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_43,type,
semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_44,type,
semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_45,type,
semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_46,type,
semila866907787te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_47,type,
semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_48,type,
semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_49,type,
semila10642723_sup_o: $o > $o > $o ).
thf(func_def_50,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(func_def_51,type,
evalc: com > state > state > $o ).
thf(func_def_52,type,
some_com: com > option_com ).
thf(func_def_53,type,
some_pname: pname > option_pname ).
thf(func_def_54,type,
some_H1433514562_state: hoare_1167836817_state > option1574264306_state ).
thf(func_def_55,type,
set_com: option_com > com > $o ).
thf(func_def_56,type,
set_pname: option_pname > pname > $o ).
thf(func_def_57,type,
set_Ho2131684873_state: option1574264306_state > hoare_1167836817_state > $o ).
thf(func_def_58,type,
the_com: option_com > com ).
thf(func_def_59,type,
bot_bot_pname_o_o: ( pname > $o ) > $o ).
thf(func_def_60,type,
bot_bo691907561te_o_o: ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_61,type,
bot_bot_com_o: com > $o ).
thf(func_def_62,type,
bot_bot_pname_o: pname > $o ).
thf(func_def_63,type,
bot_bo70021908tate_o: hoare_1167836817_state > $o ).
thf(func_def_65,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_66,type,
ord_le741939125te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
thf(func_def_67,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_68,type,
ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_69,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_70,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_71,type,
collec1218656682te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
thf(func_def_72,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_73,type,
collec269976083tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_74,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(func_def_75,type,
collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_76,type,
image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_77,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_78,type,
image_1381916541_state: ( ( pname > $o ) > hoare_1167836817_state ) > ( ( pname > $o ) > $o ) > hoare_1167836817_state > $o ).
thf(func_def_79,type,
image_1488525317tate_o: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_80,type,
image_980295115_pname: ( ( hoare_1167836817_state > $o ) > pname ) > ( ( hoare_1167836817_state > $o ) > $o ) > pname > $o ).
thf(func_def_81,type,
image_635813834_state: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
thf(func_def_82,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_83,type,
image_475339327tate_o: ( pname > hoare_1167836817_state > $o ) > ( pname > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_84,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_85,type,
image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o ).
thf(func_def_86,type,
image_2066861949name_o: ( hoare_1167836817_state > pname > $o ) > ( hoare_1167836817_state > $o ) > ( pname > $o ) > $o ).
thf(func_def_87,type,
image_1745649338tate_o: ( hoare_1167836817_state > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_88,type,
image_8178176_pname: ( hoare_1167836817_state > pname ) > ( hoare_1167836817_state > $o ) > pname > $o ).
thf(func_def_89,type,
image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_90,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_91,type,
insert999278200tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_92,type,
insert_com: com > ( com > $o ) > com > $o ).
thf(func_def_93,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(func_def_94,type,
insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_95,type,
the_elem_pname: ( pname > $o ) > pname ).
thf(func_def_96,type,
the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_97,type,
fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_98,type,
fequal1486222077tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_99,type,
fequal_pname: pname > pname > $o ).
thf(func_def_100,type,
fequal_state: state > state > $o ).
thf(func_def_101,type,
fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o ).
thf(func_def_102,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_103,type,
member864234961tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
thf(func_def_104,type,
member_com: com > ( com > $o ) > $o ).
thf(func_def_105,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(func_def_106,type,
member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
thf(func_def_107,type,
fa: hoare_1167836817_state > $o ).
thf(func_def_108,type,
pn: pname ).
thf(func_def_109,type,
y: com ).
thf(func_def_123,type,
sK0: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_124,type,
sK1: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_125,type,
sK2: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_126,type,
sK3: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_127,type,
sK4: hoare_1167836817_state > $o ).
thf(func_def_128,type,
sK5: hoare_1167836817_state > $o ).
thf(func_def_129,type,
sK6: hoare_1167836817_state > $o ).
thf(func_def_130,type,
sK7: ( hoare_1167836817_state > $o ) > ( pname > $o ) > ( pname > hoare_1167836817_state ) > pname ).
thf(func_def_131,type,
sK8: ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_132,type,
sK9: ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_133,type,
sK10: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_134,type,
sK11: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_135,type,
sK12: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_136,type,
sK13: ( hoare_1167836817_state > $o ) > ( pname > $o ) > ( pname > hoare_1167836817_state ) > pname > $o ).
thf(func_def_137,type,
sK14: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state ).
thf(func_def_138,type,
sK15: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
thf(func_def_139,type,
sK16: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state ).
thf(func_def_140,type,
sK17: ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_141,type,
sK18: ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_142,type,
sK19: ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_143,type,
sK20: ( ( pname > $o ) > $o ) > pname ).
thf(func_def_144,type,
sK21: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_145,type,
sK22: ( ( pname > $o ) > $o ) > pname ).
thf(func_def_146,type,
sK23: state > state ).
thf(func_def_147,type,
sK24: ( ( pname > $o ) > $o ) > pname ).
thf(func_def_148,type,
sK25: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_149,type,
sK26: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_150,type,
sK27: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname ).
thf(func_def_151,type,
sK28: ( pname > state > state > $o ) > ( pname > state > state > $o ) > ( pname > state > state > $o ) > ( hoare_1167836817_state > $o ) > ( pname > com ) > ( pname > state > state > $o ) > pname ).
thf(func_def_152,type,
sK29: hoare_1167836817_state > $o ).
thf(func_def_153,type,
sK30: hoare_1167836817_state > $o ).
thf(func_def_154,type,
sK31: hoare_1167836817_state > $o ).
thf(func_def_155,type,
sK32: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_156,type,
sK33: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_157,type,
sK34: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_158,type,
sK35: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_159,type,
sK36: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_160,type,
sK37: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_161,type,
sK38: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_162,type,
sK39: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_163,type,
sK40: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_164,type,
sK41: state > com > state > ( state > $o ) > state ).
thf(func_def_165,type,
sK42: ( pname > $o ) > pname ).
thf(func_def_166,type,
sK43: ( pname > $o ) > pname > $o ).
thf(func_def_167,type,
sK44: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state ).
thf(func_def_168,type,
sK45: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
thf(func_def_169,type,
sK46: ( pname > $o ) > ( pname > hoare_1167836817_state ) > hoare_1167836817_state > pname ).
thf(func_def_170,type,
sK47: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > hoare_1167836817_state > $o ).
thf(func_def_171,type,
sK48: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_172,type,
sK49: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_173,type,
sK50: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > hoare_1167836817_state > $o ).
thf(func_def_174,type,
sK51: hoare_1167836817_state > ( pname > hoare_1167836817_state ) > ( pname > $o ) > pname ).
thf(func_def_175,type,
sK52: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_176,type,
sK53: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_177,type,
sK54: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_178,type,
sK55: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_179,type,
sK56: hoare_1167836817_state > com ).
thf(func_def_180,type,
sK57: hoare_1167836817_state > state > state > $o ).
thf(func_def_181,type,
sK58: hoare_1167836817_state > state > state > $o ).
thf(func_def_182,type,
sK59: ( pname > $o ) > pname ).
thf(func_def_183,type,
sK60: ( pname > $o ) > pname > pname > $o ).
thf(func_def_184,type,
sK61: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_185,type,
sK62: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_186,type,
sK63: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_187,type,
sK64: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(func_def_188,type,
sK65: pname > ( pname > option_com ) > com ).
thf(func_def_189,type,
sK66: ( pname > hoare_1167836817_state ) > ( pname > $o ) > ( hoare_1167836817_state > $o ) > pname > $o ).
thf(func_def_190,type,
sK67: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_191,type,
sK68: ( state > state > $o ) > ( state > state > $o ) > ( hoare_1167836817_state > $o ) > com > state ).
thf(func_def_192,type,
sK69: ( state > state > $o ) > ( state > state > $o ) > ( hoare_1167836817_state > $o ) > com > state ).
thf(func_def_193,type,
sK70: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_194,type,
sK71: ( pname > $o ) > ( pname > hoare_1167836817_state ) > ( pname > hoare_1167836817_state ) > pname ).
thf(func_def_195,type,
sK72: ( pname > $o ) > pname > $o ).
thf(func_def_196,type,
sK73: ( pname > $o ) > pname ).
thf(func_def_197,type,
sK74: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_198,type,
sK75: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_199,type,
sK76: ( pname > $o ) > pname ).
thf(func_def_200,type,
sK77: ( pname > $o ) > pname > pname > $o ).
thf(func_def_201,type,
sK78: ( hoare_1167836817_state > $o ) > pname ).
thf(func_def_202,type,
sK79: pname > com ).
thf(func_def_203,type,
sK80: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_204,type,
sK81: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_205,type,
sK82: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(func_def_206,type,
sK83: state ).
thf(func_def_207,type,
sK84: state ).
thf(func_def_208,type,
sK85: ( pname > $o ) > pname ).
thf(func_def_210,type,
ph87:
!>[X0: $tType] : X0 ).
thf(f3924,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3923,f3388]) ).
thf(f3388,plain,
( $true
= ( wt @ y ) ),
inference(equality_resolution,[status(thm)],[f3381]) ).
thf(f3381,plain,
! [X0: com] :
( ( ( some_com @ y )
!= ( some_com @ X0 ) )
| ( $true
= ( wt @ X0 ) ) ),
inference(superposition,[status(thm)],[f3367,f2780]) ).
thf(f2780,plain,
( ( body @ pn )
= ( some_com @ y ) ),
inference(cnf_transformation,[status(thm)],[f721]) ).
thf(f721,axiom,
( ( body @ pn )
= ( some_com @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_5) ).
thf(f3367,plain,
! [X0: pname,X1: com] :
( ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( $true
= ( wt @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3256]) ).
thf(f3256,plain,
! [X0: pname,X1: com] :
( ( $true != $true )
| ( $true
= ( wt @ X1 ) )
| ( ( some_com @ X1 )
!= ( body @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f2849,f2662]) ).
thf(f2662,plain,
wT_bodies = $true,
inference(cnf_transformation,[status(thm)],[f1563]) ).
thf(f1563,plain,
wT_bodies = $true,
inference(fool_elimination,[status(thm)],[f1562]) ).
thf(f1562,plain,
wT_bodies,
inference(rectify,[status(thm)],[f717]) ).
thf(f717,axiom,
wT_bodies,
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_1) ).
thf(f2849,plain,
! [X0: pname,X1: com] :
( ( $true
= ( wt @ X1 ) )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( wT_bodies != $true ) ),
inference(cnf_transformation,[status(thm)],[f2363]) ).
thf(f2363,plain,
! [X0: pname,X1: com] :
( ( $true
= ( wt @ X1 ) )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( wT_bodies != $true ) ),
inference(flattening,[status(thm)],[f2362]) ).
thf(f2362,plain,
! [X0: pname,X1: com] :
( ( $true
= ( wt @ X1 ) )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( wT_bodies != $true ) ),
inference(ennf_transformation,[status(thm)],[f1051]) ).
thf(f1051,plain,
! [X0: pname,X1: com] :
( ( wT_bodies = $true )
=> ( ( ( some_com @ X1 )
= ( body @ X0 ) )
=> ( $true
= ( wt @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1050]) ).
thf(f1050,plain,
! [X0: pname,X1: com] :
( wT_bodies
=> ( ( ( some_com @ X1 )
= ( body @ X0 ) )
=> ( wt @ X1 ) ) ),
inference(rectify,[status(thm)],[f216]) ).
thf(f216,axiom,
! [X18: pname,X192: com] :
( wT_bodies
=> ( ( ( body @ X18 )
= ( some_com @ X192 ) )
=> ( wt @ X192 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_215_WT__bodiesD) ).
thf(f3923,plain,
( $true
!= ( wt @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f3915]) ).
thf(f3915,plain,
( ( $true
!= ( wt @ y ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3810,f3362]) ).
thf(f3362,plain,
! [X0: com] :
( ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) )
| ( $true
!= ( wt @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3361]) ).
thf(f3361,plain,
! [X0: com] :
( ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f3257]) ).
thf(f3257,plain,
! [X0: com] :
( ( $true != $true )
| ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3070,f2662,f2813]) ).
thf(f2813,plain,
hoare_1201148605gleton = $true,
inference(cnf_transformation,[status(thm)],[f1849]) ).
thf(f1849,plain,
hoare_1201148605gleton = $true,
inference(fool_elimination,[status(thm)],[f1848]) ).
thf(f1848,plain,
hoare_1201148605gleton,
inference(rectify,[status(thm)],[f716]) ).
thf(f716,axiom,
hoare_1201148605gleton,
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_0) ).
thf(f3070,plain,
! [X0: com] :
( ( wT_bodies != $true )
| ( hoare_1201148605gleton != $true )
| ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) ) ),
inference(cnf_transformation,[status(thm)],[f2091]) ).
thf(f2091,plain,
! [X0: com] :
( ( wT_bodies != $true )
| ( hoare_1201148605gleton != $true )
| ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) ) ),
inference(flattening,[status(thm)],[f2090]) ).
thf(f2090,plain,
! [X0: com] :
( ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) )
| ( $true
!= ( wt @ X0 ) )
| ( wT_bodies != $true )
| ( hoare_1201148605gleton != $true ) ),
inference(ennf_transformation,[status(thm)],[f1789]) ).
thf(f1789,plain,
! [X0: com] :
( ( hoare_1201148605gleton = $true )
=> ( ( wT_bodies = $true )
=> ( ( $true
= ( wt @ X0 ) )
=> ( $true
= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f1788]) ).
thf(f1788,plain,
! [X0: com] :
( hoare_1201148605gleton
=> ( wT_bodies
=> ( ( wt @ X0 )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo70021908tate_o ) ) ) ) ),
inference(rectify,[status(thm)],[f54]) ).
thf(f54,axiom,
! [X42: com] :
( hoare_1201148605gleton
=> ( wT_bodies
=> ( ( wt @ X42 )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X42 ) @ bot_bo70021908tate_o ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_53_MGF) ).
thf(f3810,plain,
( $true
!= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3800]) ).
thf(f3800,plain,
( ( $true != $true )
| ( $true
!= ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ) ),
inference(superposition,[status(thm)],[f3465,f3164]) ).
thf(f3164,plain,
! [X0: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ X0 @ bot_bo70021908tate_o )
= $true ),
inference(cnf_transformation,[status(thm)],[f833]) ).
thf(f833,plain,
! [X0: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ X0 @ bot_bo70021908tate_o )
= $true ),
inference(fool_elimination,[status(thm)],[f832]) ).
thf(f832,plain,
! [X0: hoare_1167836817_state > $o] : ( hoare_123228589_state @ X0 @ bot_bo70021908tate_o ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: hoare_1167836817_state > $o] : ( hoare_123228589_state @ X0 @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_0_empty) ).
thf(f3465,plain,
! [X0: hoare_1167836817_state > $o] :
( ( $true
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ X0 ) )
| ( $true
!= ( hoare_123228589_state @ X0 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3454]) ).
thf(f3454,plain,
! [X0: hoare_1167836817_state > $o] :
( ( $true
!= ( hoare_123228589_state @ X0 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) )
| ( $true
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3149,f3002]) ).
thf(f3002,plain,
! [X2: hoare_1167836817_state > $o,X0: hoare_1167836817_state > $o,X1: hoare_1167836817_state > $o] :
( ( $true
= ( hoare_123228589_state @ X1 @ X0 ) )
| ( $true
!= ( hoare_123228589_state @ X1 @ X2 ) )
| ( ( hoare_123228589_state @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2193]) ).
thf(f2193,plain,
! [X0: hoare_1167836817_state > $o,X1: hoare_1167836817_state > $o,X2: hoare_1167836817_state > $o] :
( ( $true
!= ( hoare_123228589_state @ X1 @ X2 ) )
| ( $true
= ( hoare_123228589_state @ X1 @ X0 ) )
| ( ( hoare_123228589_state @ X2 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f2192]) ).
thf(f2192,plain,
! [X0: hoare_1167836817_state > $o,X1: hoare_1167836817_state > $o,X2: hoare_1167836817_state > $o] :
( ( $true
= ( hoare_123228589_state @ X1 @ X0 ) )
| ( $true
!= ( hoare_123228589_state @ X1 @ X2 ) )
| ( ( hoare_123228589_state @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f891]) ).
thf(f891,plain,
! [X0: hoare_1167836817_state > $o,X1: hoare_1167836817_state > $o,X2: hoare_1167836817_state > $o] :
( ( ( hoare_123228589_state @ X2 @ X0 )
= $true )
=> ( ( $true
= ( hoare_123228589_state @ X1 @ X2 ) )
=> ( $true
= ( hoare_123228589_state @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f890]) ).
thf(f890,plain,
! [X0: hoare_1167836817_state > $o,X1: hoare_1167836817_state > $o,X2: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ X2 @ X0 )
=> ( ( hoare_123228589_state @ X1 @ X2 )
=> ( hoare_123228589_state @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X11: hoare_1167836817_state > $o,X9: hoare_1167836817_state > $o,X10: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ X10 @ X11 )
=> ( ( hoare_123228589_state @ X9 @ X10 )
=> ( hoare_123228589_state @ X9 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_4_cut) ).
thf(f3149,plain,
( $true
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ),
inference(cnf_transformation,[status(thm)],[f1934]) ).
thf(f1934,plain,
( $true
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ),
inference(flattening,[status(thm)],[f1721]) ).
thf(f1721,plain,
( $true
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ),
inference(fool_elimination,[status(thm)],[f1720]) ).
thf(f1720,plain,
~ ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ),
inference(rectify,[status(thm)],[f724]) ).
thf(f724,negated_conjecture,
~ ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X217: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X217 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ),
inference(negated_conjecture,[status(cth)],[f723]) ).
thf(f723,conjecture,
( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X217: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X217 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_7) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW474^2 : 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
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 13:40:57 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : SWW474^2 : TPTP v9.2.1. Released v5.3.0.
% 0.28/0.45 % Domain : Software Verification
% 0.28/0.45 % Problem : Hoare's Logic with Procedures line 440, 500 axioms selected
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.28/0.45 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Bla11]
% 0.28/0.45 % Names : hoare_500_thf_l440 [Bla11]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % 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, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0
% 0.28/0.45 % Syntax : Number of formulae : 833 ( 176 unt; 110 typ; 0 def)
% 0.28/0.45 % Number of atoms : 3278 ( 594 equ; 75 cnn)
% 0.28/0.45 % Maximal formula atoms : 12 ( 4 avg)
% 0.28/0.45 % Number of connectives : 6419 ( 233 ~; 55 |; 150 &;5021 @)
% 0.28/0.45 % ( 116 <=>; 844 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 19 ( 7 avg)
% 0.28/0.45 % Number of types : 8 ( 7 usr)
% 0.28/0.45 % Number of type conns : 2404 (2404 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 110 ( 103 usr; 12 con; 0-3 aty)
% 0.28/0.45 % Number of variables : 2030 ( 131 ^;1851 !; 48 ?;2030 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.28/0.45 % 2011-08-09 19:43:11
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 %----Should-be-implicit typings (7)
% 0.28/0.45 thf(ty_ty_tc__Com__Ocom,type,
% 0.28/0.45 com: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_ty_tc__Com__Opname,type,
% 0.28/0.45 pname: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_ty_tc__Com__Ostate,type,
% 0.28/0.45 state: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.28/0.45 hoare_1167836817_state: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.28/0.45 option_com: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Com__Opname_J,type,
% 0.28/0.45 option_pname: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,
% 0.28/0.45 option1574264306_state: $tType ).
% 0.28/0.45
% 0.28/0.45 %----Explicit typings (103)
% 0.28/0.45 thf(sy_c_Com_OWT,type,
% 0.28/0.45 wt: com > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Com_OWT__bodies,type,
% 0.28/0.45 wT_bodies: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Com_Obody,type,
% 0.28/0.45 body: pname > option_com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Com_Ocom_OBODY,type,
% 0.28/0.45 body_1: pname > com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.28/0.45 skip: com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Com_Ocom_OSemi,type,
% 0.28/0.45 semi: com > com > com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Com_Ocom_OWhile,type,
% 0.28/0.45 while: ( state > $o ) > com > com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.28/0.45 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 0.28/0.45 finite33115244te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.28/0.45 finite1380128977tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.28/0.45 finite_finite_pname: ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C,type,
% 0.28/0.45 finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 0.28/0.45 finite979047547tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 0.28/0.45 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.28/0.45 finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____srushsum,type,
% 0.28/0.45 finite671847800tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 0.28/0.45 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 0.28/0.45 finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.28/0.45 minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____srushs,type,
% 0.28/0.45 minus_1708687022te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__,type,
% 0.28/0.45 minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HOL_OThe_000tc__Com__Opname,type,
% 0.28/0.45 the_pname: ( pname > $o ) > pname ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_,type,
% 0.28/0.45 the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Hoare__Mirabelle__srushsumbx_OMGT,type,
% 0.28/0.45 hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.28/0.45 hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate,type,
% 0.28/0.45 hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ostate__not__singleton,type,
% 0.28/0.45 hoare_1201148605gleton: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate,type,
% 0.28/0.45 hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.28/0.45 if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.28/0.45 if_option_com: $o > option_com > option_com > option_com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.28/0.45 semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.28/0.45 semila1758709489te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s,type,
% 0.28/0.45 semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.28/0.45 semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.28/0.45 semila866907787te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s,type,
% 0.28/0.45 semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,
% 0.28/0.45 semila10642723_sup_o: $o > $o > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
% 0.28/0.45 dom_pname_com: ( pname > option_com ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Natural_Oevalc,type,
% 0.28/0.45 evalc: com > state > state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,
% 0.28/0.45 some_com: com > option_com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Ooption_OSome_000tc__Com__Opname,type,
% 0.28/0.45 some_pname: pname > option_pname ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__,type,
% 0.28/0.45 some_H1433514562_state: hoare_1167836817_state > option1574264306_state ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Oset_000tc__Com__Ocom,type,
% 0.28/0.45 set_com: option_com > com > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Oset_000tc__Com__Opname,type,
% 0.28/0.45 set_pname: option_pname > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Oset_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,
% 0.28/0.45 set_Ho2131684873_state: option1574264306_state > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.28/0.45 the_com: option_com > com ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.28/0.45 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu,type,
% 0.28/0.45 bot_bo691907561te_o_o: ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 0.28/0.45 bot_bot_com_o: com > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 bot_bot_pname_o: pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,
% 0.28/0.45 bot_bo70021908tate_o: hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.28/0.45 bot_bot_o: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.28/0.45 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____sr,type,
% 0.28/0.45 ord_le741939125te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____srushsum,type,
% 0.28/0.45 ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 0.28/0.45 ord_less_eq_o: $o > $o > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.28/0.45 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_I,type,
% 0.28/0.45 collec1218656682te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,
% 0.28/0.45 collec269976083tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.28/0.45 collect_pname: ( pname > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 0.28/0.45 collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.28/0.45 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____sru,type,
% 0.28/0.45 image_1381916541_state: ( ( pname > $o ) > hoare_1167836817_state ) > ( ( pname > $o ) > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_,type,
% 0.28/0.45 image_1488525317tate_o: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__001,type,
% 0.28/0.45 image_980295115_pname: ( ( hoare_1167836817_state > $o ) > pname ) > ( ( hoare_1167836817_state > $o ) > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__002,type,
% 0.28/0.45 image_635813834_state: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____srushsumbx,type,
% 0.28/0.45 image_475339327tate_o: ( pname > hoare_1167836817_state > $o ) > ( pname > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.28/0.45 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri,type,
% 0.28/0.45 image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat,type,
% 0.28/0.45 image_2066861949name_o: ( hoare_1167836817_state > pname > $o ) > ( hoare_1167836817_state > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_003,type,
% 0.28/0.45 image_1745649338tate_o: ( hoare_1167836817_state > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_004,type,
% 0.28/0.45 image_8178176_pname: ( hoare_1167836817_state > pname ) > ( hoare_1167836817_state > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_005,type,
% 0.28/0.45 image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,type,
% 0.28/0.45 insert999278200tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_000tc__Com__Ocom,type,
% 0.28/0.45 insert_com: com > ( com > $o ) > com > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.28/0.45 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,
% 0.28/0.45 insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Othe__elem_000tc__Com__Opname,type,
% 0.28/0.45 the_elem_pname: ( pname > $o ) > pname ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O,type,
% 0.28/0.45 the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 0.28/0.45 fequal1486222077tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.28/0.45 fequal_pname: pname > pname > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_fequal_000tc__Com__Ostate,type,
% 0.28/0.45 fequal_state: state > state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.28/0.45 fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.28/0.45 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 0.28/0.45 member864234961tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_000tc__Com__Ocom,type,
% 0.28/0.45 member_com: com > ( com > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_000tc__Com__Opname,type,
% 0.28/0.45 member_pname: pname > ( pname > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.28/0.45 member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_Fa,type,
% 0.28/0.45 fa: hoare_1167836817_state > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_pn,type,
% 0.28/0.45 pn: pname ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_y,type,
% 0.28/0.45 y: com ).
% 0.28/0.45
% 0.28/0.45 %----Relevant facts (699)
% 0.28/0.45 thf(fact_0_empty,axiom,
% 0.28/0.45 ! [G_3: hoare_1167836817_state > $o] : ( hoare_123228589_state @ G_3 @ bot_bo70021908tate_o ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_1_asm,axiom,
% 0.28/0.45 ! [Ts_7: hoare_1167836817_state > $o,G_35: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( ord_le827224136tate_o @ Ts_7 @ G_35 )
% 0.28/0.45 => ( hoare_123228589_state @ G_35 @ Ts_7 ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_2_weaken,axiom,
% 0.28/0.45 ! [Ts_6: hoare_1167836817_state > $o,G_34: hoare_1167836817_state > $o,Ts_5: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( hoare_123228589_state @ G_34 @ Ts_5 )
% 0.28/0.45 => ( ( ord_le827224136tate_o @ Ts_6 @ Ts_5 )
% 0.28/0.45 => ( hoare_123228589_state @ G_34 @ Ts_6 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_3_thin,axiom,
% 0.28/0.45 ! [G_33: hoare_1167836817_state > $o,G_32: hoare_1167836817_state > $o,Ts_4: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( hoare_123228589_state @ G_32 @ Ts_4 )
% 0.28/0.45 => ( ( ord_le827224136tate_o @ G_32 @ G_33 )
% 0.28/0.45 => ( hoare_123228589_state @ G_33 @ Ts_4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_4_cut,axiom,
% 0.28/0.45 ! [G_31: hoare_1167836817_state > $o,G_30: hoare_1167836817_state > $o,Ts_3: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( hoare_123228589_state @ G_30 @ Ts_3 )
% 0.28/0.45 => ( ( hoare_123228589_state @ G_31 @ G_30 )
% 0.28/0.45 => ( hoare_123228589_state @ G_31 @ Ts_3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 0.28/0.45 ! [Ts_2: hoare_1167836817_state > $o,G_29: hoare_1167836817_state > $o,T_3: hoare_1167836817_state] :
% 0.28/0.45 ( ( hoare_123228589_state @ G_29 @ ( insert2134838167_state @ T_3 @ bot_bo70021908tate_o ) )
% 0.28/0.45 => ( ( hoare_123228589_state @ G_29 @ Ts_2 )
% 0.28/0.45 => ( hoare_123228589_state @ G_29 @ ( insert2134838167_state @ T_3 @ Ts_2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_6_derivs__insertD,axiom,
% 0.28/0.45 ! [G_28: hoare_1167836817_state > $o,T_2: hoare_1167836817_state,Ts_1: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( hoare_123228589_state @ G_28 @ ( insert2134838167_state @ T_2 @ Ts_1 ) )
% 0.28/0.45 => ( ( hoare_123228589_state @ G_28 @ ( insert2134838167_state @ T_2 @ bot_bo70021908tate_o ) )
% 0.28/0.45 & ( hoare_123228589_state @ G_28 @ Ts_1 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_7_MGT__BodyN,axiom,
% 0.28/0.45 ! [Pn_1: pname,G_3: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G_3 ) @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo70021908tate_o ) )
% 0.28/0.45 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_8_finite__Collect__subsets,axiom,
% 0.28/0.45 ! [A_201: ( pname > $o ) > $o] :
% 0.28/0.45 ( ( finite297249702name_o @ A_201 )
% 0.28/0.45 => ( finite1066544169me_o_o
% 0.28/0.45 @ ( collect_pname_o_o
% 0.28/0.45 @ ^ [B_43: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_43 @ A_201 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_9_finite__Collect__subsets,axiom,
% 0.28/0.45 ! [A_201: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.45 ( ( finite1380128977tate_o @ A_201 )
% 0.28/0.45 => ( finite33115244te_o_o
% 0.28/0.45 @ ( collec1218656682te_o_o
% 0.28/0.45 @ ^ [B_43: ( hoare_1167836817_state > $o ) > $o] : ( ord_le741939125te_o_o @ B_43 @ A_201 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_10_finite__Collect__subsets,axiom,
% 0.28/0.45 ! [A_201: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( finite1084549118_state @ A_201 )
% 0.28/0.45 => ( finite1380128977tate_o
% 0.28/0.45 @ ( collec269976083tate_o
% 0.28/0.45 @ ^ [B_43: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ B_43 @ A_201 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_11_finite__Collect__subsets,axiom,
% 0.28/0.45 ! [A_201: pname > $o] :
% 0.28/0.45 ( ( finite_finite_pname @ A_201 )
% 0.28/0.45 => ( finite297249702name_o
% 0.28/0.45 @ ( collect_pname_o
% 0.28/0.45 @ ^ [B_43: pname > $o] : ( ord_less_eq_pname_o @ B_43 @ A_201 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_12_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: hoare_1167836817_state > pname > $o,F_61: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( finite1084549118_state @ F_61 )
% 0.28/0.45 => ( finite297249702name_o @ ( image_2066861949name_o @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_13_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: hoare_1167836817_state > hoare_1167836817_state > $o,F_61: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( finite1084549118_state @ F_61 )
% 0.28/0.45 => ( finite1380128977tate_o @ ( image_1745649338tate_o @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_14_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: pname > pname > $o,F_61: pname > $o] :
% 0.28/0.45 ( ( finite_finite_pname @ F_61 )
% 0.28/0.45 => ( finite297249702name_o @ ( image_pname_pname_o @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_15_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: pname > hoare_1167836817_state > $o,F_61: pname > $o] :
% 0.28/0.45 ( ( finite_finite_pname @ F_61 )
% 0.28/0.45 => ( finite1380128977tate_o @ ( image_475339327tate_o @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_16_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: ( pname > $o ) > hoare_1167836817_state,F_61: ( pname > $o ) > $o] :
% 0.28/0.45 ( ( finite297249702name_o @ F_61 )
% 0.28/0.45 => ( finite1084549118_state @ ( image_1381916541_state @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_17_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,F_61: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.45 ( ( finite1380128977tate_o @ F_61 )
% 0.28/0.45 => ( finite1084549118_state @ ( image_635813834_state @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_18_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: ( pname > $o ) > pname,F_61: ( pname > $o ) > $o] :
% 0.28/0.45 ( ( finite297249702name_o @ F_61 )
% 0.28/0.45 => ( finite_finite_pname @ ( image_pname_o_pname @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_19_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: ( hoare_1167836817_state > $o ) > pname,F_61: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.45 ( ( finite1380128977tate_o @ F_61 )
% 0.28/0.45 => ( finite_finite_pname @ ( image_980295115_pname @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_20_finite__imageI,axiom,
% 0.28/0.45 ! [H_1: pname > hoare_1167836817_state,F_61: pname > $o] :
% 0.28/0.45 ( ( finite_finite_pname @ F_61 )
% 0.28/0.45 => ( finite1084549118_state @ ( image_575578384_state @ H_1 @ F_61 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_21_empty__subsetI,axiom,
% 0.28/0.45 ! [A_200: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_200 ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_22_empty__subsetI,axiom,
% 0.28/0.45 ! [A_200: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_200 ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_23_finite_OinsertI,axiom,
% 0.28/0.45 ! [A_199: pname > $o,A_198: ( pname > $o ) > $o] :
% 0.28/0.45 ( ( finite297249702name_o @ A_198 )
% 0.28/0.45 => ( finite297249702name_o @ ( insert_pname_o @ A_199 @ A_198 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_24_finite_OinsertI,axiom,
% 0.28/0.45 ! [A_199: hoare_1167836817_state > $o,A_198: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.45 ( ( finite1380128977tate_o @ A_198 )
% 0.28/0.45 => ( finite1380128977tate_o @ ( insert999278200tate_o @ A_199 @ A_198 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_25_finite_OinsertI,axiom,
% 0.28/0.45 ! [A_199: pname,A_198: pname > $o] :
% 0.28/0.45 ( ( finite_finite_pname @ A_198 )
% 0.28/0.45 => ( finite_finite_pname @ ( insert_pname @ A_199 @ A_198 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_26_finite_OinsertI,axiom,
% 0.28/0.45 ! [A_199: hoare_1167836817_state,A_198: hoare_1167836817_state > $o] :
% 0.28/0.45 ( ( finite1084549118_state @ A_198 )
% 0.28/0.45 => ( finite1084549118_state @ ( insert2134838167_state @ A_199 @ A_198 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(fact_27_finite_OemptyI,axiom,
% 0.28/0.45 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.28/0.45
% 0.28/0.45 thf(fact_28_finite_OemptyI,axiom,
% 0.28/0.45 finite1380128977tate_o @ bot_bo691907561te_o_o ).
% 0.28/0.45
% 0.28/0.45 thf(fact_29_finite_OemptyI,axiom,
% 0.28/0.45 finite1084549118_state @ bot_bo70021908tate_o ).
% 0.28/0.45
% 0.28/0.45 thf(fact_30_finite_OemptyI,axiom,
% 0.28/0.45 finite_finite_pname @ bot_bot_pname_o ).
% 0.28/0.45
% 0.28/0.45 thf(fact_31_finite__Collect__conjI,axiom,
% 0.28/0.45 ! [Q_24: ( pname > $o ) > $o,P_42: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_42 ) )
% 0.28/0.46 | ( finite297249702name_o @ ( collect_pname_o @ Q_24 ) ) )
% 0.28/0.46 => ( finite297249702name_o
% 0.28/0.46 @ ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_32_finite__Collect__conjI,axiom,
% 0.28/0.46 ! [Q_24: ( hoare_1167836817_state > $o ) > $o,P_42: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( ( finite1380128977tate_o @ ( collec269976083tate_o @ P_42 ) )
% 0.28/0.46 | ( finite1380128977tate_o @ ( collec269976083tate_o @ Q_24 ) ) )
% 0.28/0.46 => ( finite1380128977tate_o
% 0.28/0.46 @ ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_33_finite__Collect__conjI,axiom,
% 0.28/0.46 ! [Q_24: hoare_1167836817_state > $o,P_42: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( finite1084549118_state @ ( collec1027672124_state @ P_42 ) )
% 0.28/0.46 | ( finite1084549118_state @ ( collec1027672124_state @ Q_24 ) ) )
% 0.28/0.46 => ( finite1084549118_state
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_34_finite__Collect__conjI,axiom,
% 0.28/0.46 ! [Q_24: pname > $o,P_42: pname > $o] :
% 0.28/0.46 ( ( ( finite_finite_pname @ ( collect_pname @ P_42 ) )
% 0.28/0.46 | ( finite_finite_pname @ ( collect_pname @ Q_24 ) ) )
% 0.28/0.46 => ( finite_finite_pname
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_35_image__constant__conv,axiom,
% 0.28/0.46 ! [C_54: pname,A_197: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( A_197 = bot_bo70021908tate_o )
% 0.28/0.46 => ( ( image_8178176_pname
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : C_54
% 0.28/0.46 @ A_197 )
% 0.28/0.46 = bot_bot_pname_o ) )
% 0.28/0.46 & ( ( A_197 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ( image_8178176_pname
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : C_54
% 0.28/0.46 @ A_197 )
% 0.28/0.46 = ( insert_pname @ C_54 @ bot_bot_pname_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_36_image__constant__conv,axiom,
% 0.28/0.46 ! [C_54: hoare_1167836817_state,A_197: pname > $o] :
% 0.28/0.46 ( ( ( A_197 = bot_bot_pname_o )
% 0.28/0.46 => ( ( image_575578384_state
% 0.28/0.46 @ ^ [X_5: pname] : C_54
% 0.28/0.46 @ A_197 )
% 0.28/0.46 = bot_bo70021908tate_o ) )
% 0.28/0.46 & ( ( A_197 != bot_bot_pname_o )
% 0.28/0.46 => ( ( image_575578384_state
% 0.28/0.46 @ ^ [X_5: pname] : C_54
% 0.28/0.46 @ A_197 )
% 0.28/0.46 = ( insert2134838167_state @ C_54 @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_37_image__constant,axiom,
% 0.28/0.46 ! [C_53: pname,X_101: hoare_1167836817_state,A_196: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ X_101 @ A_196 )
% 0.28/0.46 => ( ( image_8178176_pname
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : C_53
% 0.28/0.46 @ A_196 )
% 0.28/0.46 = ( insert_pname @ C_53 @ bot_bot_pname_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_38_image__constant,axiom,
% 0.28/0.46 ! [C_53: hoare_1167836817_state,X_101: pname,A_196: pname > $o] :
% 0.28/0.46 ( ( member_pname @ X_101 @ A_196 )
% 0.28/0.46 => ( ( image_575578384_state
% 0.28/0.46 @ ^ [X_5: pname] : C_53
% 0.28/0.46 @ A_196 )
% 0.28/0.46 = ( insert2134838167_state @ C_53 @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_39_insert__dom,axiom,
% 0.28/0.46 ! [F_60: pname > option_com,X_100: pname,Y_49: com] :
% 0.28/0.46 ( ( ( F_60 @ X_100 )
% 0.28/0.46 = ( some_com @ Y_49 ) )
% 0.28/0.46 => ( ( insert_pname @ X_100 @ ( dom_pname_com @ F_60 ) )
% 0.28/0.46 = ( dom_pname_com @ F_60 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_40_finite__surj,axiom,
% 0.28/0.46 ! [B_130: ( pname > $o ) > $o,F_59: hoare_1167836817_state > pname > $o,A_195: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ A_195 )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ B_130 @ ( image_2066861949name_o @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite297249702name_o @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_41_finite__surj,axiom,
% 0.28/0.46 ! [B_130: ( hoare_1167836817_state > $o ) > $o,F_59: hoare_1167836817_state > hoare_1167836817_state > $o,A_195: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ A_195 )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ B_130 @ ( image_1745649338tate_o @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite1380128977tate_o @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_42_finite__surj,axiom,
% 0.28/0.46 ! [B_130: pname > $o,F_59: hoare_1167836817_state > pname,A_195: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ A_195 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_8178176_pname @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite_finite_pname @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_43_finite__surj,axiom,
% 0.28/0.46 ! [B_130: ( pname > $o ) > $o,F_59: pname > pname > $o,A_195: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ A_195 )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ B_130 @ ( image_pname_pname_o @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite297249702name_o @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_44_finite__surj,axiom,
% 0.28/0.46 ! [B_130: ( hoare_1167836817_state > $o ) > $o,F_59: pname > hoare_1167836817_state > $o,A_195: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ A_195 )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ B_130 @ ( image_475339327tate_o @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite1380128977tate_o @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_45_finite__surj,axiom,
% 0.28/0.46 ! [B_130: pname > $o,F_59: pname > pname,A_195: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ A_195 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_pname_pname @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite_finite_pname @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_46_finite__surj,axiom,
% 0.28/0.46 ! [B_130: hoare_1167836817_state > $o,F_59: ( pname > $o ) > hoare_1167836817_state,A_195: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ A_195 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_130 @ ( image_1381916541_state @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite1084549118_state @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_47_finite__surj,axiom,
% 0.28/0.46 ! [B_130: hoare_1167836817_state > $o,F_59: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_195: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ A_195 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_130 @ ( image_635813834_state @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite1084549118_state @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_48_finite__surj,axiom,
% 0.28/0.46 ! [B_130: pname > $o,F_59: ( pname > $o ) > pname,A_195: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ A_195 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_pname_o_pname @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite_finite_pname @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_49_finite__surj,axiom,
% 0.28/0.46 ! [B_130: pname > $o,F_59: ( hoare_1167836817_state > $o ) > pname,A_195: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ A_195 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_980295115_pname @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite_finite_pname @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_50_finite__surj,axiom,
% 0.28/0.46 ! [B_130: hoare_1167836817_state > $o,F_59: pname > hoare_1167836817_state,A_195: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ A_195 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_130 @ ( image_575578384_state @ F_59 @ A_195 ) )
% 0.28/0.46 => ( finite1084549118_state @ B_130 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_51_subset__singletonD,axiom,
% 0.28/0.46 ! [A_194: pname > $o,X_99: pname] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_194 @ ( insert_pname @ X_99 @ bot_bot_pname_o ) )
% 0.28/0.46 => ( ( A_194 = bot_bot_pname_o )
% 0.28/0.46 | ( A_194
% 0.28/0.46 = ( insert_pname @ X_99 @ bot_bot_pname_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_52_subset__singletonD,axiom,
% 0.28/0.46 ! [A_194: hoare_1167836817_state > $o,X_99: hoare_1167836817_state] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_194 @ ( insert2134838167_state @ X_99 @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ( A_194 = bot_bo70021908tate_o )
% 0.28/0.46 | ( A_194
% 0.28/0.46 = ( insert2134838167_state @ X_99 @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_53_MGF,axiom,
% 0.28/0.46 ! [C_21: com] :
% 0.28/0.46 ( hoare_1201148605gleton
% 0.28/0.46 => ( wT_bodies
% 0.28/0.46 => ( ( wt @ C_21 )
% 0.28/0.46 => ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_54_emptyE,axiom,
% 0.28/0.46 ! [A_193: pname] :
% 0.28/0.46 ~ ( member_pname @ A_193 @ bot_bot_pname_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_55_emptyE,axiom,
% 0.28/0.46 ! [A_193: hoare_1167836817_state] :
% 0.28/0.46 ~ ( member2058392318_state @ A_193 @ bot_bo70021908tate_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_56_insertCI,axiom,
% 0.28/0.46 ! [B_129: pname,A_192: pname,B_128: pname > $o] :
% 0.28/0.46 ( ( ~ ( member_pname @ A_192 @ B_128 )
% 0.28/0.46 => ( A_192 = B_129 ) )
% 0.28/0.46 => ( member_pname @ A_192 @ ( insert_pname @ B_129 @ B_128 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_57_insertCI,axiom,
% 0.28/0.46 ! [B_129: hoare_1167836817_state,A_192: hoare_1167836817_state,B_128: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ~ ( member2058392318_state @ A_192 @ B_128 )
% 0.28/0.46 => ( A_192 = B_129 ) )
% 0.28/0.46 => ( member2058392318_state @ A_192 @ ( insert2134838167_state @ B_129 @ B_128 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_58_insertE,axiom,
% 0.28/0.46 ! [A_191: pname,B_127: pname,A_190: pname > $o] :
% 0.28/0.46 ( ( member_pname @ A_191 @ ( insert_pname @ B_127 @ A_190 ) )
% 0.28/0.46 => ( ( A_191 != B_127 )
% 0.28/0.46 => ( member_pname @ A_191 @ A_190 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_59_insertE,axiom,
% 0.28/0.46 ! [A_191: hoare_1167836817_state,B_127: hoare_1167836817_state,A_190: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ A_191 @ ( insert2134838167_state @ B_127 @ A_190 ) )
% 0.28/0.46 => ( ( A_191 != B_127 )
% 0.28/0.46 => ( member2058392318_state @ A_191 @ A_190 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_60_equalityI,axiom,
% 0.28/0.46 ! [A_189: pname > $o,B_126: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_189 @ B_126 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_126 @ A_189 )
% 0.28/0.46 => ( A_189 = B_126 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_61_equalityI,axiom,
% 0.28/0.46 ! [A_189: hoare_1167836817_state > $o,B_126: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_189 @ B_126 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_126 @ A_189 )
% 0.28/0.46 => ( A_189 = B_126 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_62_subsetD,axiom,
% 0.28/0.46 ! [C_52: pname,A_188: pname > $o,B_125: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_188 @ B_125 )
% 0.28/0.46 => ( ( member_pname @ C_52 @ A_188 )
% 0.28/0.46 => ( member_pname @ C_52 @ B_125 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_63_subsetD,axiom,
% 0.28/0.46 ! [C_52: hoare_1167836817_state,A_188: hoare_1167836817_state > $o,B_125: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_188 @ B_125 )
% 0.28/0.46 => ( ( member2058392318_state @ C_52 @ A_188 )
% 0.28/0.46 => ( member2058392318_state @ C_52 @ B_125 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_64_image__eqI,axiom,
% 0.28/0.46 ! [A_187: hoare_1167836817_state > $o,B_124: pname,F_58: hoare_1167836817_state > pname,X_98: hoare_1167836817_state] :
% 0.28/0.46 ( ( B_124
% 0.28/0.46 = ( F_58 @ X_98 ) )
% 0.28/0.46 => ( ( member2058392318_state @ X_98 @ A_187 )
% 0.28/0.46 => ( member_pname @ B_124 @ ( image_8178176_pname @ F_58 @ A_187 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_65_image__eqI,axiom,
% 0.28/0.46 ! [A_187: pname > $o,B_124: hoare_1167836817_state,F_58: pname > hoare_1167836817_state,X_98: pname] :
% 0.28/0.46 ( ( B_124
% 0.28/0.46 = ( F_58 @ X_98 ) )
% 0.28/0.46 => ( ( member_pname @ X_98 @ A_187 )
% 0.28/0.46 => ( member2058392318_state @ B_124 @ ( image_575578384_state @ F_58 @ A_187 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_66_equals0D,axiom,
% 0.28/0.46 ! [A_186: pname,A_185: pname > $o] :
% 0.28/0.46 ( ( A_185 = bot_bot_pname_o )
% 0.28/0.46 => ~ ( member_pname @ A_186 @ A_185 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_67_equals0D,axiom,
% 0.28/0.46 ! [A_186: hoare_1167836817_state,A_185: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_185 = bot_bo70021908tate_o )
% 0.28/0.46 => ~ ( member2058392318_state @ A_186 @ A_185 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_68_Collect__empty__eq,axiom,
% 0.28/0.46 ! [P_41: pname > $o] :
% 0.28/0.46 ( ( ( collect_pname @ P_41 )
% 0.28/0.46 = bot_bot_pname_o )
% 0.28/0.46 <=> ! [X_5: pname] :
% 0.28/0.46 ~ ( P_41 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_69_Collect__empty__eq,axiom,
% 0.28/0.46 ! [P_41: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( ( collect_pname_o @ P_41 )
% 0.28/0.46 = bot_bot_pname_o_o )
% 0.28/0.46 <=> ! [X_5: pname > $o] :
% 0.28/0.46 ~ ( P_41 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_70_Collect__empty__eq,axiom,
% 0.28/0.46 ! [P_41: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( ( collec269976083tate_o @ P_41 )
% 0.28/0.46 = bot_bo691907561te_o_o )
% 0.28/0.46 <=> ! [X_5: hoare_1167836817_state > $o] :
% 0.28/0.46 ~ ( P_41 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_71_Collect__empty__eq,axiom,
% 0.28/0.46 ! [P_41: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( collec1027672124_state @ P_41 )
% 0.28/0.46 = bot_bo70021908tate_o )
% 0.28/0.46 <=> ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ~ ( P_41 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_72_empty__iff,axiom,
% 0.28/0.46 ! [C_51: pname] :
% 0.28/0.46 ~ ( member_pname @ C_51 @ bot_bot_pname_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_73_empty__iff,axiom,
% 0.28/0.46 ! [C_51: hoare_1167836817_state] :
% 0.28/0.46 ~ ( member2058392318_state @ C_51 @ bot_bo70021908tate_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_74_empty__Collect__eq,axiom,
% 0.28/0.46 ! [P_40: pname > $o] :
% 0.28/0.46 ( ( bot_bot_pname_o
% 0.28/0.46 = ( collect_pname @ P_40 ) )
% 0.28/0.46 <=> ! [X_5: pname] :
% 0.28/0.46 ~ ( P_40 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_75_empty__Collect__eq,axiom,
% 0.28/0.46 ! [P_40: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( bot_bot_pname_o_o
% 0.28/0.46 = ( collect_pname_o @ P_40 ) )
% 0.28/0.46 <=> ! [X_5: pname > $o] :
% 0.28/0.46 ~ ( P_40 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_76_empty__Collect__eq,axiom,
% 0.28/0.46 ! [P_40: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( bot_bo691907561te_o_o
% 0.28/0.46 = ( collec269976083tate_o @ P_40 ) )
% 0.28/0.46 <=> ! [X_5: hoare_1167836817_state > $o] :
% 0.28/0.46 ~ ( P_40 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_77_empty__Collect__eq,axiom,
% 0.28/0.46 ! [P_40: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( bot_bo70021908tate_o
% 0.28/0.46 = ( collec1027672124_state @ P_40 ) )
% 0.28/0.46 <=> ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ~ ( P_40 @ X_5 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_78_ex__in__conv,axiom,
% 0.28/0.46 ! [A_184: pname > $o] :
% 0.28/0.46 ( ? [X_5: pname] : ( member_pname @ X_5 @ A_184 )
% 0.28/0.46 <=> ( A_184 != bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_79_ex__in__conv,axiom,
% 0.28/0.46 ! [A_184: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ? [X_5: hoare_1167836817_state] : ( member2058392318_state @ X_5 @ A_184 )
% 0.28/0.46 <=> ( A_184 != bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_80_all__not__in__conv,axiom,
% 0.28/0.46 ! [A_183: pname > $o] :
% 0.28/0.46 ( ! [X_5: pname] :
% 0.28/0.46 ~ ( member_pname @ X_5 @ A_183 )
% 0.28/0.46 <=> ( A_183 = bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_81_all__not__in__conv,axiom,
% 0.28/0.46 ! [A_183: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ~ ( member2058392318_state @ X_5 @ A_183 )
% 0.28/0.46 <=> ( A_183 = bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_82_empty__def,axiom,
% 0.28/0.46 ( bot_bot_pname_o
% 0.28/0.46 = ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : $false ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_83_empty__def,axiom,
% 0.28/0.46 ( bot_bot_pname_o_o
% 0.28/0.46 = ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : $false ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_84_empty__def,axiom,
% 0.28/0.46 ( bot_bo691907561te_o_o
% 0.28/0.46 = ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : $false ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_85_empty__def,axiom,
% 0.28/0.46 ( bot_bo70021908tate_o
% 0.28/0.46 = ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : $false ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_86_insert__absorb,axiom,
% 0.28/0.46 ! [A_182: pname,A_181: pname > $o] :
% 0.28/0.46 ( ( member_pname @ A_182 @ A_181 )
% 0.28/0.46 => ( ( insert_pname @ A_182 @ A_181 )
% 0.28/0.46 = A_181 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_87_insert__absorb,axiom,
% 0.28/0.46 ! [A_182: hoare_1167836817_state,A_181: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ A_182 @ A_181 )
% 0.28/0.46 => ( ( insert2134838167_state @ A_182 @ A_181 )
% 0.28/0.46 = A_181 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_88_insertI2,axiom,
% 0.28/0.46 ! [B_123: pname,A_180: pname,B_122: pname > $o] :
% 0.28/0.46 ( ( member_pname @ A_180 @ B_122 )
% 0.28/0.46 => ( member_pname @ A_180 @ ( insert_pname @ B_123 @ B_122 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_89_insertI2,axiom,
% 0.28/0.46 ! [B_123: hoare_1167836817_state,A_180: hoare_1167836817_state,B_122: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ A_180 @ B_122 )
% 0.28/0.46 => ( member2058392318_state @ A_180 @ ( insert2134838167_state @ B_123 @ B_122 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_90_insert__ident,axiom,
% 0.28/0.46 ! [B_121: pname > $o,X_97: pname,A_179: pname > $o] :
% 0.28/0.46 ( ~ ( member_pname @ X_97 @ A_179 )
% 0.28/0.46 => ( ~ ( member_pname @ X_97 @ B_121 )
% 0.28/0.46 => ( ( ( insert_pname @ X_97 @ A_179 )
% 0.28/0.46 = ( insert_pname @ X_97 @ B_121 ) )
% 0.28/0.46 <=> ( A_179 = B_121 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_91_insert__ident,axiom,
% 0.28/0.46 ! [B_121: hoare_1167836817_state > $o,X_97: hoare_1167836817_state,A_179: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ~ ( member2058392318_state @ X_97 @ A_179 )
% 0.28/0.46 => ( ~ ( member2058392318_state @ X_97 @ B_121 )
% 0.28/0.46 => ( ( ( insert2134838167_state @ X_97 @ A_179 )
% 0.28/0.46 = ( insert2134838167_state @ X_97 @ B_121 ) )
% 0.28/0.46 <=> ( A_179 = B_121 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_92_insert__code,axiom,
% 0.28/0.46 ! [Y_48: pname,A_178: pname > $o,X_96: pname] :
% 0.28/0.46 ( ( insert_pname @ Y_48 @ A_178 @ X_96 )
% 0.28/0.46 <=> ( ( Y_48 = X_96 )
% 0.28/0.46 | ( A_178 @ X_96 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_93_insert__code,axiom,
% 0.28/0.46 ! [Y_48: hoare_1167836817_state,A_178: hoare_1167836817_state > $o,X_96: hoare_1167836817_state] :
% 0.28/0.46 ( ( insert2134838167_state @ Y_48 @ A_178 @ X_96 )
% 0.28/0.46 <=> ( ( Y_48 = X_96 )
% 0.28/0.46 | ( A_178 @ X_96 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_94_insert__iff,axiom,
% 0.28/0.46 ! [A_177: pname,B_120: pname,A_176: pname > $o] :
% 0.28/0.46 ( ( member_pname @ A_177 @ ( insert_pname @ B_120 @ A_176 ) )
% 0.28/0.46 <=> ( ( A_177 = B_120 )
% 0.28/0.46 | ( member_pname @ A_177 @ A_176 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_95_insert__iff,axiom,
% 0.28/0.46 ! [A_177: hoare_1167836817_state,B_120: hoare_1167836817_state,A_176: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ A_177 @ ( insert2134838167_state @ B_120 @ A_176 ) )
% 0.28/0.46 <=> ( ( A_177 = B_120 )
% 0.28/0.46 | ( member2058392318_state @ A_177 @ A_176 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_96_insert__commute,axiom,
% 0.28/0.46 ! [X_95: pname,Y_47: pname,A_175: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ X_95 @ ( insert_pname @ Y_47 @ A_175 ) )
% 0.28/0.46 = ( insert_pname @ Y_47 @ ( insert_pname @ X_95 @ A_175 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_97_insert__commute,axiom,
% 0.28/0.46 ! [X_95: hoare_1167836817_state,Y_47: hoare_1167836817_state,A_175: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ X_95 @ ( insert2134838167_state @ Y_47 @ A_175 ) )
% 0.28/0.46 = ( insert2134838167_state @ Y_47 @ ( insert2134838167_state @ X_95 @ A_175 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_98_insert__absorb2,axiom,
% 0.28/0.46 ! [X_94: pname,A_174: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ X_94 @ ( insert_pname @ X_94 @ A_174 ) )
% 0.28/0.46 = ( insert_pname @ X_94 @ A_174 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_99_insert__absorb2,axiom,
% 0.28/0.46 ! [X_94: hoare_1167836817_state,A_174: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ X_94 @ ( insert2134838167_state @ X_94 @ A_174 ) )
% 0.28/0.46 = ( insert2134838167_state @ X_94 @ A_174 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_100_insert__Collect,axiom,
% 0.28/0.46 ! [A_173: pname,P_39: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ A_173 @ ( collect_pname @ P_39 ) )
% 0.28/0.46 = ( collect_pname
% 0.28/0.46 @ ^ [U_2: pname] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_101_insert__Collect,axiom,
% 0.28/0.46 ! [A_173: pname > $o,P_39: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( insert_pname_o @ A_173 @ ( collect_pname_o @ P_39 ) )
% 0.28/0.46 = ( collect_pname_o
% 0.28/0.46 @ ^ [U_2: pname > $o] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_102_insert__Collect,axiom,
% 0.28/0.46 ! [A_173: hoare_1167836817_state > $o,P_39: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( insert999278200tate_o @ A_173 @ ( collec269976083tate_o @ P_39 ) )
% 0.28/0.46 = ( collec269976083tate_o
% 0.28/0.46 @ ^ [U_2: hoare_1167836817_state > $o] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_103_insert__Collect,axiom,
% 0.28/0.46 ! [A_173: hoare_1167836817_state,P_39: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ A_173 @ ( collec1027672124_state @ P_39 ) )
% 0.28/0.46 = ( collec1027672124_state
% 0.28/0.46 @ ^ [U_2: hoare_1167836817_state] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_104_insert__compr,axiom,
% 0.28/0.46 ! [A_172: pname,B_119: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ A_172 @ B_119 )
% 0.28/0.46 = ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (|) @ ( X_5 = A_172 ) @ ( member_pname @ X_5 @ B_119 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_105_insert__compr,axiom,
% 0.28/0.46 ! [A_172: pname > $o,B_119: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( insert_pname_o @ A_172 @ B_119 )
% 0.28/0.46 = ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (|) @ ( X_5 = A_172 ) @ ( member_pname_o @ X_5 @ B_119 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_106_insert__compr,axiom,
% 0.28/0.46 ! [A_172: hoare_1167836817_state > $o,B_119: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( insert999278200tate_o @ A_172 @ B_119 )
% 0.28/0.46 = ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( X_5 = A_172 ) @ ( member864234961tate_o @ X_5 @ B_119 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_107_insert__compr,axiom,
% 0.28/0.46 ! [A_172: hoare_1167836817_state,B_119: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ A_172 @ B_119 )
% 0.28/0.46 = ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( X_5 = A_172 ) @ ( member2058392318_state @ X_5 @ B_119 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_108_insertI1,axiom,
% 0.28/0.46 ! [A_171: pname,B_118: pname > $o] : ( member_pname @ A_171 @ ( insert_pname @ A_171 @ B_118 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_109_insertI1,axiom,
% 0.28/0.46 ! [A_171: hoare_1167836817_state,B_118: hoare_1167836817_state > $o] : ( member2058392318_state @ A_171 @ ( insert2134838167_state @ A_171 @ B_118 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_110_equalityE,axiom,
% 0.28/0.46 ! [A_170: pname > $o,B_117: pname > $o] :
% 0.28/0.46 ( ( A_170 = B_117 )
% 0.28/0.46 => ~ ( ( ord_less_eq_pname_o @ A_170 @ B_117 )
% 0.28/0.46 => ~ ( ord_less_eq_pname_o @ B_117 @ A_170 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_111_equalityE,axiom,
% 0.28/0.46 ! [A_170: hoare_1167836817_state > $o,B_117: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_170 = B_117 )
% 0.28/0.46 => ~ ( ( ord_le827224136tate_o @ A_170 @ B_117 )
% 0.28/0.46 => ~ ( ord_le827224136tate_o @ B_117 @ A_170 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_112_subset__trans,axiom,
% 0.28/0.46 ! [C_50: pname > $o,A_169: pname > $o,B_116: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_169 @ B_116 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_116 @ C_50 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ A_169 @ C_50 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_113_subset__trans,axiom,
% 0.28/0.46 ! [C_50: hoare_1167836817_state > $o,A_169: hoare_1167836817_state > $o,B_116: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_169 @ B_116 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_116 @ C_50 )
% 0.28/0.46 => ( ord_le827224136tate_o @ A_169 @ C_50 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_114_set__mp,axiom,
% 0.28/0.46 ! [X_93: pname,A_168: pname > $o,B_115: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_168 @ B_115 )
% 0.28/0.46 => ( ( member_pname @ X_93 @ A_168 )
% 0.28/0.46 => ( member_pname @ X_93 @ B_115 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_115_set__mp,axiom,
% 0.28/0.46 ! [X_93: hoare_1167836817_state,A_168: hoare_1167836817_state > $o,B_115: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_168 @ B_115 )
% 0.28/0.46 => ( ( member2058392318_state @ X_93 @ A_168 )
% 0.28/0.46 => ( member2058392318_state @ X_93 @ B_115 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_116_set__rev__mp,axiom,
% 0.28/0.46 ! [B_114: pname > $o,X_92: pname,A_167: pname > $o] :
% 0.28/0.46 ( ( member_pname @ X_92 @ A_167 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ A_167 @ B_114 )
% 0.28/0.46 => ( member_pname @ X_92 @ B_114 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_117_set__rev__mp,axiom,
% 0.28/0.46 ! [B_114: hoare_1167836817_state > $o,X_92: hoare_1167836817_state,A_167: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ X_92 @ A_167 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ A_167 @ B_114 )
% 0.28/0.46 => ( member2058392318_state @ X_92 @ B_114 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_118_in__mono,axiom,
% 0.28/0.46 ! [X_91: pname,A_166: pname > $o,B_113: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_166 @ B_113 )
% 0.28/0.46 => ( ( member_pname @ X_91 @ A_166 )
% 0.28/0.46 => ( member_pname @ X_91 @ B_113 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_119_in__mono,axiom,
% 0.28/0.46 ! [X_91: hoare_1167836817_state,A_166: hoare_1167836817_state > $o,B_113: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_166 @ B_113 )
% 0.28/0.46 => ( ( member2058392318_state @ X_91 @ A_166 )
% 0.28/0.46 => ( member2058392318_state @ X_91 @ B_113 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_120_equalityD2,axiom,
% 0.28/0.46 ! [A_165: pname > $o,B_112: pname > $o] :
% 0.28/0.46 ( ( A_165 = B_112 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ B_112 @ A_165 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_121_equalityD2,axiom,
% 0.28/0.46 ! [A_165: hoare_1167836817_state > $o,B_112: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_165 = B_112 )
% 0.28/0.46 => ( ord_le827224136tate_o @ B_112 @ A_165 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_122_equalityD1,axiom,
% 0.28/0.46 ! [A_164: pname > $o,B_111: pname > $o] :
% 0.28/0.46 ( ( A_164 = B_111 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ A_164 @ B_111 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_123_equalityD1,axiom,
% 0.28/0.46 ! [A_164: hoare_1167836817_state > $o,B_111: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_164 = B_111 )
% 0.28/0.46 => ( ord_le827224136tate_o @ A_164 @ B_111 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_124_set__eq__subset,axiom,
% 0.28/0.46 ! [A_163: pname > $o,B_110: pname > $o] :
% 0.28/0.46 ( ( A_163 = B_110 )
% 0.28/0.46 <=> ( ( ord_less_eq_pname_o @ A_163 @ B_110 )
% 0.28/0.46 & ( ord_less_eq_pname_o @ B_110 @ A_163 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_125_set__eq__subset,axiom,
% 0.28/0.46 ! [A_163: hoare_1167836817_state > $o,B_110: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_163 = B_110 )
% 0.28/0.46 <=> ( ( ord_le827224136tate_o @ A_163 @ B_110 )
% 0.28/0.46 & ( ord_le827224136tate_o @ B_110 @ A_163 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_126_subset__refl,axiom,
% 0.28/0.46 ! [A_162: pname > $o] : ( ord_less_eq_pname_o @ A_162 @ A_162 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_127_subset__refl,axiom,
% 0.28/0.46 ! [A_162: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A_162 @ A_162 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_128_rev__image__eqI,axiom,
% 0.28/0.46 ! [B_109: pname,F_57: hoare_1167836817_state > pname,X_90: hoare_1167836817_state,A_161: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ X_90 @ A_161 )
% 0.28/0.46 => ( ( B_109
% 0.28/0.46 = ( F_57 @ X_90 ) )
% 0.28/0.46 => ( member_pname @ B_109 @ ( image_8178176_pname @ F_57 @ A_161 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_129_rev__image__eqI,axiom,
% 0.28/0.46 ! [B_109: hoare_1167836817_state,F_57: pname > hoare_1167836817_state,X_90: pname,A_161: pname > $o] :
% 0.28/0.46 ( ( member_pname @ X_90 @ A_161 )
% 0.28/0.46 => ( ( B_109
% 0.28/0.46 = ( F_57 @ X_90 ) )
% 0.28/0.46 => ( member2058392318_state @ B_109 @ ( image_575578384_state @ F_57 @ A_161 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_130_imageI,axiom,
% 0.28/0.46 ! [F_56: hoare_1167836817_state > pname,X_89: hoare_1167836817_state,A_160: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ X_89 @ A_160 )
% 0.28/0.46 => ( member_pname @ ( F_56 @ X_89 ) @ ( image_8178176_pname @ F_56 @ A_160 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_131_imageI,axiom,
% 0.28/0.46 ! [F_56: pname > hoare_1167836817_state,X_89: pname,A_160: pname > $o] :
% 0.28/0.46 ( ( member_pname @ X_89 @ A_160 )
% 0.28/0.46 => ( member2058392318_state @ ( F_56 @ X_89 ) @ ( image_575578384_state @ F_56 @ A_160 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_132_image__iff,axiom,
% 0.28/0.46 ! [Z_21: hoare_1167836817_state,F_55: pname > hoare_1167836817_state,A_159: pname > $o] :
% 0.28/0.46 ( ( member2058392318_state @ Z_21 @ ( image_575578384_state @ F_55 @ A_159 ) )
% 0.28/0.46 <=> ? [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_159 )
% 0.28/0.46 & ( Z_21
% 0.28/0.46 = ( F_55 @ X_5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_133_finite__Collect__disjI,axiom,
% 0.28/0.46 ! [P_38: ( pname > $o ) > $o,Q_23: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o
% 0.28/0.46 @ ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 0.28/0.46 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_38 ) )
% 0.28/0.46 & ( finite297249702name_o @ ( collect_pname_o @ Q_23 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_134_finite__Collect__disjI,axiom,
% 0.28/0.46 ! [P_38: ( hoare_1167836817_state > $o ) > $o,Q_23: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o
% 0.28/0.46 @ ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 0.28/0.46 <=> ( ( finite1380128977tate_o @ ( collec269976083tate_o @ P_38 ) )
% 0.28/0.46 & ( finite1380128977tate_o @ ( collec269976083tate_o @ Q_23 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_135_finite__Collect__disjI,axiom,
% 0.28/0.46 ! [P_38: hoare_1167836817_state > $o,Q_23: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 0.28/0.46 <=> ( ( finite1084549118_state @ ( collec1027672124_state @ P_38 ) )
% 0.28/0.46 & ( finite1084549118_state @ ( collec1027672124_state @ Q_23 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_136_finite__Collect__disjI,axiom,
% 0.28/0.46 ! [P_38: pname > $o,Q_23: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 0.28/0.46 <=> ( ( finite_finite_pname @ ( collect_pname @ P_38 ) )
% 0.28/0.46 & ( finite_finite_pname @ ( collect_pname @ Q_23 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_137_insert__compr__raw,axiom,
% 0.28/0.46 ! [X_5: pname,Xa: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ X_5 @ Xa )
% 0.28/0.46 = ( collect_pname
% 0.28/0.46 @ ^ [Y_2: pname] : ( (|) @ ( Y_2 = X_5 ) @ ( member_pname @ Y_2 @ Xa ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_138_insert__compr__raw,axiom,
% 0.28/0.46 ! [X_5: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( insert_pname_o @ X_5 @ Xa )
% 0.28/0.46 = ( collect_pname_o
% 0.28/0.46 @ ^ [Y_2: pname > $o] : ( (|) @ ( Y_2 = X_5 ) @ ( member_pname_o @ Y_2 @ Xa ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_139_insert__compr__raw,axiom,
% 0.28/0.46 ! [X_5: hoare_1167836817_state > $o,Xa: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( insert999278200tate_o @ X_5 @ Xa )
% 0.28/0.46 = ( collec269976083tate_o
% 0.28/0.46 @ ^ [Y_2: hoare_1167836817_state > $o] : ( (|) @ ( Y_2 = X_5 ) @ ( member864234961tate_o @ Y_2 @ Xa ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_140_insert__compr__raw,axiom,
% 0.28/0.46 ! [X_5: hoare_1167836817_state,Xa: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ X_5 @ Xa )
% 0.28/0.46 = ( collec1027672124_state
% 0.28/0.46 @ ^ [Y_2: hoare_1167836817_state] : ( (|) @ ( Y_2 = X_5 ) @ ( member2058392318_state @ Y_2 @ Xa ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_141_singleton__inject,axiom,
% 0.28/0.46 ! [A_158: pname,B_108: pname] :
% 0.28/0.46 ( ( ( insert_pname @ A_158 @ bot_bot_pname_o )
% 0.28/0.46 = ( insert_pname @ B_108 @ bot_bot_pname_o ) )
% 0.28/0.46 => ( A_158 = B_108 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_142_singleton__inject,axiom,
% 0.28/0.46 ! [A_158: hoare_1167836817_state,B_108: hoare_1167836817_state] :
% 0.28/0.46 ( ( ( insert2134838167_state @ A_158 @ bot_bo70021908tate_o )
% 0.28/0.46 = ( insert2134838167_state @ B_108 @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( A_158 = B_108 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_143_singletonE,axiom,
% 0.28/0.46 ! [B_107: pname,A_157: pname] :
% 0.28/0.46 ( ( member_pname @ B_107 @ ( insert_pname @ A_157 @ bot_bot_pname_o ) )
% 0.28/0.46 => ( B_107 = A_157 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_144_singletonE,axiom,
% 0.28/0.46 ! [B_107: hoare_1167836817_state,A_157: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ B_107 @ ( insert2134838167_state @ A_157 @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( B_107 = A_157 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_145_doubleton__eq__iff,axiom,
% 0.28/0.46 ! [A_156: pname,B_106: pname,C_49: pname,D_6: pname] :
% 0.28/0.46 ( ( ( insert_pname @ A_156 @ ( insert_pname @ B_106 @ bot_bot_pname_o ) )
% 0.28/0.46 = ( insert_pname @ C_49 @ ( insert_pname @ D_6 @ bot_bot_pname_o ) ) )
% 0.28/0.46 <=> ( ( ( A_156 = C_49 )
% 0.28/0.46 & ( B_106 = D_6 ) )
% 0.28/0.46 | ( ( A_156 = D_6 )
% 0.28/0.46 & ( B_106 = C_49 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_146_doubleton__eq__iff,axiom,
% 0.28/0.46 ! [A_156: hoare_1167836817_state,B_106: hoare_1167836817_state,C_49: hoare_1167836817_state,D_6: hoare_1167836817_state] :
% 0.28/0.46 ( ( ( insert2134838167_state @ A_156 @ ( insert2134838167_state @ B_106 @ bot_bo70021908tate_o ) )
% 0.28/0.46 = ( insert2134838167_state @ C_49 @ ( insert2134838167_state @ D_6 @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 <=> ( ( ( A_156 = C_49 )
% 0.28/0.46 & ( B_106 = D_6 ) )
% 0.28/0.46 | ( ( A_156 = D_6 )
% 0.28/0.46 & ( B_106 = C_49 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_147_singleton__iff,axiom,
% 0.28/0.46 ! [B_105: pname,A_155: pname] :
% 0.28/0.46 ( ( member_pname @ B_105 @ ( insert_pname @ A_155 @ bot_bot_pname_o ) )
% 0.28/0.46 <=> ( B_105 = A_155 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_148_singleton__iff,axiom,
% 0.28/0.46 ! [B_105: hoare_1167836817_state,A_155: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ B_105 @ ( insert2134838167_state @ A_155 @ bot_bo70021908tate_o ) )
% 0.28/0.46 <=> ( B_105 = A_155 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_149_insert__not__empty,axiom,
% 0.28/0.46 ! [A_154: pname,A_153: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ A_154 @ A_153 )
% 0.28/0.46 != bot_bot_pname_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_150_insert__not__empty,axiom,
% 0.28/0.46 ! [A_154: hoare_1167836817_state,A_153: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ A_154 @ A_153 )
% 0.28/0.46 != bot_bo70021908tate_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_151_empty__not__insert,axiom,
% 0.28/0.46 ! [A_152: pname,A_151: pname > $o] :
% 0.28/0.46 ( bot_bot_pname_o
% 0.28/0.46 != ( insert_pname @ A_152 @ A_151 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_152_empty__not__insert,axiom,
% 0.28/0.46 ! [A_152: hoare_1167836817_state,A_151: hoare_1167836817_state > $o] :
% 0.28/0.46 ( bot_bo70021908tate_o
% 0.28/0.46 != ( insert2134838167_state @ A_152 @ A_151 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_153_finite__insert,axiom,
% 0.28/0.46 ! [A_150: pname > $o,A_149: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ ( insert_pname_o @ A_150 @ A_149 ) )
% 0.28/0.46 <=> ( finite297249702name_o @ A_149 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_154_finite__insert,axiom,
% 0.28/0.46 ! [A_150: hoare_1167836817_state > $o,A_149: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ ( insert999278200tate_o @ A_150 @ A_149 ) )
% 0.28/0.46 <=> ( finite1380128977tate_o @ A_149 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_155_finite__insert,axiom,
% 0.28/0.46 ! [A_150: pname,A_149: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ ( insert_pname @ A_150 @ A_149 ) )
% 0.28/0.46 <=> ( finite_finite_pname @ A_149 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_156_finite__insert,axiom,
% 0.28/0.46 ! [A_150: hoare_1167836817_state,A_149: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ ( insert2134838167_state @ A_150 @ A_149 ) )
% 0.28/0.46 <=> ( finite1084549118_state @ A_149 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_157_subset__empty,axiom,
% 0.28/0.46 ! [A_148: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_148 @ bot_bot_pname_o )
% 0.28/0.46 <=> ( A_148 = bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_158_subset__empty,axiom,
% 0.28/0.46 ! [A_148: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_148 @ bot_bo70021908tate_o )
% 0.28/0.46 <=> ( A_148 = bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_159_image__is__empty,axiom,
% 0.28/0.46 ! [F_54: hoare_1167836817_state > pname,A_147: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( image_8178176_pname @ F_54 @ A_147 )
% 0.28/0.46 = bot_bot_pname_o )
% 0.28/0.46 <=> ( A_147 = bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_160_image__is__empty,axiom,
% 0.28/0.46 ! [F_54: pname > hoare_1167836817_state,A_147: pname > $o] :
% 0.28/0.46 ( ( ( image_575578384_state @ F_54 @ A_147 )
% 0.28/0.46 = bot_bo70021908tate_o )
% 0.28/0.46 <=> ( A_147 = bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_161_image__empty,axiom,
% 0.28/0.46 ! [F_53: hoare_1167836817_state > pname] :
% 0.28/0.46 ( ( image_8178176_pname @ F_53 @ bot_bo70021908tate_o )
% 0.28/0.46 = bot_bot_pname_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_162_image__empty,axiom,
% 0.28/0.46 ! [F_53: pname > hoare_1167836817_state] :
% 0.28/0.46 ( ( image_575578384_state @ F_53 @ bot_bot_pname_o )
% 0.28/0.46 = bot_bo70021908tate_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_163_empty__is__image,axiom,
% 0.28/0.46 ! [F_52: hoare_1167836817_state > pname,A_146: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( bot_bot_pname_o
% 0.28/0.46 = ( image_8178176_pname @ F_52 @ A_146 ) )
% 0.28/0.46 <=> ( A_146 = bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_164_empty__is__image,axiom,
% 0.28/0.46 ! [F_52: pname > hoare_1167836817_state,A_146: pname > $o] :
% 0.28/0.46 ( ( bot_bo70021908tate_o
% 0.28/0.46 = ( image_575578384_state @ F_52 @ A_146 ) )
% 0.28/0.46 <=> ( A_146 = bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_165_finite__subset,axiom,
% 0.28/0.46 ! [A_145: ( pname > $o ) > $o,B_104: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( ord_le1205211808me_o_o @ A_145 @ B_104 )
% 0.28/0.46 => ( ( finite297249702name_o @ B_104 )
% 0.28/0.46 => ( finite297249702name_o @ A_145 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_166_finite__subset,axiom,
% 0.28/0.46 ! [A_145: ( hoare_1167836817_state > $o ) > $o,B_104: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( ord_le741939125te_o_o @ A_145 @ B_104 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ B_104 )
% 0.28/0.46 => ( finite1380128977tate_o @ A_145 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_167_finite__subset,axiom,
% 0.28/0.46 ! [A_145: hoare_1167836817_state > $o,B_104: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_145 @ B_104 )
% 0.28/0.46 => ( ( finite1084549118_state @ B_104 )
% 0.28/0.46 => ( finite1084549118_state @ A_145 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_168_finite__subset,axiom,
% 0.28/0.46 ! [A_145: pname > $o,B_104: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_145 @ B_104 )
% 0.28/0.46 => ( ( finite_finite_pname @ B_104 )
% 0.28/0.46 => ( finite_finite_pname @ A_145 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_169_rev__finite__subset,axiom,
% 0.28/0.46 ! [A_144: ( pname > $o ) > $o,B_103: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ B_103 )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ A_144 @ B_103 )
% 0.28/0.46 => ( finite297249702name_o @ A_144 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_170_rev__finite__subset,axiom,
% 0.28/0.46 ! [A_144: ( hoare_1167836817_state > $o ) > $o,B_103: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ B_103 )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ A_144 @ B_103 )
% 0.28/0.46 => ( finite1380128977tate_o @ A_144 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_171_rev__finite__subset,axiom,
% 0.28/0.46 ! [A_144: hoare_1167836817_state > $o,B_103: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ B_103 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ A_144 @ B_103 )
% 0.28/0.46 => ( finite1084549118_state @ A_144 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_172_rev__finite__subset,axiom,
% 0.28/0.46 ! [A_144: pname > $o,B_103: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ B_103 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ A_144 @ B_103 )
% 0.28/0.46 => ( finite_finite_pname @ A_144 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_173_insert__mono,axiom,
% 0.28/0.46 ! [A_143: pname,C_48: pname > $o,D_5: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ C_48 @ D_5 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( insert_pname @ A_143 @ C_48 ) @ ( insert_pname @ A_143 @ D_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_174_insert__mono,axiom,
% 0.28/0.46 ! [A_143: hoare_1167836817_state,C_48: hoare_1167836817_state > $o,D_5: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ C_48 @ D_5 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( insert2134838167_state @ A_143 @ C_48 ) @ ( insert2134838167_state @ A_143 @ D_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_175_mem__def,axiom,
% 0.28/0.46 ! [X_88: pname,A_142: pname > $o] :
% 0.28/0.46 ( ( member_pname @ X_88 @ A_142 )
% 0.28/0.46 <=> ( A_142 @ X_88 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_176_mem__def,axiom,
% 0.28/0.46 ! [X_88: hoare_1167836817_state,A_142: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ X_88 @ A_142 )
% 0.28/0.46 <=> ( A_142 @ X_88 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_177_Collect__def,axiom,
% 0.28/0.46 ! [P_37: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( collec1027672124_state @ P_37 )
% 0.28/0.46 = P_37 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_178_Collect__def,axiom,
% 0.28/0.46 ! [P_37: pname > $o] :
% 0.28/0.46 ( ( collect_pname @ P_37 )
% 0.28/0.46 = P_37 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_179_Collect__def,axiom,
% 0.28/0.46 ! [P_37: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( collect_pname_o @ P_37 )
% 0.28/0.46 = P_37 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_180_Collect__def,axiom,
% 0.28/0.46 ! [P_37: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( collec269976083tate_o @ P_37 )
% 0.28/0.46 = P_37 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_181_subset__insertI2,axiom,
% 0.28/0.46 ! [B_102: pname,A_141: pname > $o,B_101: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_141 @ B_101 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ A_141 @ ( insert_pname @ B_102 @ B_101 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_182_subset__insertI2,axiom,
% 0.28/0.46 ! [B_102: hoare_1167836817_state,A_141: hoare_1167836817_state > $o,B_101: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_141 @ B_101 )
% 0.28/0.46 => ( ord_le827224136tate_o @ A_141 @ ( insert2134838167_state @ B_102 @ B_101 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_183_subset__insert,axiom,
% 0.28/0.46 ! [B_100: pname > $o,X_87: pname,A_140: pname > $o] :
% 0.28/0.46 ( ~ ( member_pname @ X_87 @ A_140 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ A_140 @ ( insert_pname @ X_87 @ B_100 ) )
% 0.28/0.46 <=> ( ord_less_eq_pname_o @ A_140 @ B_100 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_184_subset__insert,axiom,
% 0.28/0.46 ! [B_100: hoare_1167836817_state > $o,X_87: hoare_1167836817_state,A_140: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ~ ( member2058392318_state @ X_87 @ A_140 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ A_140 @ ( insert2134838167_state @ X_87 @ B_100 ) )
% 0.28/0.46 <=> ( ord_le827224136tate_o @ A_140 @ B_100 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_185_insert__subset,axiom,
% 0.28/0.46 ! [X_86: pname,A_139: pname > $o,B_99: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_86 @ A_139 ) @ B_99 )
% 0.28/0.46 <=> ( ( member_pname @ X_86 @ B_99 )
% 0.28/0.46 & ( ord_less_eq_pname_o @ A_139 @ B_99 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_186_insert__subset,axiom,
% 0.28/0.46 ! [X_86: hoare_1167836817_state,A_139: hoare_1167836817_state > $o,B_99: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ ( insert2134838167_state @ X_86 @ A_139 ) @ B_99 )
% 0.28/0.46 <=> ( ( member2058392318_state @ X_86 @ B_99 )
% 0.28/0.46 & ( ord_le827224136tate_o @ A_139 @ B_99 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_187_subset__insertI,axiom,
% 0.28/0.46 ! [B_98: pname > $o,A_138: pname] : ( ord_less_eq_pname_o @ B_98 @ ( insert_pname @ A_138 @ B_98 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_188_subset__insertI,axiom,
% 0.28/0.46 ! [B_98: hoare_1167836817_state > $o,A_138: hoare_1167836817_state] : ( ord_le827224136tate_o @ B_98 @ ( insert2134838167_state @ A_138 @ B_98 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_189_insert__image,axiom,
% 0.28/0.46 ! [F_51: hoare_1167836817_state > pname,X_85: hoare_1167836817_state,A_137: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ X_85 @ A_137 )
% 0.28/0.46 => ( ( insert_pname @ ( F_51 @ X_85 ) @ ( image_8178176_pname @ F_51 @ A_137 ) )
% 0.28/0.46 = ( image_8178176_pname @ F_51 @ A_137 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_190_insert__image,axiom,
% 0.28/0.46 ! [F_51: pname > hoare_1167836817_state,X_85: pname,A_137: pname > $o] :
% 0.28/0.46 ( ( member_pname @ X_85 @ A_137 )
% 0.28/0.46 => ( ( insert2134838167_state @ ( F_51 @ X_85 ) @ ( image_575578384_state @ F_51 @ A_137 ) )
% 0.28/0.46 = ( image_575578384_state @ F_51 @ A_137 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_191_image__insert,axiom,
% 0.28/0.46 ! [F_50: hoare_1167836817_state > pname,A_136: hoare_1167836817_state,B_97: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( image_8178176_pname @ F_50 @ ( insert2134838167_state @ A_136 @ B_97 ) )
% 0.28/0.46 = ( insert_pname @ ( F_50 @ A_136 ) @ ( image_8178176_pname @ F_50 @ B_97 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_192_image__insert,axiom,
% 0.28/0.46 ! [F_50: pname > hoare_1167836817_state,A_136: pname,B_97: pname > $o] :
% 0.28/0.46 ( ( image_575578384_state @ F_50 @ ( insert_pname @ A_136 @ B_97 ) )
% 0.28/0.46 = ( insert2134838167_state @ ( F_50 @ A_136 ) @ ( image_575578384_state @ F_50 @ B_97 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_193_image__mono,axiom,
% 0.28/0.46 ! [F_49: hoare_1167836817_state > pname,A_135: hoare_1167836817_state > $o,B_96: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_135 @ B_96 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( image_8178176_pname @ F_49 @ A_135 ) @ ( image_8178176_pname @ F_49 @ B_96 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_194_image__mono,axiom,
% 0.28/0.46 ! [F_49: pname > hoare_1167836817_state,A_135: pname > $o,B_96: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_135 @ B_96 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( image_575578384_state @ F_49 @ A_135 ) @ ( image_575578384_state @ F_49 @ B_96 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_195_subset__image__iff,axiom,
% 0.28/0.46 ! [B_95: pname > $o,F_48: hoare_1167836817_state > pname,A_134: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ B_95 @ ( image_8178176_pname @ F_48 @ A_134 ) )
% 0.28/0.46 <=> ? [AA: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ AA @ A_134 )
% 0.28/0.46 & ( B_95
% 0.28/0.46 = ( image_8178176_pname @ F_48 @ AA ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_196_subset__image__iff,axiom,
% 0.28/0.46 ! [B_95: hoare_1167836817_state > $o,F_48: pname > hoare_1167836817_state,A_134: pname > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ B_95 @ ( image_575578384_state @ F_48 @ A_134 ) )
% 0.28/0.46 <=> ? [AA: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ AA @ A_134 )
% 0.28/0.46 & ( B_95
% 0.28/0.46 = ( image_575578384_state @ F_48 @ AA ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_197_domI,axiom,
% 0.28/0.46 ! [M_2: pname > option_com,A_133: pname,B_94: com] :
% 0.28/0.46 ( ( ( M_2 @ A_133 )
% 0.28/0.46 = ( some_com @ B_94 ) )
% 0.28/0.46 => ( member_pname @ A_133 @ ( dom_pname_com @ M_2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_198_Collect__conv__if,axiom,
% 0.28/0.46 ! [P_36: pname > $o,A_132: pname] :
% 0.28/0.46 ( ( ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = ( insert_pname @ A_132 @ bot_bot_pname_o ) ) )
% 0.28/0.46 & ( ~ ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = bot_bot_pname_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_199_Collect__conv__if,axiom,
% 0.28/0.46 ! [P_36: ( pname > $o ) > $o,A_132: pname > $o] :
% 0.28/0.46 ( ( ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = ( insert_pname_o @ A_132 @ bot_bot_pname_o_o ) ) )
% 0.28/0.46 & ( ~ ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = bot_bot_pname_o_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_200_Collect__conv__if,axiom,
% 0.28/0.46 ! [P_36: ( hoare_1167836817_state > $o ) > $o,A_132: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = ( insert999278200tate_o @ A_132 @ bot_bo691907561te_o_o ) ) )
% 0.28/0.46 & ( ~ ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = bot_bo691907561te_o_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_201_Collect__conv__if,axiom,
% 0.28/0.46 ! [P_36: hoare_1167836817_state > $o,A_132: hoare_1167836817_state] :
% 0.28/0.46 ( ( ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = ( insert2134838167_state @ A_132 @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 & ( ~ ( P_36 @ A_132 )
% 0.28/0.46 => ( ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 0.28/0.46 = bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_202_Collect__conv__if2,axiom,
% 0.28/0.46 ! [P_35: pname > $o,A_131: pname] :
% 0.28/0.46 ( ( ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = ( insert_pname @ A_131 @ bot_bot_pname_o ) ) )
% 0.28/0.46 & ( ~ ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = bot_bot_pname_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_203_Collect__conv__if2,axiom,
% 0.28/0.46 ! [P_35: ( pname > $o ) > $o,A_131: pname > $o] :
% 0.28/0.46 ( ( ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = ( insert_pname_o @ A_131 @ bot_bot_pname_o_o ) ) )
% 0.28/0.46 & ( ~ ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = bot_bot_pname_o_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_204_Collect__conv__if2,axiom,
% 0.28/0.46 ! [P_35: ( hoare_1167836817_state > $o ) > $o,A_131: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = ( insert999278200tate_o @ A_131 @ bot_bo691907561te_o_o ) ) )
% 0.28/0.46 & ( ~ ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = bot_bo691907561te_o_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_205_Collect__conv__if2,axiom,
% 0.28/0.46 ! [P_35: hoare_1167836817_state > $o,A_131: hoare_1167836817_state] :
% 0.28/0.46 ( ( ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = ( insert2134838167_state @ A_131 @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 & ( ~ ( P_35 @ A_131 )
% 0.28/0.46 => ( ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 0.28/0.46 = bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_206_singleton__conv,axiom,
% 0.28/0.46 ! [A_130: pname] :
% 0.28/0.46 ( ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( X_5 = A_130 ) )
% 0.28/0.46 = ( insert_pname @ A_130 @ bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_207_singleton__conv,axiom,
% 0.28/0.46 ! [A_130: pname > $o] :
% 0.28/0.46 ( ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( X_5 = A_130 ) )
% 0.28/0.46 = ( insert_pname_o @ A_130 @ bot_bot_pname_o_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_208_singleton__conv,axiom,
% 0.28/0.46 ! [A_130: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( X_5 = A_130 ) )
% 0.28/0.46 = ( insert999278200tate_o @ A_130 @ bot_bo691907561te_o_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_209_singleton__conv,axiom,
% 0.28/0.46 ! [A_130: hoare_1167836817_state] :
% 0.28/0.46 ( ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( X_5 = A_130 ) )
% 0.28/0.46 = ( insert2134838167_state @ A_130 @ bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_210_singleton__conv2,axiom,
% 0.28/0.46 ! [A_129: pname] :
% 0.28/0.46 ( ( collect_pname @ ( fequal_pname @ A_129 ) )
% 0.28/0.46 = ( insert_pname @ A_129 @ bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_211_singleton__conv2,axiom,
% 0.28/0.46 ! [A_129: pname > $o] :
% 0.28/0.46 ( ( collect_pname_o @ ( fequal_pname_o @ A_129 ) )
% 0.28/0.46 = ( insert_pname_o @ A_129 @ bot_bot_pname_o_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_212_singleton__conv2,axiom,
% 0.28/0.46 ! [A_129: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( collec269976083tate_o @ ( fequal1486222077tate_o @ A_129 ) )
% 0.28/0.46 = ( insert999278200tate_o @ A_129 @ bot_bo691907561te_o_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_213_singleton__conv2,axiom,
% 0.28/0.46 ! [A_129: hoare_1167836817_state] :
% 0.28/0.46 ( ( collec1027672124_state @ ( fequal1831255762_state @ A_129 ) )
% 0.28/0.46 = ( insert2134838167_state @ A_129 @ bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_214_MGF__lemma1,axiom,
% 0.28/0.46 ! [C_21: com,G_3: hoare_1167836817_state > $o] :
% 0.28/0.46 ( hoare_1201148605gleton
% 0.28/0.46 => ( ! [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ ( dom_pname_com @ body ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_5 ) ) @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 => ( ( wt @ C_21 )
% 0.28/0.46 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_215_WT__bodiesD,axiom,
% 0.28/0.46 ! [Pn_1: pname,B_42: com] :
% 0.28/0.46 ( wT_bodies
% 0.28/0.46 => ( ( ( body @ Pn_1 )
% 0.28/0.46 = ( some_com @ B_42 ) )
% 0.28/0.46 => ( wt @ B_42 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_216_imageE,axiom,
% 0.28/0.46 ! [B_93: pname,F_47: hoare_1167836817_state > pname,A_128: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member_pname @ B_93 @ ( image_8178176_pname @ F_47 @ A_128 ) )
% 0.28/0.46 => ~ ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( B_93
% 0.28/0.46 = ( F_47 @ X_5 ) )
% 0.28/0.46 => ~ ( member2058392318_state @ X_5 @ A_128 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_217_imageE,axiom,
% 0.28/0.46 ! [B_93: hoare_1167836817_state,F_47: pname > hoare_1167836817_state,A_128: pname > $o] :
% 0.28/0.46 ( ( member2058392318_state @ B_93 @ ( image_575578384_state @ F_47 @ A_128 ) )
% 0.28/0.46 => ~ ! [X_5: pname] :
% 0.28/0.46 ( ( B_93
% 0.28/0.46 = ( F_47 @ X_5 ) )
% 0.28/0.46 => ~ ( member_pname @ X_5 @ A_128 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_218_finite__subset__induct,axiom,
% 0.28/0.46 ! [P_34: ( ( pname > $o ) > $o ) > $o,A_127: ( pname > $o ) > $o,F_46: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_46 )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ F_46 @ A_127 )
% 0.28/0.46 => ( ( P_34 @ bot_bot_pname_o_o )
% 0.28/0.46 => ( ! [A_122: pname > $o,F_26: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_26 )
% 0.28/0.46 => ( ( member_pname_o @ A_122 @ A_127 )
% 0.28/0.46 => ( ~ ( member_pname_o @ A_122 @ F_26 )
% 0.28/0.46 => ( ( P_34 @ F_26 )
% 0.28/0.46 => ( P_34 @ ( insert_pname_o @ A_122 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_34 @ F_46 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_219_finite__subset__induct,axiom,
% 0.28/0.46 ! [P_34: ( ( hoare_1167836817_state > $o ) > $o ) > $o,A_127: ( hoare_1167836817_state > $o ) > $o,F_46: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_46 )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ F_46 @ A_127 )
% 0.28/0.46 => ( ( P_34 @ bot_bo691907561te_o_o )
% 0.28/0.46 => ( ! [A_122: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_26 )
% 0.28/0.46 => ( ( member864234961tate_o @ A_122 @ A_127 )
% 0.28/0.46 => ( ~ ( member864234961tate_o @ A_122 @ F_26 )
% 0.28/0.46 => ( ( P_34 @ F_26 )
% 0.28/0.46 => ( P_34 @ ( insert999278200tate_o @ A_122 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_34 @ F_46 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_220_finite__subset__induct,axiom,
% 0.28/0.46 ! [P_34: ( pname > $o ) > $o,A_127: pname > $o,F_46: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_46 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ F_46 @ A_127 )
% 0.28/0.46 => ( ( P_34 @ bot_bot_pname_o )
% 0.28/0.46 => ( ! [A_122: pname,F_26: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_26 )
% 0.28/0.46 => ( ( member_pname @ A_122 @ A_127 )
% 0.28/0.46 => ( ~ ( member_pname @ A_122 @ F_26 )
% 0.28/0.46 => ( ( P_34 @ F_26 )
% 0.28/0.46 => ( P_34 @ ( insert_pname @ A_122 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_34 @ F_46 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_221_finite__subset__induct,axiom,
% 0.28/0.46 ! [P_34: ( hoare_1167836817_state > $o ) > $o,A_127: hoare_1167836817_state > $o,F_46: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_46 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ F_46 @ A_127 )
% 0.28/0.46 => ( ( P_34 @ bot_bo70021908tate_o )
% 0.28/0.46 => ( ! [A_122: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_26 )
% 0.28/0.46 => ( ( member2058392318_state @ A_122 @ A_127 )
% 0.28/0.46 => ( ~ ( member2058392318_state @ A_122 @ F_26 )
% 0.28/0.46 => ( ( P_34 @ F_26 )
% 0.28/0.46 => ( P_34 @ ( insert2134838167_state @ A_122 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_34 @ F_46 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_222_WTs__elim__cases_I7_J,axiom,
% 0.28/0.46 ! [P: pname] :
% 0.28/0.46 ( ( wt @ ( body_1 @ P ) )
% 0.28/0.46 => ~ ! [Y_2: com] :
% 0.28/0.46 ( ( body @ P )
% 0.28/0.46 != ( some_com @ Y_2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_223_subsetI,axiom,
% 0.28/0.46 ! [B_92: pname > $o,A_126: pname > $o] :
% 0.28/0.46 ( ! [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_126 )
% 0.28/0.46 => ( member_pname @ X_5 @ B_92 ) )
% 0.28/0.46 => ( ord_less_eq_pname_o @ A_126 @ B_92 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_224_subsetI,axiom,
% 0.28/0.46 ! [B_92: hoare_1167836817_state > $o,A_126: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_126 )
% 0.28/0.46 => ( member2058392318_state @ X_5 @ B_92 ) )
% 0.28/0.46 => ( ord_le827224136tate_o @ A_126 @ B_92 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_225_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: ( pname > $o ) > hoare_1167836817_state,A_125: ( pname > $o ) > $o,B_91: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ B_91 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_91 @ ( image_1381916541_state @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( ord_le1205211808me_o_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite297249702name_o @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_1381916541_state @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_226_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_125: ( hoare_1167836817_state > $o ) > $o,B_91: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ B_91 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_91 @ ( image_635813834_state @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( ord_le741939125te_o_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite1380128977tate_o @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_635813834_state @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_227_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: ( pname > $o ) > pname,A_125: ( pname > $o ) > $o,B_91: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ B_91 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_pname_o_pname @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( ord_le1205211808me_o_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite297249702name_o @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_pname_o_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_228_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: ( hoare_1167836817_state > $o ) > pname,A_125: ( hoare_1167836817_state > $o ) > $o,B_91: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ B_91 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_980295115_pname @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( ord_le741939125te_o_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite1380128977tate_o @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_980295115_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_229_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: hoare_1167836817_state > pname > $o,A_125: hoare_1167836817_state > $o,B_91: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ B_91 )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ B_91 @ ( image_2066861949name_o @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite1084549118_state @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_2066861949name_o @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_230_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: hoare_1167836817_state > hoare_1167836817_state > $o,A_125: hoare_1167836817_state > $o,B_91: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ B_91 )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ B_91 @ ( image_1745649338tate_o @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite1084549118_state @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_1745649338tate_o @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_231_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: hoare_1167836817_state > pname,A_125: hoare_1167836817_state > $o,B_91: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ B_91 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_8178176_pname @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite1084549118_state @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_8178176_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_232_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: pname > pname > $o,A_125: pname > $o,B_91: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ B_91 )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ B_91 @ ( image_pname_pname_o @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite_finite_pname @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_pname_pname_o @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_233_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: pname > hoare_1167836817_state > $o,A_125: pname > $o,B_91: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ B_91 )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ B_91 @ ( image_475339327tate_o @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite_finite_pname @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_475339327tate_o @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_234_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: pname > pname,A_125: pname > $o,B_91: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ B_91 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_pname_pname @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite_finite_pname @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_pname_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_235_finite__subset__image,axiom,
% 0.28/0.46 ! [F_45: pname > hoare_1167836817_state,A_125: pname > $o,B_91: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ B_91 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_91 @ ( image_575578384_state @ F_45 @ A_125 ) )
% 0.28/0.46 => ? [C_47: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 0.28/0.46 & ( finite_finite_pname @ C_47 )
% 0.28/0.46 & ( B_91
% 0.28/0.46 = ( image_575578384_state @ F_45 @ C_47 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_236_finite__dom__body,axiom,
% 0.28/0.46 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_237_finite__induct,axiom,
% 0.28/0.46 ! [P_33: ( ( pname > $o ) > $o ) > $o,F_44: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_44 )
% 0.28/0.46 => ( ( P_33 @ bot_bot_pname_o_o )
% 0.28/0.46 => ( ! [X_5: pname > $o,F_26: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_26 )
% 0.28/0.46 => ( ~ ( member_pname_o @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_33 @ F_26 )
% 0.28/0.46 => ( P_33 @ ( insert_pname_o @ X_5 @ F_26 ) ) ) ) )
% 0.28/0.46 => ( P_33 @ F_44 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_238_finite__induct,axiom,
% 0.28/0.46 ! [P_33: ( ( hoare_1167836817_state > $o ) > $o ) > $o,F_44: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_44 )
% 0.28/0.46 => ( ( P_33 @ bot_bo691907561te_o_o )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_26 )
% 0.28/0.46 => ( ~ ( member864234961tate_o @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_33 @ F_26 )
% 0.28/0.46 => ( P_33 @ ( insert999278200tate_o @ X_5 @ F_26 ) ) ) ) )
% 0.28/0.46 => ( P_33 @ F_44 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_239_finite__induct,axiom,
% 0.28/0.46 ! [P_33: ( pname > $o ) > $o,F_44: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_44 )
% 0.28/0.46 => ( ( P_33 @ bot_bot_pname_o )
% 0.28/0.46 => ( ! [X_5: pname,F_26: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_26 )
% 0.28/0.46 => ( ~ ( member_pname @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_33 @ F_26 )
% 0.28/0.46 => ( P_33 @ ( insert_pname @ X_5 @ F_26 ) ) ) ) )
% 0.28/0.46 => ( P_33 @ F_44 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_240_finite__induct,axiom,
% 0.28/0.46 ! [P_33: ( hoare_1167836817_state > $o ) > $o,F_44: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_44 )
% 0.28/0.46 => ( ( P_33 @ bot_bo70021908tate_o )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_26 )
% 0.28/0.46 => ( ~ ( member2058392318_state @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_33 @ F_26 )
% 0.28/0.46 => ( P_33 @ ( insert2134838167_state @ X_5 @ F_26 ) ) ) ) )
% 0.28/0.46 => ( P_33 @ F_44 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_241_finite_Osimps,axiom,
% 0.28/0.46 ! [A_123: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ A_123 )
% 0.28/0.46 <=> ( ( A_123 = bot_bot_pname_o_o )
% 0.28/0.46 | ? [A_124: ( pname > $o ) > $o,A_122: pname > $o] :
% 0.28/0.46 ( ( A_123
% 0.28/0.46 = ( insert_pname_o @ A_122 @ A_124 ) )
% 0.28/0.46 & ( finite297249702name_o @ A_124 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_242_finite_Osimps,axiom,
% 0.28/0.46 ! [A_123: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ A_123 )
% 0.28/0.46 <=> ( ( A_123 = bot_bo691907561te_o_o )
% 0.28/0.46 | ? [A_124: ( hoare_1167836817_state > $o ) > $o,A_122: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_123
% 0.28/0.46 = ( insert999278200tate_o @ A_122 @ A_124 ) )
% 0.28/0.46 & ( finite1380128977tate_o @ A_124 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_243_finite_Osimps,axiom,
% 0.28/0.46 ! [A_123: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ A_123 )
% 0.28/0.46 <=> ( ( A_123 = bot_bot_pname_o )
% 0.28/0.46 | ? [A_124: pname > $o,A_122: pname] :
% 0.28/0.46 ( ( A_123
% 0.28/0.46 = ( insert_pname @ A_122 @ A_124 ) )
% 0.28/0.46 & ( finite_finite_pname @ A_124 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_244_finite_Osimps,axiom,
% 0.28/0.46 ! [A_123: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ A_123 )
% 0.28/0.46 <=> ( ( A_123 = bot_bo70021908tate_o )
% 0.28/0.46 | ? [A_124: hoare_1167836817_state > $o,A_122: hoare_1167836817_state] :
% 0.28/0.46 ( ( A_123
% 0.28/0.46 = ( insert2134838167_state @ A_122 @ A_124 ) )
% 0.28/0.46 & ( finite1084549118_state @ A_124 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_245_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: pname > pname > $o,A_121: pname > $o] :
% 0.28/0.46 ( ~ ( finite_finite_pname @ A_121 )
% 0.28/0.46 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite_finite_pname
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [A_122: pname] :
% 0.28/0.46 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_246_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: pname > hoare_1167836817_state > $o,A_121: pname > $o] :
% 0.28/0.46 ( ~ ( finite_finite_pname @ A_121 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ ( image_475339327tate_o @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite_finite_pname
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [A_122: pname] :
% 0.28/0.46 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_247_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: hoare_1167836817_state > hoare_1167836817_state,A_121: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ~ ( finite1084549118_state @ A_121 )
% 0.28/0.46 => ( ( finite1084549118_state @ ( image_31595733_state @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite1084549118_state
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [A_122: hoare_1167836817_state] :
% 0.28/0.46 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_248_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: ( pname > $o ) > hoare_1167836817_state,A_121: ( pname > $o ) > $o] :
% 0.28/0.46 ( ~ ( finite297249702name_o @ A_121 )
% 0.28/0.46 => ( ( finite1084549118_state @ ( image_1381916541_state @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: pname > $o] :
% 0.28/0.46 ( ( member_pname_o @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite297249702name_o
% 0.28/0.46 @ ( collect_pname_o
% 0.28/0.46 @ ^ [A_122: pname > $o] :
% 0.28/0.46 ( (&) @ ( member_pname_o @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_249_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_121: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ~ ( finite1380128977tate_o @ A_121 )
% 0.28/0.46 => ( ( finite1084549118_state @ ( image_635813834_state @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member864234961tate_o @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite1380128977tate_o
% 0.28/0.46 @ ( collec269976083tate_o
% 0.28/0.46 @ ^ [A_122: hoare_1167836817_state > $o] :
% 0.28/0.46 ( (&) @ ( member864234961tate_o @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_250_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: pname > pname,A_121: pname > $o] :
% 0.28/0.46 ( ~ ( finite_finite_pname @ A_121 )
% 0.28/0.46 => ( ( finite_finite_pname @ ( image_pname_pname @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite_finite_pname
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [A_122: pname] :
% 0.28/0.46 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_251_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: hoare_1167836817_state > pname,A_121: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ~ ( finite1084549118_state @ A_121 )
% 0.28/0.46 => ( ( finite_finite_pname @ ( image_8178176_pname @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite1084549118_state
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [A_122: hoare_1167836817_state] :
% 0.28/0.46 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_252_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: ( pname > $o ) > pname,A_121: ( pname > $o ) > $o] :
% 0.28/0.46 ( ~ ( finite297249702name_o @ A_121 )
% 0.28/0.46 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: pname > $o] :
% 0.28/0.46 ( ( member_pname_o @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite297249702name_o
% 0.28/0.46 @ ( collect_pname_o
% 0.28/0.46 @ ^ [A_122: pname > $o] :
% 0.28/0.46 ( (&) @ ( member_pname_o @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_253_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: ( hoare_1167836817_state > $o ) > pname,A_121: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ~ ( finite1380128977tate_o @ A_121 )
% 0.28/0.46 => ( ( finite_finite_pname @ ( image_980295115_pname @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member864234961tate_o @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite1380128977tate_o
% 0.28/0.46 @ ( collec269976083tate_o
% 0.28/0.46 @ ^ [A_122: hoare_1167836817_state > $o] :
% 0.28/0.46 ( (&) @ ( member864234961tate_o @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_254_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: hoare_1167836817_state > pname > $o,A_121: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ~ ( finite1084549118_state @ A_121 )
% 0.28/0.46 => ( ( finite297249702name_o @ ( image_2066861949name_o @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite1084549118_state
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [A_122: hoare_1167836817_state] :
% 0.28/0.46 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_255_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: hoare_1167836817_state > hoare_1167836817_state > $o,A_121: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ~ ( finite1084549118_state @ A_121 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ ( image_1745649338tate_o @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite1084549118_state
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [A_122: hoare_1167836817_state] :
% 0.28/0.46 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_256_pigeonhole__infinite,axiom,
% 0.28/0.46 ! [F_43: pname > hoare_1167836817_state,A_121: pname > $o] :
% 0.28/0.46 ( ~ ( finite_finite_pname @ A_121 )
% 0.28/0.46 => ( ( finite1084549118_state @ ( image_575578384_state @ F_43 @ A_121 ) )
% 0.28/0.46 => ? [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_121 )
% 0.28/0.46 & ~ ( finite_finite_pname
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [A_122: pname] :
% 0.28/0.46 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 0.28/0.46 @ ( ( F_43 @ A_122 )
% 0.28/0.46 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_257_com_Osimps_I6_J,axiom,
% 0.28/0.46 ! [Pname_1: pname,Pname: pname] :
% 0.28/0.46 ( ( ( body_1 @ Pname_1 )
% 0.28/0.46 = ( body_1 @ Pname ) )
% 0.28/0.46 <=> ( Pname_1 = Pname ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_258_MGT__Body,axiom,
% 0.28/0.46 ! [G_3: hoare_1167836817_state > $o,Procs_3: pname > $o] :
% 0.28/0.46 ( ( hoare_123228589_state
% 0.28/0.46 @ ( semila1172322802tate_o @ G_3
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.28/0.46 @ Procs_3 ) )
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 0.28/0.46 @ Procs_3 ) )
% 0.28/0.46 => ( ( finite_finite_pname @ Procs_3 )
% 0.28/0.46 => ( hoare_123228589_state @ G_3
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.28/0.46 @ Procs_3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_259_domD,axiom,
% 0.28/0.46 ! [A_120: pname,M_1: pname > option_com] :
% 0.28/0.46 ( ( member_pname @ A_120 @ ( dom_pname_com @ M_1 ) )
% 0.28/0.46 => ? [B_90: com] :
% 0.28/0.46 ( ( M_1 @ A_120 )
% 0.28/0.46 = ( some_com @ B_90 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_260_the__elem__eq,axiom,
% 0.28/0.46 ! [X_84: pname] :
% 0.28/0.46 ( ( the_elem_pname @ ( insert_pname @ X_84 @ bot_bot_pname_o ) )
% 0.28/0.46 = X_84 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_261_the__elem__eq,axiom,
% 0.28/0.46 ! [X_84: hoare_1167836817_state] :
% 0.28/0.46 ( ( the_el323660082_state @ ( insert2134838167_state @ X_84 @ bot_bo70021908tate_o ) )
% 0.28/0.46 = X_84 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_262_image__subsetI,axiom,
% 0.28/0.46 ! [F_42: hoare_1167836817_state > pname,B_89: pname > $o,A_119: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_119 )
% 0.28/0.46 => ( member_pname @ ( F_42 @ X_5 ) @ B_89 ) )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( image_8178176_pname @ F_42 @ A_119 ) @ B_89 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_263_image__subsetI,axiom,
% 0.28/0.46 ! [F_42: pname > hoare_1167836817_state,B_89: hoare_1167836817_state > $o,A_119: pname > $o] :
% 0.28/0.46 ( ! [X_5: pname] :
% 0.28/0.46 ( ( member_pname @ X_5 @ A_119 )
% 0.28/0.46 => ( member2058392318_state @ ( F_42 @ X_5 ) @ B_89 ) )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( image_575578384_state @ F_42 @ A_119 ) @ B_89 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_264_order__refl,axiom,
% 0.28/0.46 ! [X_83: pname > $o] : ( ord_less_eq_pname_o @ X_83 @ X_83 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_265_order__refl,axiom,
% 0.28/0.46 ! [X_83: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_83 @ X_83 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_266_nonempty__iff,axiom,
% 0.28/0.46 ! [A_118: pname > $o] :
% 0.28/0.46 ( ( A_118 != bot_bot_pname_o )
% 0.28/0.46 <=> ? [X_5: pname,B_43: pname > $o] :
% 0.28/0.46 ( ( A_118
% 0.28/0.46 = ( insert_pname @ X_5 @ B_43 ) )
% 0.28/0.46 & ~ ( member_pname @ X_5 @ B_43 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_267_nonempty__iff,axiom,
% 0.28/0.46 ! [A_118: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_118 != bot_bo70021908tate_o )
% 0.28/0.46 <=> ? [X_5: hoare_1167836817_state,B_43: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_118
% 0.28/0.46 = ( insert2134838167_state @ X_5 @ B_43 ) )
% 0.28/0.46 & ~ ( member2058392318_state @ X_5 @ B_43 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_268_the_Osimps,axiom,
% 0.28/0.46 ! [X_82: com] :
% 0.28/0.46 ( ( the_com @ ( some_com @ X_82 ) )
% 0.28/0.46 = X_82 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_269_weak__Body,axiom,
% 0.28/0.46 ! [G_27: hoare_1167836817_state > $o,P_32: state > state > $o,Pn_4: pname,Q_22: state > state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_27 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_32 @ ( the_com @ ( body @ Pn_4 ) ) @ Q_22 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_27 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_32 @ ( body_1 @ Pn_4 ) @ Q_22 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_270_UnCI,axiom,
% 0.28/0.46 ! [A_117: pname > $o,C_46: pname,B_88: pname > $o] :
% 0.28/0.46 ( ( ~ ( member_pname @ C_46 @ B_88 )
% 0.28/0.46 => ( member_pname @ C_46 @ A_117 ) )
% 0.28/0.46 => ( member_pname @ C_46 @ ( semila1780557381name_o @ A_117 @ B_88 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_271_UnCI,axiom,
% 0.28/0.46 ! [A_117: hoare_1167836817_state > $o,C_46: hoare_1167836817_state,B_88: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ~ ( member2058392318_state @ C_46 @ B_88 )
% 0.28/0.46 => ( member2058392318_state @ C_46 @ A_117 ) )
% 0.28/0.46 => ( member2058392318_state @ C_46 @ ( semila1172322802tate_o @ A_117 @ B_88 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_272_UnE,axiom,
% 0.28/0.46 ! [C_45: pname,A_116: pname > $o,B_87: pname > $o] :
% 0.28/0.46 ( ( member_pname @ C_45 @ ( semila1780557381name_o @ A_116 @ B_87 ) )
% 0.28/0.46 => ( ~ ( member_pname @ C_45 @ A_116 )
% 0.28/0.46 => ( member_pname @ C_45 @ B_87 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_273_UnE,axiom,
% 0.28/0.46 ! [C_45: hoare_1167836817_state,A_116: hoare_1167836817_state > $o,B_87: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ C_45 @ ( semila1172322802tate_o @ A_116 @ B_87 ) )
% 0.28/0.46 => ( ~ ( member2058392318_state @ C_45 @ A_116 )
% 0.28/0.46 => ( member2058392318_state @ C_45 @ B_87 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_274_Collect__disj__eq,axiom,
% 0.28/0.46 ! [P_31: pname > $o,Q_21: pname > $o] :
% 0.28/0.46 ( ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 0.28/0.46 = ( semila1780557381name_o @ ( collect_pname @ P_31 ) @ ( collect_pname @ Q_21 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_275_Collect__disj__eq,axiom,
% 0.28/0.46 ! [P_31: ( pname > $o ) > $o,Q_21: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 0.28/0.46 = ( semila181081674me_o_o @ ( collect_pname_o @ P_31 ) @ ( collect_pname_o @ Q_21 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_276_Collect__disj__eq,axiom,
% 0.28/0.46 ! [P_31: ( hoare_1167836817_state > $o ) > $o,Q_21: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 0.28/0.46 = ( semila866907787te_o_o @ ( collec269976083tate_o @ P_31 ) @ ( collec269976083tate_o @ Q_21 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_277_Collect__disj__eq,axiom,
% 0.28/0.46 ! [P_31: hoare_1167836817_state > $o,Q_21: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 0.28/0.46 = ( semila1172322802tate_o @ ( collec1027672124_state @ P_31 ) @ ( collec1027672124_state @ Q_21 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_278_triple_Oinject,axiom,
% 0.28/0.46 ! [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] :
% 0.28/0.46 ( ( ( hoare_908217195_state @ Fun1_2 @ Com_4 @ Fun2_2 )
% 0.28/0.46 = ( hoare_908217195_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 0.28/0.46 <=> ( ( Fun1_2 = Fun1_1 )
% 0.28/0.46 & ( Com_4 = Com_3 )
% 0.28/0.46 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_279_UnI2,axiom,
% 0.28/0.46 ! [A_115: pname > $o,C_44: pname,B_86: pname > $o] :
% 0.28/0.46 ( ( member_pname @ C_44 @ B_86 )
% 0.28/0.46 => ( member_pname @ C_44 @ ( semila1780557381name_o @ A_115 @ B_86 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_280_UnI2,axiom,
% 0.28/0.46 ! [A_115: hoare_1167836817_state > $o,C_44: hoare_1167836817_state,B_86: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ C_44 @ B_86 )
% 0.28/0.46 => ( member2058392318_state @ C_44 @ ( semila1172322802tate_o @ A_115 @ B_86 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_281_UnI1,axiom,
% 0.28/0.46 ! [B_85: pname > $o,C_43: pname,A_114: pname > $o] :
% 0.28/0.46 ( ( member_pname @ C_43 @ A_114 )
% 0.28/0.46 => ( member_pname @ C_43 @ ( semila1780557381name_o @ A_114 @ B_85 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_282_UnI1,axiom,
% 0.28/0.46 ! [B_85: hoare_1167836817_state > $o,C_43: hoare_1167836817_state,A_114: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ C_43 @ A_114 )
% 0.28/0.46 => ( member2058392318_state @ C_43 @ ( semila1172322802tate_o @ A_114 @ B_85 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_283_ball__Un,axiom,
% 0.28/0.46 ! [P_30: hoare_1167836817_state > $o,A_113: hoare_1167836817_state > $o,B_84: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ A_113 @ B_84 ) )
% 0.28/0.46 => ( P_30 @ X_5 ) )
% 0.28/0.46 <=> ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_113 )
% 0.28/0.46 => ( P_30 @ X_5 ) )
% 0.28/0.46 & ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ B_84 )
% 0.28/0.46 => ( P_30 @ X_5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_284_bex__Un,axiom,
% 0.28/0.46 ! [P_29: hoare_1167836817_state > $o,A_112: hoare_1167836817_state > $o,B_83: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ A_112 @ B_83 ) )
% 0.28/0.46 & ( P_29 @ X_5 ) )
% 0.28/0.46 <=> ( ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ A_112 )
% 0.28/0.46 & ( P_29 @ X_5 ) )
% 0.28/0.46 | ? [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_5 @ B_83 )
% 0.28/0.46 & ( P_29 @ X_5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_285_Un__assoc,axiom,
% 0.28/0.46 ! [A_111: hoare_1167836817_state > $o,B_82: hoare_1167836817_state > $o,C_42: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_111 @ B_82 ) @ C_42 )
% 0.28/0.46 = ( semila1172322802tate_o @ A_111 @ ( semila1172322802tate_o @ B_82 @ C_42 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_286_Un__iff,axiom,
% 0.28/0.46 ! [C_41: pname,A_110: pname > $o,B_81: pname > $o] :
% 0.28/0.46 ( ( member_pname @ C_41 @ ( semila1780557381name_o @ A_110 @ B_81 ) )
% 0.28/0.46 <=> ( ( member_pname @ C_41 @ A_110 )
% 0.28/0.46 | ( member_pname @ C_41 @ B_81 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_287_Un__iff,axiom,
% 0.28/0.46 ! [C_41: hoare_1167836817_state,A_110: hoare_1167836817_state > $o,B_81: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( member2058392318_state @ C_41 @ ( semila1172322802tate_o @ A_110 @ B_81 ) )
% 0.28/0.46 <=> ( ( member2058392318_state @ C_41 @ A_110 )
% 0.28/0.46 | ( member2058392318_state @ C_41 @ B_81 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_288_Un__left__commute,axiom,
% 0.28/0.46 ! [A_109: hoare_1167836817_state > $o,B_80: hoare_1167836817_state > $o,C_40: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_109 @ ( semila1172322802tate_o @ B_80 @ C_40 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ B_80 @ ( semila1172322802tate_o @ A_109 @ C_40 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_289_Un__left__absorb,axiom,
% 0.28/0.46 ! [A_108: hoare_1167836817_state > $o,B_79: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_108 @ ( semila1172322802tate_o @ A_108 @ B_79 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ A_108 @ B_79 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_290_Un__commute,axiom,
% 0.28/0.46 ! [A_107: hoare_1167836817_state > $o,B_78: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_107 @ B_78 )
% 0.28/0.46 = ( semila1172322802tate_o @ B_78 @ A_107 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_291_Un__def,axiom,
% 0.28/0.46 ! [A_106: pname > $o,B_77: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ A_106 @ B_77 )
% 0.28/0.46 = ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( (|) @ ( member_pname @ X_5 @ A_106 ) @ ( member_pname @ X_5 @ B_77 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_292_Un__def,axiom,
% 0.28/0.46 ! [A_106: ( pname > $o ) > $o,B_77: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( semila181081674me_o_o @ A_106 @ B_77 )
% 0.28/0.46 = ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( (|) @ ( member_pname_o @ X_5 @ A_106 ) @ ( member_pname_o @ X_5 @ B_77 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_293_Un__def,axiom,
% 0.28/0.46 ! [A_106: ( hoare_1167836817_state > $o ) > $o,B_77: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( semila866907787te_o_o @ A_106 @ B_77 )
% 0.28/0.46 = ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( member864234961tate_o @ X_5 @ A_106 ) @ ( member864234961tate_o @ X_5 @ B_77 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_294_Un__def,axiom,
% 0.28/0.46 ! [A_106: hoare_1167836817_state > $o,B_77: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_106 @ B_77 )
% 0.28/0.46 = ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( member2058392318_state @ X_5 @ A_106 ) @ ( member2058392318_state @ X_5 @ B_77 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_295_Un__absorb,axiom,
% 0.28/0.46 ! [A_105: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_105 @ A_105 )
% 0.28/0.46 = A_105 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_296_Un__empty,axiom,
% 0.28/0.46 ! [A_104: pname > $o,B_76: pname > $o] :
% 0.28/0.46 ( ( ( semila1780557381name_o @ A_104 @ B_76 )
% 0.28/0.46 = bot_bot_pname_o )
% 0.28/0.46 <=> ( ( A_104 = bot_bot_pname_o )
% 0.28/0.46 & ( B_76 = bot_bot_pname_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_297_Un__empty,axiom,
% 0.28/0.46 ! [A_104: hoare_1167836817_state > $o,B_76: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( semila1172322802tate_o @ A_104 @ B_76 )
% 0.28/0.46 = bot_bo70021908tate_o )
% 0.28/0.46 <=> ( ( A_104 = bot_bo70021908tate_o )
% 0.28/0.46 & ( B_76 = bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_298_Un__empty__right,axiom,
% 0.28/0.46 ! [A_103: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ A_103 @ bot_bot_pname_o )
% 0.28/0.46 = A_103 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_299_Un__empty__right,axiom,
% 0.28/0.46 ! [A_103: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_103 @ bot_bo70021908tate_o )
% 0.28/0.46 = A_103 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_300_Un__empty__left,axiom,
% 0.28/0.46 ! [B_75: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ bot_bot_pname_o @ B_75 )
% 0.28/0.46 = B_75 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_301_Un__empty__left,axiom,
% 0.28/0.46 ! [B_75: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ B_75 )
% 0.28/0.46 = B_75 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_302_finite__UnI,axiom,
% 0.28/0.46 ! [G_26: ( pname > $o ) > $o,F_41: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_41 )
% 0.28/0.46 => ( ( finite297249702name_o @ G_26 )
% 0.28/0.46 => ( finite297249702name_o @ ( semila181081674me_o_o @ F_41 @ G_26 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_303_finite__UnI,axiom,
% 0.28/0.46 ! [G_26: ( hoare_1167836817_state > $o ) > $o,F_41: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_41 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ G_26 )
% 0.28/0.46 => ( finite1380128977tate_o @ ( semila866907787te_o_o @ F_41 @ G_26 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_304_finite__UnI,axiom,
% 0.28/0.46 ! [G_26: pname > $o,F_41: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_41 )
% 0.28/0.46 => ( ( finite_finite_pname @ G_26 )
% 0.28/0.46 => ( finite_finite_pname @ ( semila1780557381name_o @ F_41 @ G_26 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_305_finite__UnI,axiom,
% 0.28/0.46 ! [G_26: hoare_1167836817_state > $o,F_41: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_41 )
% 0.28/0.46 => ( ( finite1084549118_state @ G_26 )
% 0.28/0.46 => ( finite1084549118_state @ ( semila1172322802tate_o @ F_41 @ G_26 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_306_finite__Un,axiom,
% 0.28/0.46 ! [F_40: ( pname > $o ) > $o,G_25: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ ( semila181081674me_o_o @ F_40 @ G_25 ) )
% 0.28/0.46 <=> ( ( finite297249702name_o @ F_40 )
% 0.28/0.46 & ( finite297249702name_o @ G_25 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_307_finite__Un,axiom,
% 0.28/0.46 ! [F_40: ( hoare_1167836817_state > $o ) > $o,G_25: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ ( semila866907787te_o_o @ F_40 @ G_25 ) )
% 0.28/0.46 <=> ( ( finite1380128977tate_o @ F_40 )
% 0.28/0.46 & ( finite1380128977tate_o @ G_25 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_308_finite__Un,axiom,
% 0.28/0.46 ! [F_40: pname > $o,G_25: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ ( semila1780557381name_o @ F_40 @ G_25 ) )
% 0.28/0.46 <=> ( ( finite_finite_pname @ F_40 )
% 0.28/0.46 & ( finite_finite_pname @ G_25 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_309_finite__Un,axiom,
% 0.28/0.46 ! [F_40: hoare_1167836817_state > $o,G_25: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ ( semila1172322802tate_o @ F_40 @ G_25 ) )
% 0.28/0.46 <=> ( ( finite1084549118_state @ F_40 )
% 0.28/0.46 & ( finite1084549118_state @ G_25 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_310_Un__insert__left,axiom,
% 0.28/0.46 ! [A_102: pname,B_74: pname > $o,C_39: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ ( insert_pname @ A_102 @ B_74 ) @ C_39 )
% 0.28/0.46 = ( insert_pname @ A_102 @ ( semila1780557381name_o @ B_74 @ C_39 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_311_Un__insert__left,axiom,
% 0.28/0.46 ! [A_102: hoare_1167836817_state,B_74: hoare_1167836817_state > $o,C_39: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ ( insert2134838167_state @ A_102 @ B_74 ) @ C_39 )
% 0.28/0.46 = ( insert2134838167_state @ A_102 @ ( semila1172322802tate_o @ B_74 @ C_39 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_312_Un__insert__right,axiom,
% 0.28/0.46 ! [A_101: pname > $o,A_100: pname,B_73: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ A_101 @ ( insert_pname @ A_100 @ B_73 ) )
% 0.28/0.46 = ( insert_pname @ A_100 @ ( semila1780557381name_o @ A_101 @ B_73 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_313_Un__insert__right,axiom,
% 0.28/0.46 ! [A_101: hoare_1167836817_state > $o,A_100: hoare_1167836817_state,B_73: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_101 @ ( insert2134838167_state @ A_100 @ B_73 ) )
% 0.28/0.46 = ( insert2134838167_state @ A_100 @ ( semila1172322802tate_o @ A_101 @ B_73 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_314_Un__mono,axiom,
% 0.28/0.46 ! [B_72: pname > $o,D_4: pname > $o,A_99: pname > $o,C_38: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_99 @ C_38 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_72 @ D_4 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_99 @ B_72 ) @ ( semila1780557381name_o @ C_38 @ D_4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_315_Un__mono,axiom,
% 0.28/0.46 ! [B_72: hoare_1167836817_state > $o,D_4: hoare_1167836817_state > $o,A_99: hoare_1167836817_state > $o,C_38: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_99 @ C_38 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_72 @ D_4 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_99 @ B_72 ) @ ( semila1172322802tate_o @ C_38 @ D_4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_316_Un__least,axiom,
% 0.28/0.46 ! [B_71: pname > $o,A_98: pname > $o,C_37: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_98 @ C_37 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_71 @ C_37 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_98 @ B_71 ) @ C_37 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_317_Un__least,axiom,
% 0.28/0.46 ! [B_71: hoare_1167836817_state > $o,A_98: hoare_1167836817_state > $o,C_37: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_98 @ C_37 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_71 @ C_37 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_98 @ B_71 ) @ C_37 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_318_Un__absorb2,axiom,
% 0.28/0.46 ! [B_70: pname > $o,A_97: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ B_70 @ A_97 )
% 0.28/0.46 => ( ( semila1780557381name_o @ A_97 @ B_70 )
% 0.28/0.46 = A_97 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_319_Un__absorb2,axiom,
% 0.28/0.46 ! [B_70: hoare_1167836817_state > $o,A_97: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ B_70 @ A_97 )
% 0.28/0.46 => ( ( semila1172322802tate_o @ A_97 @ B_70 )
% 0.28/0.46 = A_97 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_320_Un__absorb1,axiom,
% 0.28/0.46 ! [A_96: pname > $o,B_69: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_96 @ B_69 )
% 0.28/0.46 => ( ( semila1780557381name_o @ A_96 @ B_69 )
% 0.28/0.46 = B_69 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_321_Un__absorb1,axiom,
% 0.28/0.46 ! [A_96: hoare_1167836817_state > $o,B_69: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_96 @ B_69 )
% 0.28/0.46 => ( ( semila1172322802tate_o @ A_96 @ B_69 )
% 0.28/0.46 = B_69 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_322_subset__Un__eq,axiom,
% 0.28/0.46 ! [A_95: pname > $o,B_68: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_95 @ B_68 )
% 0.28/0.46 <=> ( ( semila1780557381name_o @ A_95 @ B_68 )
% 0.28/0.46 = B_68 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_323_subset__Un__eq,axiom,
% 0.28/0.46 ! [A_95: hoare_1167836817_state > $o,B_68: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_95 @ B_68 )
% 0.28/0.46 <=> ( ( semila1172322802tate_o @ A_95 @ B_68 )
% 0.28/0.46 = B_68 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_324_Un__upper2,axiom,
% 0.28/0.46 ! [B_67: pname > $o,A_94: pname > $o] : ( ord_less_eq_pname_o @ B_67 @ ( semila1780557381name_o @ A_94 @ B_67 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_325_Un__upper2,axiom,
% 0.28/0.46 ! [B_67: hoare_1167836817_state > $o,A_94: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ B_67 @ ( semila1172322802tate_o @ A_94 @ B_67 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_326_Un__upper1,axiom,
% 0.28/0.46 ! [A_93: pname > $o,B_66: pname > $o] : ( ord_less_eq_pname_o @ A_93 @ ( semila1780557381name_o @ A_93 @ B_66 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_327_Un__upper1,axiom,
% 0.28/0.46 ! [A_93: hoare_1167836817_state > $o,B_66: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A_93 @ ( semila1172322802tate_o @ A_93 @ B_66 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_328_image__Un,axiom,
% 0.28/0.46 ! [F_39: pname > hoare_1167836817_state,A_92: pname > $o,B_65: pname > $o] :
% 0.28/0.46 ( ( image_575578384_state @ F_39 @ ( semila1780557381name_o @ A_92 @ B_65 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ ( image_575578384_state @ F_39 @ A_92 ) @ ( image_575578384_state @ F_39 @ B_65 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_329_insert__def,axiom,
% 0.28/0.46 ! [A_91: pname,B_64: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ A_91 @ B_64 )
% 0.28/0.46 = ( semila1780557381name_o
% 0.28/0.46 @ ( collect_pname
% 0.28/0.46 @ ^ [X_5: pname] : ( X_5 = A_91 ) )
% 0.28/0.46 @ B_64 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_330_insert__def,axiom,
% 0.28/0.46 ! [A_91: hoare_1167836817_state,B_64: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ A_91 @ B_64 )
% 0.28/0.46 = ( semila1172322802tate_o
% 0.28/0.46 @ ( collec1027672124_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( X_5 = A_91 ) )
% 0.28/0.46 @ B_64 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_331_insert__def,axiom,
% 0.28/0.46 ! [A_91: pname > $o,B_64: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( insert_pname_o @ A_91 @ B_64 )
% 0.28/0.46 = ( semila181081674me_o_o
% 0.28/0.46 @ ( collect_pname_o
% 0.28/0.46 @ ^ [X_5: pname > $o] : ( X_5 = A_91 ) )
% 0.28/0.46 @ B_64 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_332_insert__def,axiom,
% 0.28/0.46 ! [A_91: hoare_1167836817_state > $o,B_64: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( insert999278200tate_o @ A_91 @ B_64 )
% 0.28/0.46 = ( semila866907787te_o_o
% 0.28/0.46 @ ( collec269976083tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state > $o] : ( X_5 = A_91 ) )
% 0.28/0.46 @ B_64 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_333_insert__is__Un,axiom,
% 0.28/0.46 ! [A_90: pname,A_89: pname > $o] :
% 0.28/0.46 ( ( insert_pname @ A_90 @ A_89 )
% 0.28/0.46 = ( semila1780557381name_o @ ( insert_pname @ A_90 @ bot_bot_pname_o ) @ A_89 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_334_insert__is__Un,axiom,
% 0.28/0.46 ! [A_90: hoare_1167836817_state,A_89: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( insert2134838167_state @ A_90 @ A_89 )
% 0.28/0.46 = ( semila1172322802tate_o @ ( insert2134838167_state @ A_90 @ bot_bo70021908tate_o ) @ A_89 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_335_hoare__derivs_OBody,axiom,
% 0.28/0.46 ! [G_24: hoare_1167836817_state > $o,P_28: pname > state > state > $o,Q_20: pname > state > state > $o,Procs_2: pname > $o] :
% 0.28/0.46 ( ( hoare_123228589_state
% 0.28/0.46 @ ( semila1172322802tate_o @ G_24
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_20 @ P_24 ) )
% 0.28/0.46 @ Procs_2 ) )
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( the_com @ ( body @ P_24 ) ) @ ( Q_20 @ P_24 ) )
% 0.28/0.46 @ Procs_2 ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_24
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_20 @ P_24 ) )
% 0.28/0.46 @ Procs_2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_336_xt1_I6_J,axiom,
% 0.28/0.46 ! [Z_20: pname > $o,Y_46: pname > $o,X_81: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ Y_46 @ X_81 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ Z_20 @ Y_46 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ Z_20 @ X_81 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_337_xt1_I6_J,axiom,
% 0.28/0.46 ! [Z_20: hoare_1167836817_state > $o,Y_46: hoare_1167836817_state > $o,X_81: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ Y_46 @ X_81 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ Z_20 @ Y_46 )
% 0.28/0.46 => ( ord_le827224136tate_o @ Z_20 @ X_81 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_338_xt1_I5_J,axiom,
% 0.28/0.46 ! [Y_45: pname > $o,X_80: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ Y_45 @ X_80 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ X_80 @ Y_45 )
% 0.28/0.46 => ( X_80 = Y_45 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_339_xt1_I5_J,axiom,
% 0.28/0.46 ! [Y_45: hoare_1167836817_state > $o,X_80: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ Y_45 @ X_80 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ X_80 @ Y_45 )
% 0.28/0.46 => ( X_80 = Y_45 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_340_order__trans,axiom,
% 0.28/0.46 ! [Z_19: pname > $o,X_79: pname > $o,Y_44: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ X_79 @ Y_44 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ Y_44 @ Z_19 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ X_79 @ Z_19 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_341_order__trans,axiom,
% 0.28/0.46 ! [Z_19: hoare_1167836817_state > $o,X_79: hoare_1167836817_state > $o,Y_44: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ X_79 @ Y_44 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ Y_44 @ Z_19 )
% 0.28/0.46 => ( ord_le827224136tate_o @ X_79 @ Z_19 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_342_order__antisym,axiom,
% 0.28/0.46 ! [X_78: pname > $o,Y_43: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ X_78 @ Y_43 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ Y_43 @ X_78 )
% 0.28/0.46 => ( X_78 = Y_43 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_343_order__antisym,axiom,
% 0.28/0.46 ! [X_78: hoare_1167836817_state > $o,Y_43: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ X_78 @ Y_43 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ Y_43 @ X_78 )
% 0.28/0.46 => ( X_78 = Y_43 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_344_xt1_I4_J,axiom,
% 0.28/0.46 ! [C_36: pname > $o,B_63: pname > $o,A_88: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ B_63 @ A_88 )
% 0.28/0.46 => ( ( B_63 = C_36 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ C_36 @ A_88 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_345_xt1_I4_J,axiom,
% 0.28/0.46 ! [C_36: hoare_1167836817_state > $o,B_63: hoare_1167836817_state > $o,A_88: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ B_63 @ A_88 )
% 0.28/0.46 => ( ( B_63 = C_36 )
% 0.28/0.46 => ( ord_le827224136tate_o @ C_36 @ A_88 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_346_ord__le__eq__trans,axiom,
% 0.28/0.46 ! [C_35: pname > $o,A_87: pname > $o,B_62: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_87 @ B_62 )
% 0.28/0.46 => ( ( B_62 = C_35 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ A_87 @ C_35 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_347_ord__le__eq__trans,axiom,
% 0.28/0.46 ! [C_35: hoare_1167836817_state > $o,A_87: hoare_1167836817_state > $o,B_62: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_87 @ B_62 )
% 0.28/0.46 => ( ( B_62 = C_35 )
% 0.28/0.46 => ( ord_le827224136tate_o @ A_87 @ C_35 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_348_xt1_I3_J,axiom,
% 0.28/0.46 ! [C_34: pname > $o,A_86: pname > $o,B_61: pname > $o] :
% 0.28/0.46 ( ( A_86 = B_61 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ C_34 @ B_61 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ C_34 @ A_86 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_349_xt1_I3_J,axiom,
% 0.28/0.46 ! [C_34: hoare_1167836817_state > $o,A_86: hoare_1167836817_state > $o,B_61: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_86 = B_61 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ C_34 @ B_61 )
% 0.28/0.46 => ( ord_le827224136tate_o @ C_34 @ A_86 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_350_ord__eq__le__trans,axiom,
% 0.28/0.46 ! [C_33: pname > $o,A_85: pname > $o,B_60: pname > $o] :
% 0.28/0.46 ( ( A_85 = B_60 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_60 @ C_33 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ A_85 @ C_33 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_351_ord__eq__le__trans,axiom,
% 0.28/0.46 ! [C_33: hoare_1167836817_state > $o,A_85: hoare_1167836817_state > $o,B_60: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( A_85 = B_60 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_60 @ C_33 )
% 0.28/0.46 => ( ord_le827224136tate_o @ A_85 @ C_33 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_352_order__antisym__conv,axiom,
% 0.28/0.46 ! [Y_42: pname > $o,X_77: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ Y_42 @ X_77 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ X_77 @ Y_42 )
% 0.28/0.46 <=> ( X_77 = Y_42 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_353_order__antisym__conv,axiom,
% 0.28/0.46 ! [Y_42: hoare_1167836817_state > $o,X_77: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ Y_42 @ X_77 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ X_77 @ Y_42 )
% 0.28/0.46 <=> ( X_77 = Y_42 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_354_order__eq__refl,axiom,
% 0.28/0.46 ! [X_76: pname > $o,Y_41: pname > $o] :
% 0.28/0.46 ( ( X_76 = Y_41 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ X_76 @ Y_41 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_355_order__eq__refl,axiom,
% 0.28/0.46 ! [X_76: hoare_1167836817_state > $o,Y_41: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( X_76 = Y_41 )
% 0.28/0.46 => ( ord_le827224136tate_o @ X_76 @ Y_41 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_356_order__eq__iff,axiom,
% 0.28/0.46 ! [X_75: pname > $o,Y_40: pname > $o] :
% 0.28/0.46 ( ( X_75 = Y_40 )
% 0.28/0.46 <=> ( ( ord_less_eq_pname_o @ X_75 @ Y_40 )
% 0.28/0.46 & ( ord_less_eq_pname_o @ Y_40 @ X_75 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_357_order__eq__iff,axiom,
% 0.28/0.46 ! [X_75: hoare_1167836817_state > $o,Y_40: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( X_75 = Y_40 )
% 0.28/0.46 <=> ( ( ord_le827224136tate_o @ X_75 @ Y_40 )
% 0.28/0.46 & ( ord_le827224136tate_o @ Y_40 @ X_75 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_358_option_Oinject,axiom,
% 0.28/0.46 ! [A_84: com,A_83: com] :
% 0.28/0.46 ( ( ( some_com @ A_84 )
% 0.28/0.46 = ( some_com @ A_83 ) )
% 0.28/0.46 <=> ( A_84 = A_83 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_359_constant,axiom,
% 0.28/0.46 ! [G_23: hoare_1167836817_state > $o,P_27: state > state > $o,C_32: com,Q_19: state > state > $o,C_31: $o] :
% 0.28/0.46 ( ( C_31
% 0.28/0.46 => ( hoare_123228589_state @ G_23 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_27 @ C_32 @ Q_19 ) @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_23
% 0.28/0.46 @ ( insert2134838167_state
% 0.28/0.46 @ ( hoare_908217195_state
% 0.28/0.46 @ ^ [Z_11: state,S_3: state] : ( (&) @ ( P_27 @ Z_11 @ S_3 ) @ C_31 )
% 0.28/0.46 @ C_32
% 0.28/0.46 @ Q_19 )
% 0.28/0.46 @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_360_Body1,axiom,
% 0.28/0.46 ! [Pn_3: pname,G_22: hoare_1167836817_state > $o,P_26: pname > state > state > $o,Q_18: pname > state > state > $o,Procs_1: pname > $o] :
% 0.28/0.46 ( ( hoare_123228589_state
% 0.28/0.46 @ ( semila1172322802tate_o @ G_22
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_26 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_18 @ P_24 ) )
% 0.28/0.46 @ Procs_1 ) )
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_26 @ P_24 ) @ ( the_com @ ( body @ P_24 ) ) @ ( Q_18 @ P_24 ) )
% 0.28/0.46 @ Procs_1 ) )
% 0.28/0.46 => ( ( member_pname @ Pn_3 @ Procs_1 )
% 0.28/0.46 => ( hoare_123228589_state @ G_22 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_26 @ Pn_3 ) @ ( body_1 @ Pn_3 ) @ ( Q_18 @ Pn_3 ) ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_361_le__bot,axiom,
% 0.28/0.46 ! [A_82: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_82 @ bot_bot_pname_o )
% 0.28/0.46 => ( A_82 = bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_362_le__bot,axiom,
% 0.28/0.46 ! [A_82: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_82 @ bot_bo70021908tate_o )
% 0.28/0.46 => ( A_82 = bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_363_bot__unique,axiom,
% 0.28/0.46 ! [A_81: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_81 @ bot_bot_pname_o )
% 0.28/0.46 <=> ( A_81 = bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_364_bot__unique,axiom,
% 0.28/0.46 ! [A_81: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_81 @ bot_bo70021908tate_o )
% 0.28/0.46 <=> ( A_81 = bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_365_bot__least,axiom,
% 0.28/0.46 ! [A_80: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_80 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_366_bot__least,axiom,
% 0.28/0.46 ! [A_80: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_80 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_367_le__funE,axiom,
% 0.28/0.46 ! [X_74: pname,F_38: pname > $o,G_21: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ F_38 @ G_21 )
% 0.28/0.46 => ( ord_less_eq_o @ ( F_38 @ X_74 ) @ ( G_21 @ X_74 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_368_le__funE,axiom,
% 0.28/0.46 ! [X_74: hoare_1167836817_state,F_38: hoare_1167836817_state > $o,G_21: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ F_38 @ G_21 )
% 0.28/0.46 => ( ord_less_eq_o @ ( F_38 @ X_74 ) @ ( G_21 @ X_74 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_369_le__funD,axiom,
% 0.28/0.46 ! [X_73: pname,F_37: pname > $o,G_20: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ F_37 @ G_20 )
% 0.28/0.46 => ( ord_less_eq_o @ ( F_37 @ X_73 ) @ ( G_20 @ X_73 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_370_le__funD,axiom,
% 0.28/0.46 ! [X_73: hoare_1167836817_state,F_37: hoare_1167836817_state > $o,G_20: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ F_37 @ G_20 )
% 0.28/0.46 => ( ord_less_eq_o @ ( F_37 @ X_73 ) @ ( G_20 @ X_73 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_371_le__fun__def,axiom,
% 0.28/0.46 ! [F_36: pname > $o,G_19: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ F_36 @ G_19 )
% 0.28/0.46 <=> ! [X_5: pname] : ( ord_less_eq_o @ ( F_36 @ X_5 ) @ ( G_19 @ X_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_372_le__fun__def,axiom,
% 0.28/0.46 ! [F_36: hoare_1167836817_state > $o,G_19: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ F_36 @ G_19 )
% 0.28/0.46 <=> ! [X_5: hoare_1167836817_state] : ( ord_less_eq_o @ ( F_36 @ X_5 ) @ ( G_19 @ X_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_373_bot__apply,axiom,
% 0.28/0.46 ! [X_72: pname] :
% 0.28/0.46 ( ( bot_bot_pname_o @ X_72 )
% 0.28/0.46 <=> bot_bot_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_374_bot__apply,axiom,
% 0.28/0.46 ! [X_72: hoare_1167836817_state] :
% 0.28/0.46 ( ( bot_bo70021908tate_o @ X_72 )
% 0.28/0.46 <=> bot_bot_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_375_bot__fun__def,axiom,
% 0.28/0.46 ! [X_5: pname] :
% 0.28/0.46 ( ( bot_bot_pname_o @ X_5 )
% 0.28/0.46 <=> bot_bot_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_376_bot__fun__def,axiom,
% 0.28/0.46 ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( bot_bo70021908tate_o @ X_5 )
% 0.28/0.46 <=> bot_bot_o ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_377_BodyN,axiom,
% 0.28/0.46 ! [P_25: state > state > $o,Pn_2: pname,Q_17: state > state > $o,G_18: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( body_1 @ Pn_2 ) @ Q_17 ) @ G_18 ) @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( the_com @ ( body @ Pn_2 ) ) @ Q_17 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_18 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( body_1 @ Pn_2 ) @ Q_17 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_378_finite__pointwise,axiom,
% 0.28/0.46 ! [P_23: pname > state > state > $o,Q_16: pname > state > state > $o,G_17: hoare_1167836817_state > $o,P_22: pname > state > state > $o,C0_1: pname > com,Q_15: pname > state > state > $o,U_1: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ U_1 )
% 0.28/0.46 => ( ! [P_24: pname] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_17 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_22 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_15 @ P_24 ) ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_17 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_23 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_16 @ P_24 ) ) @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 => ( ( hoare_123228589_state @ G_17
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_22 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_15 @ P_24 ) )
% 0.28/0.46 @ U_1 ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_17
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_23 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_16 @ P_24 ) )
% 0.28/0.46 @ U_1 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_379_escape,axiom,
% 0.28/0.46 ! [G_16: hoare_1167836817_state > $o,C_30: com,Q_14: state > state > $o,P_21: state > state > $o] :
% 0.28/0.46 ( ! [Z_11: state,S_3: state] :
% 0.28/0.46 ( ( P_21 @ Z_11 @ S_3 )
% 0.28/0.46 => ( hoare_123228589_state @ G_16
% 0.28/0.46 @ ( insert2134838167_state
% 0.28/0.46 @ ( hoare_908217195_state
% 0.28/0.46 @ ^ [Za: state,S_4: state] : ( S_4 = S_3 )
% 0.28/0.46 @ C_30
% 0.28/0.46 @ ^ [Z_18: state] : ( Q_14 @ Z_11 ) )
% 0.28/0.46 @ bot_bo70021908tate_o ) ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_16 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ C_30 @ Q_14 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_380_Body__sound__lemma,axiom,
% 0.28/0.46 ! [G_15: hoare_1167836817_state > $o,P_20: pname > state > state > $o,Q_13: pname > state > state > $o,Procs: pname > $o] :
% 0.28/0.46 ( ( hoare_529639851_state
% 0.28/0.46 @ ( semila1172322802tate_o @ G_15
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [Pn: pname] : ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_13 @ Pn ) )
% 0.28/0.46 @ Procs ) )
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [Pn: pname] : ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( the_com @ ( body @ Pn ) ) @ ( Q_13 @ Pn ) )
% 0.28/0.46 @ Procs ) )
% 0.28/0.46 => ( hoare_529639851_state @ G_15
% 0.28/0.46 @ ( image_575578384_state
% 0.28/0.46 @ ^ [Pn: pname] : ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_13 @ Pn ) )
% 0.28/0.46 @ Procs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_381_conseq1,axiom,
% 0.28/0.46 ! [P_19: state > state > $o,G_14: hoare_1167836817_state > $o,P_18: state > state > $o,C_29: com,Q_12: state > state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_18 @ C_29 @ Q_12 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ! [Z_11: state,S_3: state] :
% 0.28/0.46 ( ( P_19 @ Z_11 @ S_3 )
% 0.28/0.46 => ( P_18 @ Z_11 @ S_3 ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_19 @ C_29 @ Q_12 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_382_conseq2,axiom,
% 0.28/0.46 ! [Q_11: state > state > $o,G_13: hoare_1167836817_state > $o,P_17: state > state > $o,C_28: com,Q_10: state > state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_13 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_28 @ Q_10 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ! [Z_11: state,S_3: state] :
% 0.28/0.46 ( ( Q_10 @ Z_11 @ S_3 )
% 0.28/0.46 => ( Q_11 @ Z_11 @ S_3 ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_13 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_28 @ Q_11 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_383_MGF__complete,axiom,
% 0.28/0.46 ! [P: state > state > $o,Q_9: state > state > $o,C_21: com] :
% 0.28/0.46 ( ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ( hoare_529639851_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ P @ C_21 @ Q_9 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ P @ C_21 @ Q_9 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_384_sup1E,axiom,
% 0.28/0.46 ! [A_79: hoare_1167836817_state > $o,B_59: hoare_1167836817_state > $o,X_71: hoare_1167836817_state] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_79 @ B_59 @ X_71 )
% 0.28/0.46 => ( ~ ( A_79 @ X_71 )
% 0.28/0.46 => ( B_59 @ X_71 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_385_sup1CI,axiom,
% 0.28/0.46 ! [A_78: hoare_1167836817_state > $o,B_58: hoare_1167836817_state > $o,X_70: hoare_1167836817_state] :
% 0.28/0.46 ( ( ~ ( B_58 @ X_70 )
% 0.28/0.46 => ( A_78 @ X_70 ) )
% 0.28/0.46 => ( semila1172322802tate_o @ A_78 @ B_58 @ X_70 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_386_hoare__sound,axiom,
% 0.28/0.46 ! [G_12: hoare_1167836817_state > $o,Ts: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_12 @ Ts )
% 0.28/0.46 => ( hoare_529639851_state @ G_12 @ Ts ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_387_bot__empty__eq,axiom,
% 0.28/0.46 ! [X_5: pname] :
% 0.28/0.46 ( ( bot_bot_pname_o @ X_5 )
% 0.28/0.46 <=> ( member_pname @ X_5 @ bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_388_bot__empty__eq,axiom,
% 0.28/0.46 ! [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( bot_bo70021908tate_o @ X_5 )
% 0.28/0.46 <=> ( member2058392318_state @ X_5 @ bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_389_rev__predicate1D,axiom,
% 0.28/0.46 ! [Q_8: pname > $o,P_16: pname > $o,X_69: pname] :
% 0.28/0.46 ( ( P_16 @ X_69 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ P_16 @ Q_8 )
% 0.28/0.46 => ( Q_8 @ X_69 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_390_rev__predicate1D,axiom,
% 0.28/0.46 ! [Q_8: hoare_1167836817_state > $o,P_16: hoare_1167836817_state > $o,X_69: hoare_1167836817_state] :
% 0.28/0.46 ( ( P_16 @ X_69 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ P_16 @ Q_8 )
% 0.28/0.46 => ( Q_8 @ X_69 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_391_predicate1D,axiom,
% 0.28/0.46 ! [X_68: pname,P_15: pname > $o,Q_7: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ P_15 @ Q_7 )
% 0.28/0.46 => ( ( P_15 @ X_68 )
% 0.28/0.46 => ( Q_7 @ X_68 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_392_predicate1D,axiom,
% 0.28/0.46 ! [X_68: hoare_1167836817_state,P_15: hoare_1167836817_state > $o,Q_7: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ P_15 @ Q_7 )
% 0.28/0.46 => ( ( P_15 @ X_68 )
% 0.28/0.46 => ( Q_7 @ X_68 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_393_sup1I2,axiom,
% 0.28/0.46 ! [A_77: hoare_1167836817_state > $o,B_57: hoare_1167836817_state > $o,X_67: hoare_1167836817_state] :
% 0.28/0.46 ( ( B_57 @ X_67 )
% 0.28/0.46 => ( semila1172322802tate_o @ A_77 @ B_57 @ X_67 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_394_sup1I1,axiom,
% 0.28/0.46 ! [B_56: hoare_1167836817_state > $o,A_76: hoare_1167836817_state > $o,X_66: hoare_1167836817_state] :
% 0.28/0.46 ( ( A_76 @ X_66 )
% 0.28/0.46 => ( semila1172322802tate_o @ A_76 @ B_56 @ X_66 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_395_pred__subset__eq,axiom,
% 0.28/0.46 ! [R_3: pname > $o,S_6: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o
% 0.28/0.46 @ ^ [X_5: pname] : ( member_pname @ X_5 @ R_3 )
% 0.28/0.46 @ ^ [X_5: pname] : ( member_pname @ X_5 @ S_6 ) )
% 0.28/0.46 <=> ( ord_less_eq_pname_o @ R_3 @ S_6 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_396_pred__subset__eq,axiom,
% 0.28/0.46 ! [R_3: hoare_1167836817_state > $o,S_6: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( member2058392318_state @ X_5 @ R_3 )
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] : ( member2058392318_state @ X_5 @ S_6 ) )
% 0.28/0.46 <=> ( ord_le827224136tate_o @ R_3 @ S_6 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_397_sup__Un__eq,axiom,
% 0.28/0.46 ! [R_2: pname > $o,S_5: pname > $o,X_5: pname] :
% 0.28/0.46 ( ( semila1780557381name_o
% 0.28/0.46 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ R_2 )
% 0.28/0.46 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ S_5 )
% 0.28/0.46 @ X_5 )
% 0.28/0.46 <=> ( member_pname @ X_5 @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_398_sup__Un__eq,axiom,
% 0.28/0.46 ! [R_2: hoare_1167836817_state > $o,S_5: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( semila1172322802tate_o
% 0.28/0.46 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ R_2 )
% 0.28/0.46 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ S_5 )
% 0.28/0.46 @ X_5 )
% 0.28/0.46 <=> ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ R_2 @ S_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_399_conseq12,axiom,
% 0.28/0.46 ! [Q_6: state > state > $o,P_14: state > state > $o,G_11: hoare_1167836817_state > $o,P_13: state > state > $o,C_27: com,Q_5: state > state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_13 @ C_27 @ Q_5 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ! [Z_11: state,S_3: state] :
% 0.28/0.46 ( ( P_14 @ Z_11 @ S_3 )
% 0.28/0.46 => ! [S_4: state] :
% 0.28/0.46 ( ! [Z_18: state] :
% 0.28/0.46 ( ( P_13 @ Z_18 @ S_3 )
% 0.28/0.46 => ( Q_5 @ Z_18 @ S_4 ) )
% 0.28/0.46 => ( Q_6 @ Z_11 @ S_4 ) ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_14 @ C_27 @ Q_6 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_400_le__funI,axiom,
% 0.28/0.46 ! [F_35: pname > $o,G_10: pname > $o] :
% 0.28/0.46 ( ! [X_5: pname] : ( ord_less_eq_o @ ( F_35 @ X_5 ) @ ( G_10 @ X_5 ) )
% 0.28/0.46 => ( ord_less_eq_pname_o @ F_35 @ G_10 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_401_le__funI,axiom,
% 0.28/0.46 ! [F_35: hoare_1167836817_state > $o,G_10: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ! [X_5: hoare_1167836817_state] : ( ord_less_eq_o @ ( F_35 @ X_5 ) @ ( G_10 @ X_5 ) )
% 0.28/0.46 => ( ord_le827224136tate_o @ F_35 @ G_10 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_402_Option_Oset_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X_65: pname] :
% 0.28/0.46 ( ( set_pname @ ( some_pname @ X_65 ) )
% 0.28/0.46 = ( insert_pname @ X_65 @ bot_bot_pname_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_403_Option_Oset_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X_65: hoare_1167836817_state] :
% 0.28/0.46 ( ( set_Ho2131684873_state @ ( some_H1433514562_state @ X_65 ) )
% 0.28/0.46 = ( insert2134838167_state @ X_65 @ bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_404_Option_Oset_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X_65: com] :
% 0.28/0.46 ( ( set_com @ ( some_com @ X_65 ) )
% 0.28/0.46 = ( insert_com @ X_65 @ bot_bot_com_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_405_elem__set,axiom,
% 0.28/0.46 ! [X_64: pname,Xo: option_pname] :
% 0.28/0.46 ( ( member_pname @ X_64 @ ( set_pname @ Xo ) )
% 0.28/0.46 <=> ( Xo
% 0.28/0.46 = ( some_pname @ X_64 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_406_elem__set,axiom,
% 0.28/0.46 ! [X_64: hoare_1167836817_state,Xo: option1574264306_state] :
% 0.28/0.46 ( ( member2058392318_state @ X_64 @ ( set_Ho2131684873_state @ Xo ) )
% 0.28/0.46 <=> ( Xo
% 0.28/0.46 = ( some_H1433514562_state @ X_64 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_407_elem__set,axiom,
% 0.28/0.46 ! [X_64: com,Xo: option_com] :
% 0.28/0.46 ( ( member_com @ X_64 @ ( set_com @ Xo ) )
% 0.28/0.46 <=> ( Xo
% 0.28/0.46 = ( some_com @ X_64 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_408_ospec,axiom,
% 0.28/0.46 ! [X_63: com,P_12: com > $o,A_75: option_com] :
% 0.28/0.46 ( ! [X_5: com] :
% 0.28/0.46 ( ( member_com @ X_5 @ ( set_com @ A_75 ) )
% 0.28/0.46 => ( P_12 @ X_5 ) )
% 0.28/0.46 => ( ( A_75
% 0.28/0.46 = ( some_com @ X_63 ) )
% 0.28/0.46 => ( P_12 @ X_63 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_409_sup__fun__def,axiom,
% 0.28/0.46 ! [F_34: hoare_1167836817_state > $o,G_9: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
% 0.28/0.46 ( ( semila1172322802tate_o @ F_34 @ G_9 @ X_5 )
% 0.28/0.46 <=> ( semila10642723_sup_o @ ( F_34 @ X_5 ) @ ( G_9 @ X_5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_410_sup__apply,axiom,
% 0.28/0.46 ! [F_33: hoare_1167836817_state > $o,G_8: hoare_1167836817_state > $o,X_62: hoare_1167836817_state] :
% 0.28/0.46 ( ( semila1172322802tate_o @ F_33 @ G_8 @ X_62 )
% 0.28/0.46 <=> ( semila10642723_sup_o @ ( F_33 @ X_62 ) @ ( G_8 @ X_62 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_411_single__stateE,axiom,
% 0.28/0.46 ( hoare_1201148605gleton
% 0.28/0.46 => ! [T_1: state] :
% 0.28/0.46 ~ ! [S_3: state] : ( S_3 = T_1 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_412_state__not__singleton__def,axiom,
% 0.28/0.46 ( hoare_1201148605gleton
% 0.28/0.46 <=> ? [S_3: state,T_1: state] : ( S_3 != T_1 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_413_sup__assoc,axiom,
% 0.28/0.46 ! [X_61: hoare_1167836817_state > $o,Y_39: hoare_1167836817_state > $o,Z_17: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_61 @ Y_39 ) @ Z_17 )
% 0.28/0.46 = ( semila1172322802tate_o @ X_61 @ ( semila1172322802tate_o @ Y_39 @ Z_17 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_414_inf__sup__aci_I6_J,axiom,
% 0.28/0.46 ! [X_60: hoare_1167836817_state > $o,Y_38: hoare_1167836817_state > $o,Z_16: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_60 @ Y_38 ) @ Z_16 )
% 0.28/0.46 = ( semila1172322802tate_o @ X_60 @ ( semila1172322802tate_o @ Y_38 @ Z_16 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_415_sup_Oassoc,axiom,
% 0.28/0.46 ! [A_74: hoare_1167836817_state > $o,B_55: hoare_1167836817_state > $o,C_26: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_74 @ B_55 ) @ C_26 )
% 0.28/0.46 = ( semila1172322802tate_o @ A_74 @ ( semila1172322802tate_o @ B_55 @ C_26 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_416_sup__left__commute,axiom,
% 0.28/0.46 ! [X_59: hoare_1167836817_state > $o,Y_37: hoare_1167836817_state > $o,Z_15: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_59 @ ( semila1172322802tate_o @ Y_37 @ Z_15 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ Y_37 @ ( semila1172322802tate_o @ X_59 @ Z_15 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_417_inf__sup__aci_I7_J,axiom,
% 0.28/0.46 ! [X_58: hoare_1167836817_state > $o,Y_36: hoare_1167836817_state > $o,Z_14: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_58 @ ( semila1172322802tate_o @ Y_36 @ Z_14 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ Y_36 @ ( semila1172322802tate_o @ X_58 @ Z_14 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_418_sup_Oleft__commute,axiom,
% 0.28/0.46 ! [B_54: hoare_1167836817_state > $o,A_73: hoare_1167836817_state > $o,C_25: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ B_54 @ ( semila1172322802tate_o @ A_73 @ C_25 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ A_73 @ ( semila1172322802tate_o @ B_54 @ C_25 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_419_sup__left__idem,axiom,
% 0.28/0.46 ! [X_57: hoare_1167836817_state > $o,Y_35: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_57 @ ( semila1172322802tate_o @ X_57 @ Y_35 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ X_57 @ Y_35 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_420_inf__sup__aci_I8_J,axiom,
% 0.28/0.46 ! [X_56: hoare_1167836817_state > $o,Y_34: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_56 @ ( semila1172322802tate_o @ X_56 @ Y_34 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ X_56 @ Y_34 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_421_sup_Oleft__idem,axiom,
% 0.28/0.46 ! [A_72: hoare_1167836817_state > $o,B_53: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_72 @ ( semila1172322802tate_o @ A_72 @ B_53 ) )
% 0.28/0.46 = ( semila1172322802tate_o @ A_72 @ B_53 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_422_sup__commute,axiom,
% 0.28/0.46 ! [X_55: hoare_1167836817_state > $o,Y_33: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_55 @ Y_33 )
% 0.28/0.46 = ( semila1172322802tate_o @ Y_33 @ X_55 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_423_inf__sup__aci_I5_J,axiom,
% 0.28/0.46 ! [X_54: hoare_1167836817_state > $o,Y_32: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_54 @ Y_32 )
% 0.28/0.46 = ( semila1172322802tate_o @ Y_32 @ X_54 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_424_sup_Ocommute,axiom,
% 0.28/0.46 ! [A_71: hoare_1167836817_state > $o,B_52: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_71 @ B_52 )
% 0.28/0.46 = ( semila1172322802tate_o @ B_52 @ A_71 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_425_sup__idem,axiom,
% 0.28/0.46 ! [X_53: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_53 @ X_53 )
% 0.28/0.46 = X_53 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_426_sup_Oidem,axiom,
% 0.28/0.46 ! [A_70: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ A_70 @ A_70 )
% 0.28/0.46 = A_70 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_427_le__supE,axiom,
% 0.28/0.46 ! [A_69: pname > $o,B_51: pname > $o,X_52: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_69 @ B_51 ) @ X_52 )
% 0.28/0.46 => ~ ( ( ord_less_eq_pname_o @ A_69 @ X_52 )
% 0.28/0.46 => ~ ( ord_less_eq_pname_o @ B_51 @ X_52 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_428_le__supE,axiom,
% 0.28/0.46 ! [A_69: hoare_1167836817_state > $o,B_51: hoare_1167836817_state > $o,X_52: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_69 @ B_51 ) @ X_52 )
% 0.28/0.46 => ~ ( ( ord_le827224136tate_o @ A_69 @ X_52 )
% 0.28/0.46 => ~ ( ord_le827224136tate_o @ B_51 @ X_52 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_429_sup__mono,axiom,
% 0.28/0.46 ! [B_50: pname > $o,D_3: pname > $o,A_68: pname > $o,C_24: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_68 @ C_24 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_50 @ D_3 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_68 @ B_50 ) @ ( semila1780557381name_o @ C_24 @ D_3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_430_sup__mono,axiom,
% 0.28/0.46 ! [B_50: hoare_1167836817_state > $o,D_3: hoare_1167836817_state > $o,A_68: hoare_1167836817_state > $o,C_24: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_68 @ C_24 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_50 @ D_3 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_68 @ B_50 ) @ ( semila1172322802tate_o @ C_24 @ D_3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_431_sup__least,axiom,
% 0.28/0.46 ! [Z_13: pname > $o,Y_31: pname > $o,X_51: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ Y_31 @ X_51 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ Z_13 @ X_51 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ Y_31 @ Z_13 ) @ X_51 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_432_sup__least,axiom,
% 0.28/0.46 ! [Z_13: hoare_1167836817_state > $o,Y_31: hoare_1167836817_state > $o,X_51: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ Y_31 @ X_51 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ Z_13 @ X_51 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ Y_31 @ Z_13 ) @ X_51 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_433_le__supI,axiom,
% 0.28/0.46 ! [B_49: pname > $o,A_67: pname > $o,X_50: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ A_67 @ X_50 )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_49 @ X_50 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_67 @ B_49 ) @ X_50 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_434_le__supI,axiom,
% 0.28/0.46 ! [B_49: hoare_1167836817_state > $o,A_67: hoare_1167836817_state > $o,X_50: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ A_67 @ X_50 )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_49 @ X_50 )
% 0.28/0.46 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_67 @ B_49 ) @ X_50 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_435_sup__absorb1,axiom,
% 0.28/0.46 ! [Y_30: pname > $o,X_49: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ Y_30 @ X_49 )
% 0.28/0.46 => ( ( semila1780557381name_o @ X_49 @ Y_30 )
% 0.28/0.46 = X_49 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_436_sup__absorb1,axiom,
% 0.28/0.46 ! [Y_30: hoare_1167836817_state > $o,X_49: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ Y_30 @ X_49 )
% 0.28/0.46 => ( ( semila1172322802tate_o @ X_49 @ Y_30 )
% 0.28/0.46 = X_49 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_437_sup__absorb2,axiom,
% 0.28/0.46 ! [X_48: pname > $o,Y_29: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ X_48 @ Y_29 )
% 0.28/0.46 => ( ( semila1780557381name_o @ X_48 @ Y_29 )
% 0.28/0.46 = Y_29 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_438_sup__absorb2,axiom,
% 0.28/0.46 ! [X_48: hoare_1167836817_state > $o,Y_29: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ X_48 @ Y_29 )
% 0.28/0.46 => ( ( semila1172322802tate_o @ X_48 @ Y_29 )
% 0.28/0.46 = Y_29 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_439_le__supI2,axiom,
% 0.28/0.46 ! [A_66: pname > $o,X_47: pname > $o,B_48: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ X_47 @ B_48 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ X_47 @ ( semila1780557381name_o @ A_66 @ B_48 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_440_le__supI2,axiom,
% 0.28/0.46 ! [A_66: hoare_1167836817_state > $o,X_47: hoare_1167836817_state > $o,B_48: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ X_47 @ B_48 )
% 0.28/0.46 => ( ord_le827224136tate_o @ X_47 @ ( semila1172322802tate_o @ A_66 @ B_48 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_441_le__supI1,axiom,
% 0.28/0.46 ! [B_47: pname > $o,X_46: pname > $o,A_65: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ X_46 @ A_65 )
% 0.28/0.46 => ( ord_less_eq_pname_o @ X_46 @ ( semila1780557381name_o @ A_65 @ B_47 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_442_le__supI1,axiom,
% 0.28/0.46 ! [B_47: hoare_1167836817_state > $o,X_46: hoare_1167836817_state > $o,A_65: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ X_46 @ A_65 )
% 0.28/0.46 => ( ord_le827224136tate_o @ X_46 @ ( semila1172322802tate_o @ A_65 @ B_47 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_443_le__sup__iff,axiom,
% 0.28/0.46 ! [X_45: pname > $o,Y_28: pname > $o,Z_12: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_45 @ Y_28 ) @ Z_12 )
% 0.28/0.46 <=> ( ( ord_less_eq_pname_o @ X_45 @ Z_12 )
% 0.28/0.46 & ( ord_less_eq_pname_o @ Y_28 @ Z_12 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_444_le__sup__iff,axiom,
% 0.28/0.46 ! [X_45: hoare_1167836817_state > $o,Y_28: hoare_1167836817_state > $o,Z_12: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ X_45 @ Y_28 ) @ Z_12 )
% 0.28/0.46 <=> ( ( ord_le827224136tate_o @ X_45 @ Z_12 )
% 0.28/0.46 & ( ord_le827224136tate_o @ Y_28 @ Z_12 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_445_le__iff__sup,axiom,
% 0.28/0.46 ! [X_44: pname > $o,Y_27: pname > $o] :
% 0.28/0.46 ( ( ord_less_eq_pname_o @ X_44 @ Y_27 )
% 0.28/0.46 <=> ( ( semila1780557381name_o @ X_44 @ Y_27 )
% 0.28/0.46 = Y_27 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_446_le__iff__sup,axiom,
% 0.28/0.46 ! [X_44: hoare_1167836817_state > $o,Y_27: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ord_le827224136tate_o @ X_44 @ Y_27 )
% 0.28/0.46 <=> ( ( semila1172322802tate_o @ X_44 @ Y_27 )
% 0.28/0.46 = Y_27 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_447_sup__ge2,axiom,
% 0.28/0.46 ! [Y_26: pname > $o,X_43: pname > $o] : ( ord_less_eq_pname_o @ Y_26 @ ( semila1780557381name_o @ X_43 @ Y_26 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_448_sup__ge2,axiom,
% 0.28/0.46 ! [Y_26: hoare_1167836817_state > $o,X_43: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ Y_26 @ ( semila1172322802tate_o @ X_43 @ Y_26 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_449_inf__sup__ord_I4_J,axiom,
% 0.28/0.46 ! [Y_25: pname > $o,X_42: pname > $o] : ( ord_less_eq_pname_o @ Y_25 @ ( semila1780557381name_o @ X_42 @ Y_25 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_450_inf__sup__ord_I4_J,axiom,
% 0.28/0.46 ! [Y_25: hoare_1167836817_state > $o,X_42: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ Y_25 @ ( semila1172322802tate_o @ X_42 @ Y_25 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_451_sup__ge1,axiom,
% 0.28/0.46 ! [X_41: pname > $o,Y_24: pname > $o] : ( ord_less_eq_pname_o @ X_41 @ ( semila1780557381name_o @ X_41 @ Y_24 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_452_sup__ge1,axiom,
% 0.28/0.46 ! [X_41: hoare_1167836817_state > $o,Y_24: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_41 @ ( semila1172322802tate_o @ X_41 @ Y_24 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_453_inf__sup__ord_I3_J,axiom,
% 0.28/0.46 ! [X_40: pname > $o,Y_23: pname > $o] : ( ord_less_eq_pname_o @ X_40 @ ( semila1780557381name_o @ X_40 @ Y_23 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_454_inf__sup__ord_I3_J,axiom,
% 0.28/0.46 ! [X_40: hoare_1167836817_state > $o,Y_23: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_40 @ ( semila1172322802tate_o @ X_40 @ Y_23 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_455_sup__eq__bot__iff,axiom,
% 0.28/0.46 ! [X_39: pname > $o,Y_22: pname > $o] :
% 0.28/0.46 ( ( ( semila1780557381name_o @ X_39 @ Y_22 )
% 0.28/0.46 = bot_bot_pname_o )
% 0.28/0.46 <=> ( ( X_39 = bot_bot_pname_o )
% 0.28/0.46 & ( Y_22 = bot_bot_pname_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_456_sup__eq__bot__iff,axiom,
% 0.28/0.46 ! [X_39: hoare_1167836817_state > $o,Y_22: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( ( semila1172322802tate_o @ X_39 @ Y_22 )
% 0.28/0.46 = bot_bo70021908tate_o )
% 0.28/0.46 <=> ( ( X_39 = bot_bo70021908tate_o )
% 0.28/0.46 & ( Y_22 = bot_bo70021908tate_o ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_457_sup__bot__right,axiom,
% 0.28/0.46 ! [X_38: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ X_38 @ bot_bot_pname_o )
% 0.28/0.46 = X_38 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_458_sup__bot__right,axiom,
% 0.28/0.46 ! [X_38: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ X_38 @ bot_bo70021908tate_o )
% 0.28/0.46 = X_38 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_459_sup__bot__left,axiom,
% 0.28/0.46 ! [X_37: pname > $o] :
% 0.28/0.46 ( ( semila1780557381name_o @ bot_bot_pname_o @ X_37 )
% 0.28/0.46 = X_37 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_460_sup__bot__left,axiom,
% 0.28/0.46 ! [X_37: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ X_37 )
% 0.28/0.46 = X_37 ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_461_folding__one__idem_Ounion__idem,axiom,
% 0.28/0.46 ! [B_46: ( pname > $o ) > $o,A_64: ( pname > $o ) > $o,F_32: ( pname > $o ) > ( pname > $o ) > pname > $o,F_31: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.46 ( ( finite697516351name_o @ F_32 @ F_31 )
% 0.28/0.46 => ( ( finite297249702name_o @ A_64 )
% 0.28/0.46 => ( ( A_64 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ( finite297249702name_o @ B_46 )
% 0.28/0.46 => ( ( B_46 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ( F_31 @ ( semila181081674me_o_o @ A_64 @ B_46 ) )
% 0.28/0.46 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_462_folding__one__idem_Ounion__idem,axiom,
% 0.28/0.46 ! [B_46: ( hoare_1167836817_state > $o ) > $o,A_64: ( hoare_1167836817_state > $o ) > $o,F_32: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_31: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite671847800tate_o @ F_32 @ F_31 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ A_64 )
% 0.28/0.46 => ( ( A_64 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ( finite1380128977tate_o @ B_46 )
% 0.28/0.46 => ( ( B_46 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ( F_31 @ ( semila866907787te_o_o @ A_64 @ B_46 ) )
% 0.28/0.46 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_463_folding__one__idem_Ounion__idem,axiom,
% 0.28/0.46 ! [B_46: pname > $o,A_64: pname > $o,F_32: pname > pname > pname,F_31: ( pname > $o ) > pname] :
% 0.28/0.46 ( ( finite89670078_pname @ F_32 @ F_31 )
% 0.28/0.46 => ( ( finite_finite_pname @ A_64 )
% 0.28/0.46 => ( ( A_64 != bot_bot_pname_o )
% 0.28/0.46 => ( ( finite_finite_pname @ B_46 )
% 0.28/0.46 => ( ( B_46 != bot_bot_pname_o )
% 0.28/0.46 => ( ( F_31 @ ( semila1780557381name_o @ A_64 @ B_46 ) )
% 0.28/0.46 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_464_folding__one__idem_Ounion__idem,axiom,
% 0.28/0.46 ! [B_46: hoare_1167836817_state > $o,A_64: hoare_1167836817_state > $o,F_32: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_31: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.46 ( ( finite806517911_state @ F_32 @ F_31 )
% 0.28/0.46 => ( ( finite1084549118_state @ A_64 )
% 0.28/0.46 => ( ( A_64 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ( finite1084549118_state @ B_46 )
% 0.28/0.46 => ( ( B_46 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ( F_31 @ ( semila1172322802tate_o @ A_64 @ B_46 ) )
% 0.28/0.46 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_465_folding__one__idem_Osubset__idem,axiom,
% 0.28/0.46 ! [B_45: ( pname > $o ) > $o,A_63: ( pname > $o ) > $o,F_30: ( pname > $o ) > ( pname > $o ) > pname > $o,F_29: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.46 ( ( finite697516351name_o @ F_30 @ F_29 )
% 0.28/0.46 => ( ( finite297249702name_o @ A_63 )
% 0.28/0.46 => ( ( B_45 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ( ord_le1205211808me_o_o @ B_45 @ A_63 )
% 0.28/0.46 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 0.28/0.46 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_466_folding__one__idem_Osubset__idem,axiom,
% 0.28/0.46 ! [B_45: ( hoare_1167836817_state > $o ) > $o,A_63: ( hoare_1167836817_state > $o ) > $o,F_30: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_29: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite671847800tate_o @ F_30 @ F_29 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ A_63 )
% 0.28/0.46 => ( ( B_45 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ( ord_le741939125te_o_o @ B_45 @ A_63 )
% 0.28/0.46 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 0.28/0.46 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_467_folding__one__idem_Osubset__idem,axiom,
% 0.28/0.46 ! [B_45: pname > $o,A_63: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
% 0.28/0.46 ( ( finite89670078_pname @ F_30 @ F_29 )
% 0.28/0.46 => ( ( finite_finite_pname @ A_63 )
% 0.28/0.46 => ( ( B_45 != bot_bot_pname_o )
% 0.28/0.46 => ( ( ord_less_eq_pname_o @ B_45 @ A_63 )
% 0.28/0.46 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 0.28/0.46 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_468_folding__one__idem_Osubset__idem,axiom,
% 0.28/0.46 ! [B_45: hoare_1167836817_state > $o,A_63: hoare_1167836817_state > $o,F_30: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_29: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.46 ( ( finite806517911_state @ F_30 @ F_29 )
% 0.28/0.46 => ( ( finite1084549118_state @ A_63 )
% 0.28/0.46 => ( ( B_45 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ( ord_le827224136tate_o @ B_45 @ A_63 )
% 0.28/0.46 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 0.28/0.46 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_469_hoare__derivs_OSkip,axiom,
% 0.28/0.46 ! [G_7: hoare_1167836817_state > $o,P_11: state > state > $o] : ( hoare_123228589_state @ G_7 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_11 @ skip @ P_11 ) @ bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_470_folding__one__idem_Oinsert__idem,axiom,
% 0.28/0.46 ! [X_36: pname,A_62: pname > $o,F_28: pname > pname > pname,F_27: ( pname > $o ) > pname] :
% 0.28/0.46 ( ( finite89670078_pname @ F_28 @ F_27 )
% 0.28/0.46 => ( ( finite_finite_pname @ A_62 )
% 0.28/0.46 => ( ( A_62 != bot_bot_pname_o )
% 0.28/0.46 => ( ( F_27 @ ( insert_pname @ X_36 @ A_62 ) )
% 0.28/0.46 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_471_folding__one__idem_Oinsert__idem,axiom,
% 0.28/0.46 ! [X_36: hoare_1167836817_state,A_62: hoare_1167836817_state > $o,F_28: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_27: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.46 ( ( finite806517911_state @ F_28 @ F_27 )
% 0.28/0.46 => ( ( finite1084549118_state @ A_62 )
% 0.28/0.46 => ( ( A_62 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ( F_27 @ ( insert2134838167_state @ X_36 @ A_62 ) )
% 0.28/0.46 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_472_folding__one__idem_Oinsert__idem,axiom,
% 0.28/0.46 ! [X_36: pname > $o,A_62: ( pname > $o ) > $o,F_28: ( pname > $o ) > ( pname > $o ) > pname > $o,F_27: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.46 ( ( finite697516351name_o @ F_28 @ F_27 )
% 0.28/0.46 => ( ( finite297249702name_o @ A_62 )
% 0.28/0.46 => ( ( A_62 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ( F_27 @ ( insert_pname_o @ X_36 @ A_62 ) )
% 0.28/0.46 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_473_folding__one__idem_Oinsert__idem,axiom,
% 0.28/0.46 ! [X_36: hoare_1167836817_state > $o,A_62: ( hoare_1167836817_state > $o ) > $o,F_28: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_27: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite671847800tate_o @ F_28 @ F_27 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ A_62 )
% 0.28/0.46 => ( ( A_62 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ( F_27 @ ( insert999278200tate_o @ X_36 @ A_62 ) )
% 0.28/0.46 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_474_finite__ne__induct,axiom,
% 0.28/0.46 ! [P_10: ( pname > $o ) > $o,F_25: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_25 )
% 0.28/0.46 => ( ( F_25 != bot_bot_pname_o )
% 0.28/0.46 => ( ! [X_5: pname] : ( P_10 @ ( insert_pname @ X_5 @ bot_bot_pname_o ) )
% 0.28/0.46 => ( ! [X_5: pname,F_26: pname > $o] :
% 0.28/0.46 ( ( finite_finite_pname @ F_26 )
% 0.28/0.46 => ( ( F_26 != bot_bot_pname_o )
% 0.28/0.46 => ( ~ ( member_pname @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_10 @ F_26 )
% 0.28/0.46 => ( P_10 @ ( insert_pname @ X_5 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_10 @ F_25 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_475_finite__ne__induct,axiom,
% 0.28/0.46 ! [P_10: ( hoare_1167836817_state > $o ) > $o,F_25: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_25 )
% 0.28/0.46 => ( ( F_25 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state] : ( P_10 @ ( insert2134838167_state @ X_5 @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite1084549118_state @ F_26 )
% 0.28/0.46 => ( ( F_26 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ~ ( member2058392318_state @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_10 @ F_26 )
% 0.28/0.46 => ( P_10 @ ( insert2134838167_state @ X_5 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_10 @ F_25 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_476_finite__ne__induct,axiom,
% 0.28/0.46 ! [P_10: ( ( pname > $o ) > $o ) > $o,F_25: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_25 )
% 0.28/0.46 => ( ( F_25 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ! [X_5: pname > $o] : ( P_10 @ ( insert_pname_o @ X_5 @ bot_bot_pname_o_o ) )
% 0.28/0.46 => ( ! [X_5: pname > $o,F_26: ( pname > $o ) > $o] :
% 0.28/0.46 ( ( finite297249702name_o @ F_26 )
% 0.28/0.46 => ( ( F_26 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ~ ( member_pname_o @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_10 @ F_26 )
% 0.28/0.46 => ( P_10 @ ( insert_pname_o @ X_5 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_10 @ F_25 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_477_finite__ne__induct,axiom,
% 0.28/0.46 ! [P_10: ( ( hoare_1167836817_state > $o ) > $o ) > $o,F_25: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_25 )
% 0.28/0.46 => ( ( F_25 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state > $o] : ( P_10 @ ( insert999278200tate_o @ X_5 @ bot_bo691907561te_o_o ) )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.46 ( ( finite1380128977tate_o @ F_26 )
% 0.28/0.46 => ( ( F_26 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ~ ( member864234961tate_o @ X_5 @ F_26 )
% 0.28/0.46 => ( ( P_10 @ F_26 )
% 0.28/0.46 => ( P_10 @ ( insert999278200tate_o @ X_5 @ F_26 ) ) ) ) ) )
% 0.28/0.46 => ( P_10 @ F_25 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_478_com_Osimps_I19_J,axiom,
% 0.28/0.46 ! [Pname: pname] :
% 0.28/0.46 ( ( body_1 @ Pname )
% 0.28/0.46 != skip ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_479_com_Osimps_I18_J,axiom,
% 0.28/0.46 ! [Pname: pname] :
% 0.28/0.46 ( skip
% 0.28/0.46 != ( body_1 @ Pname ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_480_WT_OSkip,axiom,
% 0.28/0.46 wt @ skip ).
% 0.28/0.46
% 0.28/0.46 thf(fact_481_folding__one__idem_Oin__idem,axiom,
% 0.28/0.46 ! [X_35: pname,A_61: pname > $o,F_24: pname > pname > pname,F_23: ( pname > $o ) > pname] :
% 0.28/0.46 ( ( finite89670078_pname @ F_24 @ F_23 )
% 0.28/0.46 => ( ( finite_finite_pname @ A_61 )
% 0.28/0.46 => ( ( member_pname @ X_35 @ A_61 )
% 0.28/0.46 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 0.28/0.46 = ( F_23 @ A_61 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_482_folding__one__idem_Oin__idem,axiom,
% 0.28/0.46 ! [X_35: hoare_1167836817_state,A_61: hoare_1167836817_state > $o,F_24: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_23: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.46 ( ( finite806517911_state @ F_24 @ F_23 )
% 0.28/0.46 => ( ( finite1084549118_state @ A_61 )
% 0.28/0.46 => ( ( member2058392318_state @ X_35 @ A_61 )
% 0.28/0.46 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 0.28/0.46 = ( F_23 @ A_61 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_483_folding__one__idem_Oin__idem,axiom,
% 0.28/0.46 ! [X_35: pname > $o,A_61: ( pname > $o ) > $o,F_24: ( pname > $o ) > ( pname > $o ) > pname > $o,F_23: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.46 ( ( finite697516351name_o @ F_24 @ F_23 )
% 0.28/0.46 => ( ( finite297249702name_o @ A_61 )
% 0.28/0.46 => ( ( member_pname_o @ X_35 @ A_61 )
% 0.28/0.46 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 0.28/0.46 = ( F_23 @ A_61 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_484_folding__one__idem_Oin__idem,axiom,
% 0.28/0.46 ! [X_35: hoare_1167836817_state > $o,A_61: ( hoare_1167836817_state > $o ) > $o,F_24: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_23: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite671847800tate_o @ F_24 @ F_23 )
% 0.28/0.46 => ( ( finite1380128977tate_o @ A_61 )
% 0.28/0.46 => ( ( member864234961tate_o @ X_35 @ A_61 )
% 0.28/0.46 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 0.28/0.46 = ( F_23 @ A_61 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_485_folding__one__idem_Ohom__commute,axiom,
% 0.28/0.46 ! [N_1: ( pname > $o ) > $o,H: ( pname > $o ) > pname > $o,F_22: ( pname > $o ) > ( pname > $o ) > pname > $o,F_21: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.46 ( ( finite697516351name_o @ F_22 @ F_21 )
% 0.28/0.46 => ( ! [X_5: pname > $o,Y_2: pname > $o] :
% 0.28/0.46 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 0.28/0.46 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 0.28/0.46 => ( ( finite297249702name_o @ N_1 )
% 0.28/0.46 => ( ( N_1 != bot_bot_pname_o_o )
% 0.28/0.46 => ( ( H @ ( F_21 @ N_1 ) )
% 0.28/0.46 = ( F_21 @ ( image_1085733413name_o @ H @ N_1 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_486_folding__one__idem_Ohom__commute,axiom,
% 0.28/0.46 ! [N_1: ( hoare_1167836817_state > $o ) > $o,H: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_22: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_21: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( finite671847800tate_o @ F_22 @ F_21 )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 0.28/0.46 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 0.28/0.46 => ( ( finite1380128977tate_o @ N_1 )
% 0.28/0.46 => ( ( N_1 != bot_bo691907561te_o_o )
% 0.28/0.46 => ( ( H @ ( F_21 @ N_1 ) )
% 0.28/0.46 = ( F_21 @ ( image_1488525317tate_o @ H @ N_1 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_487_folding__one__idem_Ohom__commute,axiom,
% 0.28/0.46 ! [N_1: pname > $o,H: pname > pname,F_22: pname > pname > pname,F_21: ( pname > $o ) > pname] :
% 0.28/0.46 ( ( finite89670078_pname @ F_22 @ F_21 )
% 0.28/0.46 => ( ! [X_5: pname,Y_2: pname] :
% 0.28/0.46 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 0.28/0.46 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 0.28/0.46 => ( ( finite_finite_pname @ N_1 )
% 0.28/0.46 => ( ( N_1 != bot_bot_pname_o )
% 0.28/0.46 => ( ( H @ ( F_21 @ N_1 ) )
% 0.28/0.46 = ( F_21 @ ( image_pname_pname @ H @ N_1 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_488_folding__one__idem_Ohom__commute,axiom,
% 0.28/0.46 ! [N_1: hoare_1167836817_state > $o,H: hoare_1167836817_state > hoare_1167836817_state,F_22: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_21: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.46 ( ( finite806517911_state @ F_22 @ F_21 )
% 0.28/0.46 => ( ! [X_5: hoare_1167836817_state,Y_2: hoare_1167836817_state] :
% 0.28/0.46 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 0.28/0.46 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 0.28/0.46 => ( ( finite1084549118_state @ N_1 )
% 0.28/0.46 => ( ( N_1 != bot_bo70021908tate_o )
% 0.28/0.46 => ( ( H @ ( F_21 @ N_1 ) )
% 0.28/0.46 = ( F_21 @ ( image_31595733_state @ H @ N_1 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_489_LoopF,axiom,
% 0.28/0.46 ! [G_6: hoare_1167836817_state > $o,P_9: state > state > $o,B_44: state > $o,C_23: com] :
% 0.28/0.46 ( hoare_123228589_state @ G_6
% 0.28/0.46 @ ( insert2134838167_state
% 0.28/0.46 @ ( hoare_908217195_state
% 0.28/0.46 @ ^ [Z_11: state,S_3: state] : ( (&) @ ( P_9 @ Z_11 @ S_3 ) @ ( (~) @ ( B_44 @ S_3 ) ) )
% 0.28/0.46 @ ( while @ B_44 @ C_23 )
% 0.28/0.46 @ P_9 )
% 0.28/0.46 @ bot_bo70021908tate_o ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_490_Comp,axiom,
% 0.28/0.46 ! [D_2: com,R_1: state > state > $o,G_5: hoare_1167836817_state > $o,P_8: state > state > $o,C_22: com,Q_4: state > state > $o] :
% 0.28/0.46 ( ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_8 @ C_22 @ Q_4 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ Q_4 @ D_2 @ R_1 ) @ bot_bo70021908tate_o ) )
% 0.28/0.46 => ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_8 @ ( semi @ C_22 @ D_2 ) @ R_1 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_491_the__elem__def,axiom,
% 0.28/0.46 ! [X_34: pname > $o] :
% 0.28/0.46 ( ( the_elem_pname @ X_34 )
% 0.28/0.46 = ( the_pname
% 0.28/0.46 @ ^ [X_5: pname] :
% 0.28/0.46 ( X_34
% 0.28/0.46 = ( insert_pname @ X_5 @ bot_bot_pname_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_492_the__elem__def,axiom,
% 0.28/0.46 ! [X_34: hoare_1167836817_state > $o] :
% 0.28/0.46 ( ( the_el323660082_state @ X_34 )
% 0.28/0.46 = ( the_Ho310147232_state
% 0.28/0.46 @ ^ [X_5: hoare_1167836817_state] :
% 0.28/0.46 ( X_34
% 0.28/0.46 = ( insert2134838167_state @ X_5 @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_493_WTs__elim__cases_I6_J,axiom,
% 0.28/0.46 ! [B_42: state > $o,C_21: com] :
% 0.28/0.46 ( ( wt @ ( while @ B_42 @ C_21 ) )
% 0.28/0.46 => ( wt @ C_21 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_494_WTs__elim__cases_I4_J,axiom,
% 0.28/0.46 ! [C1: com,C2: com] :
% 0.28/0.46 ( ( wt @ ( semi @ C1 @ C2 ) )
% 0.28/0.46 => ~ ( ( wt @ C1 )
% 0.28/0.46 => ~ ( wt @ C2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_495_com_Osimps_I46_J,axiom,
% 0.28/0.46 ! [Com1_1: com,Com2_1: com,Fun: state > $o,Com_1: com] :
% 0.28/0.46 ( ( semi @ Com1_1 @ Com2_1 )
% 0.28/0.46 != ( while @ Fun @ Com_1 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_496_com_Osimps_I47_J,axiom,
% 0.28/0.46 ! [Fun: state > $o,Com_1: com,Com1_1: com,Com2_1: com] :
% 0.28/0.46 ( ( while @ Fun @ Com_1 )
% 0.28/0.46 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_497_com_Osimps_I3_J,axiom,
% 0.28/0.46 ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
% 0.28/0.46 ( ( ( semi @ Com1_1 @ Com2_1 )
% 0.28/0.46 = ( semi @ Com1 @ Com2 ) )
% 0.28/0.46 <=> ( ( Com1_1 = Com1 )
% 0.28/0.46 & ( Com2_1 = Com2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(fact_498_com_Osimps_I5_J,axiom,
% 0.28/0.46 ! [Fun_1: state > $o,Com_2: com,Fun: state > $o,Com_1: com] :
% 0.28/0.46 ( ( ( while @ Fun_1 @ Com_2 )
% 0.28/0.46 = ( while @ Fun @ Com_1 ) )
% 0.28/0.47 <=> ( ( Fun_1 = Fun )
% 0.28/0.47 & ( Com_2 = Com_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_499_com_Osimps_I59_J,axiom,
% 0.28/0.47 ! [Pname: pname,Fun_1: state > $o,Com_2: com] :
% 0.28/0.47 ( ( body_1 @ Pname )
% 0.28/0.47 != ( while @ Fun_1 @ Com_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_500_com_Osimps_I58_J,axiom,
% 0.28/0.47 ! [Fun_1: state > $o,Com_2: com,Pname: pname] :
% 0.28/0.47 ( ( while @ Fun_1 @ Com_2 )
% 0.28/0.47 != ( body_1 @ Pname ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_501_While,axiom,
% 0.28/0.47 ! [B_42: state > $o,C_21: com] :
% 0.28/0.47 ( ( wt @ C_21 )
% 0.28/0.47 => ( wt @ ( while @ B_42 @ C_21 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_502_com_Osimps_I16_J,axiom,
% 0.28/0.47 ! [Fun: state > $o,Com_1: com] :
% 0.28/0.47 ( skip
% 0.28/0.47 != ( while @ Fun @ Com_1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_503_com_Osimps_I17_J,axiom,
% 0.28/0.47 ! [Fun: state > $o,Com_1: com] :
% 0.28/0.47 ( ( while @ Fun @ Com_1 )
% 0.28/0.47 != skip ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_504_com_Osimps_I49_J,axiom,
% 0.28/0.47 ! [Pname: pname,Com1_1: com,Com2_1: com] :
% 0.28/0.47 ( ( body_1 @ Pname )
% 0.28/0.47 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_505_com_Osimps_I48_J,axiom,
% 0.28/0.47 ! [Com1_1: com,Com2_1: com,Pname: pname] :
% 0.28/0.47 ( ( semi @ Com1_1 @ Com2_1 )
% 0.28/0.47 != ( body_1 @ Pname ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_506_WT_OSemi,axiom,
% 0.28/0.47 ! [C1: com,C0: com] :
% 0.28/0.47 ( ( wt @ C0 )
% 0.28/0.47 => ( ( wt @ C1 )
% 0.28/0.47 => ( wt @ ( semi @ C0 @ C1 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_507_com_Osimps_I12_J,axiom,
% 0.28/0.47 ! [Com1: com,Com2: com] :
% 0.28/0.47 ( skip
% 0.28/0.47 != ( semi @ Com1 @ Com2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_508_com_Osimps_I13_J,axiom,
% 0.28/0.47 ! [Com1: com,Com2: com] :
% 0.28/0.47 ( ( semi @ Com1 @ Com2 )
% 0.28/0.47 != skip ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_509_folding__one_Oinsert,axiom,
% 0.28/0.47 ! [X_33: pname,A_60: pname > $o,F_20: pname > pname > pname,F_19: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_20 @ F_19 )
% 0.28/0.47 => ( ( finite_finite_pname @ A_60 )
% 0.28/0.47 => ( ~ ( member_pname @ X_33 @ A_60 )
% 0.28/0.47 => ( ( A_60 != bot_bot_pname_o )
% 0.28/0.47 => ( ( F_19 @ ( insert_pname @ X_33 @ A_60 ) )
% 0.28/0.47 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_510_folding__one_Oinsert,axiom,
% 0.28/0.47 ! [X_33: hoare_1167836817_state,A_60: hoare_1167836817_state > $o,F_20: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_19: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_20 @ F_19 )
% 0.28/0.47 => ( ( finite1084549118_state @ A_60 )
% 0.28/0.47 => ( ~ ( member2058392318_state @ X_33 @ A_60 )
% 0.28/0.47 => ( ( A_60 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F_19 @ ( insert2134838167_state @ X_33 @ A_60 ) )
% 0.28/0.47 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_511_folding__one_Oinsert,axiom,
% 0.28/0.47 ! [X_33: pname > $o,A_60: ( pname > $o ) > $o,F_20: ( pname > $o ) > ( pname > $o ) > pname > $o,F_19: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.47 ( ( finite349908348name_o @ F_20 @ F_19 )
% 0.28/0.47 => ( ( finite297249702name_o @ A_60 )
% 0.28/0.47 => ( ~ ( member_pname_o @ X_33 @ A_60 )
% 0.28/0.47 => ( ( A_60 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F_19 @ ( insert_pname_o @ X_33 @ A_60 ) )
% 0.28/0.47 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_512_folding__one_Oinsert,axiom,
% 0.28/0.47 ! [X_33: hoare_1167836817_state > $o,A_60: ( hoare_1167836817_state > $o ) > $o,F_20: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_19: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite979047547tate_o @ F_20 @ F_19 )
% 0.28/0.47 => ( ( finite1380128977tate_o @ A_60 )
% 0.28/0.47 => ( ~ ( member864234961tate_o @ X_33 @ A_60 )
% 0.28/0.47 => ( ( A_60 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F_19 @ ( insert999278200tate_o @ X_33 @ A_60 ) )
% 0.28/0.47 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_513_folding__one_Osingleton,axiom,
% 0.28/0.47 ! [X_32: pname,F_18: pname > pname > pname,F_17: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_18 @ F_17 )
% 0.28/0.47 => ( ( F_17 @ ( insert_pname @ X_32 @ bot_bot_pname_o ) )
% 0.28/0.47 = X_32 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_514_folding__one_Osingleton,axiom,
% 0.28/0.47 ! [X_32: hoare_1167836817_state,F_18: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_17: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_18 @ F_17 )
% 0.28/0.47 => ( ( F_17 @ ( insert2134838167_state @ X_32 @ bot_bo70021908tate_o ) )
% 0.28/0.47 = X_32 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_515_folding__one_Oclosed,axiom,
% 0.28/0.47 ! [A_59: pname > $o,F_16: pname > pname > pname,F_15: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_16 @ F_15 )
% 0.28/0.47 => ( ( finite_finite_pname @ A_59 )
% 0.28/0.47 => ( ( A_59 != bot_bot_pname_o )
% 0.28/0.47 => ( ! [X_5: pname,Y_2: pname] : ( member_pname @ ( F_16 @ X_5 @ Y_2 ) @ ( insert_pname @ X_5 @ ( insert_pname @ Y_2 @ bot_bot_pname_o ) ) )
% 0.28/0.47 => ( member_pname @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_516_folding__one_Oclosed,axiom,
% 0.28/0.47 ! [A_59: hoare_1167836817_state > $o,F_16: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_15: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_16 @ F_15 )
% 0.28/0.47 => ( ( finite1084549118_state @ A_59 )
% 0.28/0.47 => ( ( A_59 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ! [X_5: hoare_1167836817_state,Y_2: hoare_1167836817_state] : ( member2058392318_state @ ( F_16 @ X_5 @ Y_2 ) @ ( insert2134838167_state @ X_5 @ ( insert2134838167_state @ Y_2 @ bot_bo70021908tate_o ) ) )
% 0.28/0.47 => ( member2058392318_state @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_517_folding__one_Oclosed,axiom,
% 0.28/0.47 ! [A_59: ( pname > $o ) > $o,F_16: ( pname > $o ) > ( pname > $o ) > pname > $o,F_15: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.47 ( ( finite349908348name_o @ F_16 @ F_15 )
% 0.28/0.47 => ( ( finite297249702name_o @ A_59 )
% 0.28/0.47 => ( ( A_59 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ! [X_5: pname > $o,Y_2: pname > $o] : ( member_pname_o @ ( F_16 @ X_5 @ Y_2 ) @ ( insert_pname_o @ X_5 @ ( insert_pname_o @ Y_2 @ bot_bot_pname_o_o ) ) )
% 0.28/0.47 => ( member_pname_o @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_518_folding__one_Oclosed,axiom,
% 0.28/0.47 ! [A_59: ( hoare_1167836817_state > $o ) > $o,F_16: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_15: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite979047547tate_o @ F_16 @ F_15 )
% 0.28/0.47 => ( ( finite1380128977tate_o @ A_59 )
% 0.28/0.47 => ( ( A_59 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] : ( member864234961tate_o @ ( F_16 @ X_5 @ Y_2 ) @ ( insert999278200tate_o @ X_5 @ ( insert999278200tate_o @ Y_2 @ bot_bo691907561te_o_o ) ) )
% 0.28/0.47 => ( member864234961tate_o @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_519_triple_Oexhaust,axiom,
% 0.28/0.47 ! [Y_21: hoare_1167836817_state] :
% 0.28/0.47 ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
% 0.28/0.47 ( Y_21
% 0.28/0.47 != ( hoare_908217195_state @ Fun1 @ Com @ Fun2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_520_image__cong,axiom,
% 0.28/0.47 ! [F_14: pname > hoare_1167836817_state,G_4: pname > hoare_1167836817_state,M: pname > $o,N: pname > $o] :
% 0.28/0.47 ( ( M = N )
% 0.28/0.47 => ( ! [X_5: pname] :
% 0.28/0.47 ( ( member_pname @ X_5 @ N )
% 0.28/0.47 => ( ( F_14 @ X_5 )
% 0.28/0.47 = ( G_4 @ X_5 ) ) )
% 0.28/0.47 => ( ( image_575578384_state @ F_14 @ M )
% 0.28/0.47 = ( image_575578384_state @ G_4 @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_521_Collect__mono,axiom,
% 0.28/0.47 ! [Q_3: hoare_1167836817_state > $o,P_7: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.47 ( ( P_7 @ X_5 )
% 0.28/0.47 => ( Q_3 @ X_5 ) )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( collec1027672124_state @ P_7 ) @ ( collec1027672124_state @ Q_3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_522_Collect__mono,axiom,
% 0.28/0.47 ! [Q_3: pname > $o,P_7: pname > $o] :
% 0.28/0.47 ( ! [X_5: pname] :
% 0.28/0.47 ( ( P_7 @ X_5 )
% 0.28/0.47 => ( Q_3 @ X_5 ) )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( collect_pname @ P_7 ) @ ( collect_pname @ Q_3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_523_Collect__mono,axiom,
% 0.28/0.47 ! [Q_3: ( pname > $o ) > $o,P_7: ( pname > $o ) > $o] :
% 0.28/0.47 ( ! [X_5: pname > $o] :
% 0.28/0.47 ( ( P_7 @ X_5 )
% 0.28/0.47 => ( Q_3 @ X_5 ) )
% 0.28/0.47 => ( ord_le1205211808me_o_o @ ( collect_pname_o @ P_7 ) @ ( collect_pname_o @ Q_3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_524_Collect__mono,axiom,
% 0.28/0.47 ! [Q_3: ( hoare_1167836817_state > $o ) > $o,P_7: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ! [X_5: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( P_7 @ X_5 )
% 0.28/0.47 => ( Q_3 @ X_5 ) )
% 0.28/0.47 => ( ord_le741939125te_o_o @ ( collec269976083tate_o @ P_7 ) @ ( collec269976083tate_o @ Q_3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_525_predicate1I,axiom,
% 0.28/0.47 ! [Q_2: pname > $o,P_6: pname > $o] :
% 0.28/0.47 ( ! [X_5: pname] :
% 0.28/0.47 ( ( P_6 @ X_5 )
% 0.28/0.47 => ( Q_2 @ X_5 ) )
% 0.28/0.47 => ( ord_less_eq_pname_o @ P_6 @ Q_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_526_predicate1I,axiom,
% 0.28/0.47 ! [Q_2: hoare_1167836817_state > $o,P_6: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.47 ( ( P_6 @ X_5 )
% 0.28/0.47 => ( Q_2 @ X_5 ) )
% 0.28/0.47 => ( ord_le827224136tate_o @ P_6 @ Q_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_527_mk__disjoint__insert,axiom,
% 0.28/0.47 ! [A_58: pname,A_57: pname > $o] :
% 0.28/0.47 ( ( member_pname @ A_58 @ A_57 )
% 0.28/0.47 => ? [B_43: pname > $o] :
% 0.28/0.47 ( ( A_57
% 0.28/0.47 = ( insert_pname @ A_58 @ B_43 ) )
% 0.28/0.47 & ~ ( member_pname @ A_58 @ B_43 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_528_mk__disjoint__insert,axiom,
% 0.28/0.47 ! [A_58: hoare_1167836817_state,A_57: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ A_58 @ A_57 )
% 0.28/0.47 => ? [B_43: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( A_57
% 0.28/0.47 = ( insert2134838167_state @ A_58 @ B_43 ) )
% 0.28/0.47 & ~ ( member2058392318_state @ A_58 @ B_43 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_529_Set_Oset__insert,axiom,
% 0.28/0.47 ! [X_31: pname,A_56: pname > $o] :
% 0.28/0.47 ( ( member_pname @ X_31 @ A_56 )
% 0.28/0.47 => ~ ! [B_43: pname > $o] :
% 0.28/0.47 ( ( A_56
% 0.28/0.47 = ( insert_pname @ X_31 @ B_43 ) )
% 0.28/0.47 => ( member_pname @ X_31 @ B_43 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_530_Set_Oset__insert,axiom,
% 0.28/0.47 ! [X_31: hoare_1167836817_state,A_56: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ X_31 @ A_56 )
% 0.28/0.47 => ~ ! [B_43: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( A_56
% 0.28/0.47 = ( insert2134838167_state @ X_31 @ B_43 ) )
% 0.28/0.47 => ( member2058392318_state @ X_31 @ B_43 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_531_equals0I,axiom,
% 0.28/0.47 ! [A_55: pname > $o] :
% 0.28/0.47 ( ! [Y_2: pname] :
% 0.28/0.47 ~ ( member_pname @ Y_2 @ A_55 )
% 0.28/0.47 => ( A_55 = bot_bot_pname_o ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_532_equals0I,axiom,
% 0.28/0.47 ! [A_55: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ! [Y_2: hoare_1167836817_state] :
% 0.28/0.47 ~ ( member2058392318_state @ Y_2 @ A_55 )
% 0.28/0.47 => ( A_55 = bot_bo70021908tate_o ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_533_MGT__alternD,axiom,
% 0.28/0.47 ! [G_3: hoare_1167836817_state > $o,C_21: com] :
% 0.28/0.47 ( hoare_1201148605gleton
% 0.28/0.47 => ( ( hoare_123228589_state @ G_3
% 0.28/0.47 @ ( insert2134838167_state
% 0.28/0.47 @ ( hoare_908217195_state
% 0.28/0.47 @ ^ [Z_11: state,S0_1: state] :
% 0.28/0.47 ! [S1: state] : ( (=>) @ ( evalc @ C_21 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 0.28/0.47 @ C_21
% 0.28/0.47 @ fequal_state )
% 0.28/0.47 @ bot_bo70021908tate_o ) )
% 0.28/0.47 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_534_MGT__alternI,axiom,
% 0.28/0.47 ! [G_3: hoare_1167836817_state > $o,C_21: com] :
% 0.28/0.47 ( ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) )
% 0.28/0.47 => ( hoare_123228589_state @ G_3
% 0.28/0.47 @ ( insert2134838167_state
% 0.28/0.47 @ ( hoare_908217195_state
% 0.28/0.47 @ ^ [Z_11: state,S0_1: state] :
% 0.28/0.47 ! [S1: state] : ( (=>) @ ( evalc @ C_21 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 0.28/0.47 @ C_21
% 0.28/0.47 @ fequal_state )
% 0.28/0.47 @ bot_bo70021908tate_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_535_MGT__def,axiom,
% 0.28/0.47 ! [C_21: com] :
% 0.28/0.47 ( ( hoare_Mirabelle_MGT @ C_21 )
% 0.28/0.47 = ( hoare_908217195_state @ fequal_state @ C_21 @ ( evalc @ C_21 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_536_evalc_OBody,axiom,
% 0.28/0.47 ! [Pn_1: pname,S0: state,S1_1: state] :
% 0.28/0.47 ( ( evalc @ ( the_com @ ( body @ Pn_1 ) ) @ S0 @ S1_1 )
% 0.28/0.47 => ( evalc @ ( body_1 @ Pn_1 ) @ S0 @ S1_1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_537_evalc__elim__cases_I6_J,axiom,
% 0.28/0.47 ! [P: pname,S_2: state,S1_1: state] :
% 0.28/0.47 ( ( evalc @ ( body_1 @ P ) @ S_2 @ S1_1 )
% 0.28/0.47 => ( evalc @ ( the_com @ ( body @ P ) ) @ S_2 @ S1_1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_538_evalc__elim__cases_I1_J,axiom,
% 0.28/0.47 ! [S_2: state,T: state] :
% 0.28/0.47 ( ( evalc @ skip @ S_2 @ T )
% 0.28/0.47 => ( T = S_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_539_evalc_OWhileFalse,axiom,
% 0.28/0.47 ! [C_21: com,B_42: state > $o,S_2: state] :
% 0.28/0.47 ( ~ ( B_42 @ S_2 )
% 0.28/0.47 => ( evalc @ ( while @ B_42 @ C_21 ) @ S_2 @ S_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_540_evalc_OWhileTrue,axiom,
% 0.28/0.47 ! [S2: state,C_21: com,S1_1: state,B_42: state > $o,S0: state] :
% 0.28/0.47 ( ( B_42 @ S0 )
% 0.28/0.47 => ( ( evalc @ C_21 @ S0 @ S1_1 )
% 0.28/0.47 => ( ( evalc @ ( while @ B_42 @ C_21 ) @ S1_1 @ S2 )
% 0.28/0.47 => ( evalc @ ( while @ B_42 @ C_21 ) @ S0 @ S2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_541_evalc_OSemi,axiom,
% 0.28/0.47 ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
% 0.28/0.47 ( ( evalc @ C0 @ S0 @ S1_1 )
% 0.28/0.47 => ( ( evalc @ C1 @ S1_1 @ S2 )
% 0.28/0.47 => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_542_evalc_OSkip,axiom,
% 0.28/0.47 ! [S_2: state] : ( evalc @ skip @ S_2 @ S_2 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_543_com__det,axiom,
% 0.28/0.47 ! [U: state,C_21: com,S_2: state,T: state] :
% 0.28/0.47 ( ( evalc @ C_21 @ S_2 @ T )
% 0.28/0.47 => ( ( evalc @ C_21 @ S_2 @ U )
% 0.28/0.47 => ( U = T ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_544_evalc__elim__cases_I4_J,axiom,
% 0.28/0.47 ! [C1: com,C2: com,S_2: state,T: state] :
% 0.28/0.47 ( ( evalc @ ( semi @ C1 @ C2 ) @ S_2 @ T )
% 0.28/0.47 => ~ ! [S1: state] :
% 0.28/0.47 ( ( evalc @ C1 @ S_2 @ S1 )
% 0.28/0.47 => ~ ( evalc @ C2 @ S1 @ T ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_545_evalc__WHILE__case,axiom,
% 0.28/0.47 ! [B_42: state > $o,C_21: com,S_2: state,T: state] :
% 0.28/0.47 ( ( evalc @ ( while @ B_42 @ C_21 ) @ S_2 @ T )
% 0.28/0.47 => ( ( ( T = S_2 )
% 0.28/0.47 => ( B_42 @ S_2 ) )
% 0.28/0.47 => ~ ( ( B_42 @ S_2 )
% 0.28/0.47 => ! [S1: state] :
% 0.28/0.47 ( ( evalc @ C_21 @ S_2 @ S1 )
% 0.28/0.47 => ~ ( evalc @ ( while @ B_42 @ C_21 ) @ S1 @ T ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_546_xt1_I15_J,axiom,
% 0.28/0.47 ! [C_20: pname > $o,A_54: pname > $o,F_13: ( pname > $o ) > pname > $o,B_41: pname > $o] :
% 0.28/0.47 ( ( A_54
% 0.28/0.47 = ( F_13 @ B_41 ) )
% 0.28/0.47 => ( ( ord_less_eq_pname_o @ C_20 @ B_41 )
% 0.28/0.47 => ( ! [X_5: pname > $o,Y_2: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ Y_2 @ X_5 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( F_13 @ Y_2 ) @ ( F_13 @ X_5 ) ) )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( F_13 @ C_20 ) @ A_54 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_547_xt1_I15_J,axiom,
% 0.28/0.47 ! [C_20: hoare_1167836817_state > $o,A_54: hoare_1167836817_state > $o,F_13: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B_41: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( A_54
% 0.28/0.47 = ( F_13 @ B_41 ) )
% 0.28/0.47 => ( ( ord_le827224136tate_o @ C_20 @ B_41 )
% 0.28/0.47 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ Y_2 @ X_5 )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( F_13 @ Y_2 ) @ ( F_13 @ X_5 ) ) )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( F_13 @ C_20 ) @ A_54 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_548_xt1_I16_J,axiom,
% 0.28/0.47 ! [F_12: ( pname > $o ) > pname > $o,C_19: pname > $o,B_40: pname > $o,A_53: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ B_40 @ A_53 )
% 0.28/0.47 => ( ( ( F_12 @ B_40 )
% 0.28/0.47 = C_19 )
% 0.28/0.47 => ( ! [X_5: pname > $o,Y_2: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ Y_2 @ X_5 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( F_12 @ Y_2 ) @ ( F_12 @ X_5 ) ) )
% 0.28/0.47 => ( ord_less_eq_pname_o @ C_19 @ ( F_12 @ A_53 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_549_xt1_I16_J,axiom,
% 0.28/0.47 ! [F_12: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,C_19: hoare_1167836817_state > $o,B_40: hoare_1167836817_state > $o,A_53: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ B_40 @ A_53 )
% 0.28/0.47 => ( ( ( F_12 @ B_40 )
% 0.28/0.47 = C_19 )
% 0.28/0.47 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ Y_2 @ X_5 )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( F_12 @ Y_2 ) @ ( F_12 @ X_5 ) ) )
% 0.28/0.47 => ( ord_le827224136tate_o @ C_19 @ ( F_12 @ A_53 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_550_folding__one_Ounion__inter,axiom,
% 0.28/0.47 ! [B_39: ( pname > $o ) > $o,A_52: ( pname > $o ) > $o,F_11: ( pname > $o ) > ( pname > $o ) > pname > $o,F_10: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.47 ( ( finite349908348name_o @ F_11 @ F_10 )
% 0.28/0.47 => ( ( finite297249702name_o @ A_52 )
% 0.28/0.47 => ( ( finite297249702name_o @ B_39 )
% 0.28/0.47 => ( ( ( semila2013987940me_o_o @ A_52 @ B_39 )
% 0.28/0.47 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F_11 @ ( F_10 @ ( semila181081674me_o_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila2013987940me_o_o @ A_52 @ B_39 ) ) )
% 0.28/0.47 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_551_folding__one_Ounion__inter,axiom,
% 0.28/0.47 ! [B_39: ( hoare_1167836817_state > $o ) > $o,A_52: ( hoare_1167836817_state > $o ) > $o,F_11: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_10: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite979047547tate_o @ F_11 @ F_10 )
% 0.28/0.47 => ( ( finite1380128977tate_o @ A_52 )
% 0.28/0.47 => ( ( finite1380128977tate_o @ B_39 )
% 0.28/0.47 => ( ( ( semila1758709489te_o_o @ A_52 @ B_39 )
% 0.28/0.47 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F_11 @ ( F_10 @ ( semila866907787te_o_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila1758709489te_o_o @ A_52 @ B_39 ) ) )
% 0.28/0.47 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_552_folding__one_Ounion__inter,axiom,
% 0.28/0.47 ! [B_39: pname > $o,A_52: pname > $o,F_11: pname > pname > pname,F_10: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_11 @ F_10 )
% 0.28/0.47 => ( ( finite_finite_pname @ A_52 )
% 0.28/0.47 => ( ( finite_finite_pname @ B_39 )
% 0.28/0.47 => ( ( ( semila1673364395name_o @ A_52 @ B_39 )
% 0.28/0.47 != bot_bot_pname_o )
% 0.28/0.47 => ( ( F_11 @ ( F_10 @ ( semila1780557381name_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila1673364395name_o @ A_52 @ B_39 ) ) )
% 0.28/0.47 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_553_folding__one_Ounion__inter,axiom,
% 0.28/0.47 ! [B_39: hoare_1167836817_state > $o,A_52: hoare_1167836817_state > $o,F_11: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_10: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_11 @ F_10 )
% 0.28/0.47 => ( ( finite1084549118_state @ A_52 )
% 0.28/0.47 => ( ( finite1084549118_state @ B_39 )
% 0.28/0.47 => ( ( ( semila179895820tate_o @ A_52 @ B_39 )
% 0.28/0.47 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F_11 @ ( F_10 @ ( semila1172322802tate_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila179895820tate_o @ A_52 @ B_39 ) ) )
% 0.28/0.47 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_554_folding__one_Ounion__disjoint,axiom,
% 0.28/0.47 ! [B_38: ( pname > $o ) > $o,A_51: ( pname > $o ) > $o,F_9: ( pname > $o ) > ( pname > $o ) > pname > $o,F_8: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.47 ( ( finite349908348name_o @ F_9 @ F_8 )
% 0.28/0.47 => ( ( finite297249702name_o @ A_51 )
% 0.28/0.47 => ( ( A_51 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ( finite297249702name_o @ B_38 )
% 0.28/0.47 => ( ( B_38 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ( ( semila2013987940me_o_o @ A_51 @ B_38 )
% 0.28/0.47 = bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F_8 @ ( semila181081674me_o_o @ A_51 @ B_38 ) )
% 0.28/0.47 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_555_folding__one_Ounion__disjoint,axiom,
% 0.28/0.47 ! [B_38: ( hoare_1167836817_state > $o ) > $o,A_51: ( hoare_1167836817_state > $o ) > $o,F_9: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_8: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite979047547tate_o @ F_9 @ F_8 )
% 0.28/0.47 => ( ( finite1380128977tate_o @ A_51 )
% 0.28/0.47 => ( ( A_51 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( finite1380128977tate_o @ B_38 )
% 0.28/0.47 => ( ( B_38 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( ( semila1758709489te_o_o @ A_51 @ B_38 )
% 0.28/0.47 = bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F_8 @ ( semila866907787te_o_o @ A_51 @ B_38 ) )
% 0.28/0.47 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_556_folding__one_Ounion__disjoint,axiom,
% 0.28/0.47 ! [B_38: pname > $o,A_51: pname > $o,F_9: pname > pname > pname,F_8: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_9 @ F_8 )
% 0.28/0.47 => ( ( finite_finite_pname @ A_51 )
% 0.28/0.47 => ( ( A_51 != bot_bot_pname_o )
% 0.28/0.47 => ( ( finite_finite_pname @ B_38 )
% 0.28/0.47 => ( ( B_38 != bot_bot_pname_o )
% 0.28/0.47 => ( ( ( semila1673364395name_o @ A_51 @ B_38 )
% 0.28/0.47 = bot_bot_pname_o )
% 0.28/0.47 => ( ( F_8 @ ( semila1780557381name_o @ A_51 @ B_38 ) )
% 0.28/0.47 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_557_folding__one_Ounion__disjoint,axiom,
% 0.28/0.47 ! [B_38: hoare_1167836817_state > $o,A_51: hoare_1167836817_state > $o,F_9: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_8: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_9 @ F_8 )
% 0.28/0.47 => ( ( finite1084549118_state @ A_51 )
% 0.28/0.47 => ( ( A_51 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ( finite1084549118_state @ B_38 )
% 0.28/0.47 => ( ( B_38 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ( ( semila179895820tate_o @ A_51 @ B_38 )
% 0.28/0.47 = bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F_8 @ ( semila1172322802tate_o @ A_51 @ B_38 ) )
% 0.28/0.47 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_558_IntI,axiom,
% 0.28/0.47 ! [B_37: pname > $o,C_18: pname,A_50: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C_18 @ A_50 )
% 0.28/0.47 => ( ( member_pname @ C_18 @ B_37 )
% 0.28/0.47 => ( member_pname @ C_18 @ ( semila1673364395name_o @ A_50 @ B_37 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_559_IntI,axiom,
% 0.28/0.47 ! [B_37: hoare_1167836817_state > $o,C_18: hoare_1167836817_state,A_50: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C_18 @ A_50 )
% 0.28/0.47 => ( ( member2058392318_state @ C_18 @ B_37 )
% 0.28/0.47 => ( member2058392318_state @ C_18 @ ( semila179895820tate_o @ A_50 @ B_37 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_560_IntE,axiom,
% 0.28/0.47 ! [C_17: pname,A_49: pname > $o,B_36: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C_17 @ ( semila1673364395name_o @ A_49 @ B_36 ) )
% 0.28/0.47 => ~ ( ( member_pname @ C_17 @ A_49 )
% 0.28/0.47 => ~ ( member_pname @ C_17 @ B_36 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_561_IntE,axiom,
% 0.28/0.47 ! [C_17: hoare_1167836817_state,A_49: hoare_1167836817_state > $o,B_36: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C_17 @ ( semila179895820tate_o @ A_49 @ B_36 ) )
% 0.28/0.47 => ~ ( ( member2058392318_state @ C_17 @ A_49 )
% 0.28/0.47 => ~ ( member2058392318_state @ C_17 @ B_36 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_562_finite__Int,axiom,
% 0.28/0.47 ! [G_2: ( pname > $o ) > $o,F_7: ( pname > $o ) > $o] :
% 0.28/0.47 ( ( ( finite297249702name_o @ F_7 )
% 0.28/0.47 | ( finite297249702name_o @ G_2 ) )
% 0.28/0.47 => ( finite297249702name_o @ ( semila2013987940me_o_o @ F_7 @ G_2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_563_finite__Int,axiom,
% 0.28/0.47 ! [G_2: ( hoare_1167836817_state > $o ) > $o,F_7: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ( ( finite1380128977tate_o @ F_7 )
% 0.28/0.47 | ( finite1380128977tate_o @ G_2 ) )
% 0.28/0.47 => ( finite1380128977tate_o @ ( semila1758709489te_o_o @ F_7 @ G_2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_564_finite__Int,axiom,
% 0.28/0.47 ! [G_2: pname > $o,F_7: pname > $o] :
% 0.28/0.47 ( ( ( finite_finite_pname @ F_7 )
% 0.28/0.47 | ( finite_finite_pname @ G_2 ) )
% 0.28/0.47 => ( finite_finite_pname @ ( semila1673364395name_o @ F_7 @ G_2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_565_finite__Int,axiom,
% 0.28/0.47 ! [G_2: hoare_1167836817_state > $o,F_7: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ( finite1084549118_state @ F_7 )
% 0.28/0.47 | ( finite1084549118_state @ G_2 ) )
% 0.28/0.47 => ( finite1084549118_state @ ( semila179895820tate_o @ F_7 @ G_2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_566_disjoint__iff__not__equal,axiom,
% 0.28/0.47 ! [A_48: pname > $o,B_35: pname > $o] :
% 0.28/0.47 ( ( ( semila1673364395name_o @ A_48 @ B_35 )
% 0.28/0.47 = bot_bot_pname_o )
% 0.28/0.47 <=> ! [X_5: pname] :
% 0.28/0.47 ( ( member_pname @ X_5 @ A_48 )
% 0.28/0.47 => ! [Xa: pname] :
% 0.28/0.47 ( ( member_pname @ Xa @ B_35 )
% 0.28/0.47 => ( X_5 != Xa ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_567_disjoint__iff__not__equal,axiom,
% 0.28/0.47 ! [A_48: hoare_1167836817_state > $o,B_35: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ( semila179895820tate_o @ A_48 @ B_35 )
% 0.28/0.47 = bot_bo70021908tate_o )
% 0.28/0.47 <=> ! [X_5: hoare_1167836817_state] :
% 0.28/0.47 ( ( member2058392318_state @ X_5 @ A_48 )
% 0.28/0.47 => ! [Xa: hoare_1167836817_state] :
% 0.28/0.47 ( ( member2058392318_state @ Xa @ B_35 )
% 0.28/0.47 => ( X_5 != Xa ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_568_Int__empty__right,axiom,
% 0.28/0.47 ! [A_47: pname > $o] :
% 0.28/0.47 ( ( semila1673364395name_o @ A_47 @ bot_bot_pname_o )
% 0.28/0.47 = bot_bot_pname_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_569_Int__empty__right,axiom,
% 0.28/0.47 ! [A_47: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ A_47 @ bot_bo70021908tate_o )
% 0.28/0.47 = bot_bo70021908tate_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_570_Int__empty__left,axiom,
% 0.28/0.47 ! [B_34: pname > $o] :
% 0.28/0.47 ( ( semila1673364395name_o @ bot_bot_pname_o @ B_34 )
% 0.28/0.47 = bot_bot_pname_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_571_Int__empty__left,axiom,
% 0.28/0.47 ! [B_34: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ bot_bo70021908tate_o @ B_34 )
% 0.28/0.47 = bot_bo70021908tate_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_572_Int__def,axiom,
% 0.28/0.47 ! [A_46: pname > $o,B_33: pname > $o] :
% 0.28/0.47 ( ( semila1673364395name_o @ A_46 @ B_33 )
% 0.28/0.47 = ( collect_pname
% 0.28/0.47 @ ^ [X_5: pname] : ( (&) @ ( member_pname @ X_5 @ A_46 ) @ ( member_pname @ X_5 @ B_33 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_573_Int__def,axiom,
% 0.28/0.47 ! [A_46: hoare_1167836817_state > $o,B_33: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ A_46 @ B_33 )
% 0.28/0.47 = ( collec1027672124_state
% 0.28/0.47 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( member2058392318_state @ X_5 @ A_46 ) @ ( member2058392318_state @ X_5 @ B_33 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_574_Int__def,axiom,
% 0.28/0.47 ! [A_46: ( pname > $o ) > $o,B_33: ( pname > $o ) > $o] :
% 0.28/0.47 ( ( semila2013987940me_o_o @ A_46 @ B_33 )
% 0.28/0.47 = ( collect_pname_o
% 0.28/0.47 @ ^ [X_5: pname > $o] : ( (&) @ ( member_pname_o @ X_5 @ A_46 ) @ ( member_pname_o @ X_5 @ B_33 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_575_Int__def,axiom,
% 0.28/0.47 ! [A_46: ( hoare_1167836817_state > $o ) > $o,B_33: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ( semila1758709489te_o_o @ A_46 @ B_33 )
% 0.28/0.47 = ( collec269976083tate_o
% 0.28/0.47 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( member864234961tate_o @ X_5 @ A_46 ) @ ( member864234961tate_o @ X_5 @ B_33 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_576_Int__iff,axiom,
% 0.28/0.47 ! [C_16: pname,A_45: pname > $o,B_32: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C_16 @ ( semila1673364395name_o @ A_45 @ B_32 ) )
% 0.28/0.47 <=> ( ( member_pname @ C_16 @ A_45 )
% 0.28/0.47 & ( member_pname @ C_16 @ B_32 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_577_Int__iff,axiom,
% 0.28/0.47 ! [C_16: hoare_1167836817_state,A_45: hoare_1167836817_state > $o,B_32: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C_16 @ ( semila179895820tate_o @ A_45 @ B_32 ) )
% 0.28/0.47 <=> ( ( member2058392318_state @ C_16 @ A_45 )
% 0.28/0.47 & ( member2058392318_state @ C_16 @ B_32 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_578_IntD1,axiom,
% 0.28/0.47 ! [C_15: pname,A_44: pname > $o,B_31: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C_15 @ ( semila1673364395name_o @ A_44 @ B_31 ) )
% 0.28/0.47 => ( member_pname @ C_15 @ A_44 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_579_IntD1,axiom,
% 0.28/0.47 ! [C_15: hoare_1167836817_state,A_44: hoare_1167836817_state > $o,B_31: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C_15 @ ( semila179895820tate_o @ A_44 @ B_31 ) )
% 0.28/0.47 => ( member2058392318_state @ C_15 @ A_44 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_580_IntD2,axiom,
% 0.28/0.47 ! [C_14: pname,A_43: pname > $o,B_30: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C_14 @ ( semila1673364395name_o @ A_43 @ B_30 ) )
% 0.28/0.47 => ( member_pname @ C_14 @ B_30 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_581_IntD2,axiom,
% 0.28/0.47 ! [C_14: hoare_1167836817_state,A_43: hoare_1167836817_state > $o,B_30: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C_14 @ ( semila179895820tate_o @ A_43 @ B_30 ) )
% 0.28/0.47 => ( member2058392318_state @ C_14 @ B_30 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_582_Collect__conj__eq,axiom,
% 0.28/0.47 ! [P_5: hoare_1167836817_state > $o,Q_1: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( collec1027672124_state
% 0.28/0.47 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 0.28/0.47 = ( semila179895820tate_o @ ( collec1027672124_state @ P_5 ) @ ( collec1027672124_state @ Q_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_583_Collect__conj__eq,axiom,
% 0.28/0.47 ! [P_5: pname > $o,Q_1: pname > $o] :
% 0.28/0.47 ( ( collect_pname
% 0.28/0.47 @ ^ [X_5: pname] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 0.28/0.47 = ( semila1673364395name_o @ ( collect_pname @ P_5 ) @ ( collect_pname @ Q_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_584_Collect__conj__eq,axiom,
% 0.28/0.47 ! [P_5: ( pname > $o ) > $o,Q_1: ( pname > $o ) > $o] :
% 0.28/0.47 ( ( collect_pname_o
% 0.28/0.47 @ ^ [X_5: pname > $o] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 0.28/0.47 = ( semila2013987940me_o_o @ ( collect_pname_o @ P_5 ) @ ( collect_pname_o @ Q_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_585_Collect__conj__eq,axiom,
% 0.28/0.47 ! [P_5: ( hoare_1167836817_state > $o ) > $o,Q_1: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ( collec269976083tate_o
% 0.28/0.47 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 0.28/0.47 = ( semila1758709489te_o_o @ ( collec269976083tate_o @ P_5 ) @ ( collec269976083tate_o @ Q_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_586_Int__Collect,axiom,
% 0.28/0.47 ! [X_30: pname,A_42: pname > $o,P_4: pname > $o] :
% 0.28/0.47 ( ( member_pname @ X_30 @ ( semila1673364395name_o @ A_42 @ ( collect_pname @ P_4 ) ) )
% 0.28/0.47 <=> ( ( member_pname @ X_30 @ A_42 )
% 0.28/0.47 & ( P_4 @ X_30 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_587_Int__Collect,axiom,
% 0.28/0.47 ! [X_30: hoare_1167836817_state,A_42: hoare_1167836817_state > $o,P_4: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ X_30 @ ( semila179895820tate_o @ A_42 @ ( collec1027672124_state @ P_4 ) ) )
% 0.28/0.47 <=> ( ( member2058392318_state @ X_30 @ A_42 )
% 0.28/0.47 & ( P_4 @ X_30 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_588_Int__Collect,axiom,
% 0.28/0.47 ! [X_30: pname > $o,A_42: ( pname > $o ) > $o,P_4: ( pname > $o ) > $o] :
% 0.28/0.47 ( ( member_pname_o @ X_30 @ ( semila2013987940me_o_o @ A_42 @ ( collect_pname_o @ P_4 ) ) )
% 0.28/0.47 <=> ( ( member_pname_o @ X_30 @ A_42 )
% 0.28/0.47 & ( P_4 @ X_30 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_589_Int__Collect,axiom,
% 0.28/0.47 ! [X_30: hoare_1167836817_state > $o,A_42: ( hoare_1167836817_state > $o ) > $o,P_4: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ( member864234961tate_o @ X_30 @ ( semila1758709489te_o_o @ A_42 @ ( collec269976083tate_o @ P_4 ) ) )
% 0.28/0.47 <=> ( ( member864234961tate_o @ X_30 @ A_42 )
% 0.28/0.47 & ( P_4 @ X_30 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_590_inf__Int__eq,axiom,
% 0.28/0.47 ! [R: pname > $o,S_1: pname > $o,X_5: pname] :
% 0.28/0.47 ( ( semila1673364395name_o
% 0.28/0.47 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ R )
% 0.28/0.47 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ S_1 )
% 0.28/0.47 @ X_5 )
% 0.28/0.47 <=> ( member_pname @ X_5 @ ( semila1673364395name_o @ R @ S_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_591_inf__Int__eq,axiom,
% 0.28/0.47 ! [R: hoare_1167836817_state > $o,S_1: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
% 0.28/0.47 ( ( semila179895820tate_o
% 0.28/0.47 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ R )
% 0.28/0.47 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ S_1 )
% 0.28/0.47 @ X_5 )
% 0.28/0.47 <=> ( member2058392318_state @ X_5 @ ( semila179895820tate_o @ R @ S_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_592_Un__Int__crazy,axiom,
% 0.28/0.47 ! [A_41: hoare_1167836817_state > $o,B_29: hoare_1167836817_state > $o,C_13: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A_41 @ B_29 ) @ ( semila179895820tate_o @ B_29 @ C_13 ) ) @ ( semila179895820tate_o @ C_13 @ A_41 ) )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A_41 @ B_29 ) @ ( semila1172322802tate_o @ B_29 @ C_13 ) ) @ ( semila1172322802tate_o @ C_13 @ A_41 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_593_Un__Int__distrib2,axiom,
% 0.28/0.47 ! [B_28: hoare_1167836817_state > $o,C_12: hoare_1167836817_state > $o,A_40: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ ( semila179895820tate_o @ B_28 @ C_12 ) @ A_40 )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila1172322802tate_o @ B_28 @ A_40 ) @ ( semila1172322802tate_o @ C_12 @ A_40 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_594_Int__Un__distrib2,axiom,
% 0.28/0.47 ! [B_27: hoare_1167836817_state > $o,C_11: hoare_1167836817_state > $o,A_39: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ ( semila1172322802tate_o @ B_27 @ C_11 ) @ A_39 )
% 0.28/0.47 = ( semila1172322802tate_o @ ( semila179895820tate_o @ B_27 @ A_39 ) @ ( semila179895820tate_o @ C_11 @ A_39 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_595_Un__Int__distrib,axiom,
% 0.28/0.47 ! [A_38: hoare_1167836817_state > $o,B_26: hoare_1167836817_state > $o,C_10: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ A_38 @ ( semila179895820tate_o @ B_26 @ C_10 ) )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila1172322802tate_o @ A_38 @ B_26 ) @ ( semila1172322802tate_o @ A_38 @ C_10 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_596_Int__Un__distrib,axiom,
% 0.28/0.47 ! [A_37: hoare_1167836817_state > $o,B_25: hoare_1167836817_state > $o,C_9: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ A_37 @ ( semila1172322802tate_o @ B_25 @ C_9 ) )
% 0.28/0.47 = ( semila1172322802tate_o @ ( semila179895820tate_o @ A_37 @ B_25 ) @ ( semila179895820tate_o @ A_37 @ C_9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_597_Int__mono,axiom,
% 0.28/0.47 ! [B_24: pname > $o,D_1: pname > $o,A_36: pname > $o,C_8: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ A_36 @ C_8 )
% 0.28/0.47 => ( ( ord_less_eq_pname_o @ B_24 @ D_1 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_36 @ B_24 ) @ ( semila1673364395name_o @ C_8 @ D_1 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_598_Int__mono,axiom,
% 0.28/0.47 ! [B_24: hoare_1167836817_state > $o,D_1: hoare_1167836817_state > $o,A_36: hoare_1167836817_state > $o,C_8: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ A_36 @ C_8 )
% 0.28/0.47 => ( ( ord_le827224136tate_o @ B_24 @ D_1 )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_36 @ B_24 ) @ ( semila179895820tate_o @ C_8 @ D_1 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_599_Int__greatest,axiom,
% 0.28/0.47 ! [B_23: pname > $o,C_7: pname > $o,A_35: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ C_7 @ A_35 )
% 0.28/0.47 => ( ( ord_less_eq_pname_o @ C_7 @ B_23 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ C_7 @ ( semila1673364395name_o @ A_35 @ B_23 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_600_Int__greatest,axiom,
% 0.28/0.47 ! [B_23: hoare_1167836817_state > $o,C_7: hoare_1167836817_state > $o,A_35: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ C_7 @ A_35 )
% 0.28/0.47 => ( ( ord_le827224136tate_o @ C_7 @ B_23 )
% 0.28/0.47 => ( ord_le827224136tate_o @ C_7 @ ( semila179895820tate_o @ A_35 @ B_23 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_601_Int__absorb1,axiom,
% 0.28/0.47 ! [B_22: pname > $o,A_34: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ B_22 @ A_34 )
% 0.28/0.47 => ( ( semila1673364395name_o @ A_34 @ B_22 )
% 0.28/0.47 = B_22 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_602_Int__absorb1,axiom,
% 0.28/0.47 ! [B_22: hoare_1167836817_state > $o,A_34: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ B_22 @ A_34 )
% 0.28/0.47 => ( ( semila179895820tate_o @ A_34 @ B_22 )
% 0.28/0.47 = B_22 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_603_Int__absorb2,axiom,
% 0.28/0.47 ! [A_33: pname > $o,B_21: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ A_33 @ B_21 )
% 0.28/0.47 => ( ( semila1673364395name_o @ A_33 @ B_21 )
% 0.28/0.47 = A_33 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_604_Int__absorb2,axiom,
% 0.28/0.47 ! [A_33: hoare_1167836817_state > $o,B_21: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ A_33 @ B_21 )
% 0.28/0.47 => ( ( semila179895820tate_o @ A_33 @ B_21 )
% 0.28/0.47 = A_33 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_605_Int__lower2,axiom,
% 0.28/0.47 ! [A_32: pname > $o,B_20: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_32 @ B_20 ) @ B_20 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_606_Int__lower2,axiom,
% 0.28/0.47 ! [A_32: hoare_1167836817_state > $o,B_20: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_32 @ B_20 ) @ B_20 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_607_Int__lower1,axiom,
% 0.28/0.47 ! [A_31: pname > $o,B_19: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_31 @ B_19 ) @ A_31 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_608_Int__lower1,axiom,
% 0.28/0.47 ! [A_31: hoare_1167836817_state > $o,B_19: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_31 @ B_19 ) @ A_31 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_609_Int__insert__left__if1,axiom,
% 0.28/0.47 ! [B_18: pname > $o,A_30: pname,C_6: pname > $o] :
% 0.28/0.47 ( ( member_pname @ A_30 @ C_6 )
% 0.28/0.47 => ( ( semila1673364395name_o @ ( insert_pname @ A_30 @ B_18 ) @ C_6 )
% 0.28/0.47 = ( insert_pname @ A_30 @ ( semila1673364395name_o @ B_18 @ C_6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_610_Int__insert__left__if1,axiom,
% 0.28/0.47 ! [B_18: hoare_1167836817_state > $o,A_30: hoare_1167836817_state,C_6: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ A_30 @ C_6 )
% 0.28/0.47 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_30 @ B_18 ) @ C_6 )
% 0.28/0.47 = ( insert2134838167_state @ A_30 @ ( semila179895820tate_o @ B_18 @ C_6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_611_Int__insert__right__if1,axiom,
% 0.28/0.47 ! [B_17: pname > $o,A_29: pname,A_28: pname > $o] :
% 0.28/0.47 ( ( member_pname @ A_29 @ A_28 )
% 0.28/0.47 => ( ( semila1673364395name_o @ A_28 @ ( insert_pname @ A_29 @ B_17 ) )
% 0.28/0.47 = ( insert_pname @ A_29 @ ( semila1673364395name_o @ A_28 @ B_17 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_612_Int__insert__right__if1,axiom,
% 0.28/0.47 ! [B_17: hoare_1167836817_state > $o,A_29: hoare_1167836817_state,A_28: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ A_29 @ A_28 )
% 0.28/0.47 => ( ( semila179895820tate_o @ A_28 @ ( insert2134838167_state @ A_29 @ B_17 ) )
% 0.28/0.47 = ( insert2134838167_state @ A_29 @ ( semila179895820tate_o @ A_28 @ B_17 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_613_Int__insert__left__if0,axiom,
% 0.28/0.47 ! [B_16: pname > $o,A_27: pname,C_5: pname > $o] :
% 0.28/0.47 ( ~ ( member_pname @ A_27 @ C_5 )
% 0.28/0.47 => ( ( semila1673364395name_o @ ( insert_pname @ A_27 @ B_16 ) @ C_5 )
% 0.28/0.47 = ( semila1673364395name_o @ B_16 @ C_5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_614_Int__insert__left__if0,axiom,
% 0.28/0.47 ! [B_16: hoare_1167836817_state > $o,A_27: hoare_1167836817_state,C_5: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ~ ( member2058392318_state @ A_27 @ C_5 )
% 0.28/0.47 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_27 @ B_16 ) @ C_5 )
% 0.28/0.47 = ( semila179895820tate_o @ B_16 @ C_5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_615_Int__insert__right__if0,axiom,
% 0.28/0.47 ! [B_15: pname > $o,A_26: pname,A_25: pname > $o] :
% 0.28/0.47 ( ~ ( member_pname @ A_26 @ A_25 )
% 0.28/0.47 => ( ( semila1673364395name_o @ A_25 @ ( insert_pname @ A_26 @ B_15 ) )
% 0.28/0.47 = ( semila1673364395name_o @ A_25 @ B_15 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_616_Int__insert__right__if0,axiom,
% 0.28/0.47 ! [B_15: hoare_1167836817_state > $o,A_26: hoare_1167836817_state,A_25: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ~ ( member2058392318_state @ A_26 @ A_25 )
% 0.28/0.47 => ( ( semila179895820tate_o @ A_25 @ ( insert2134838167_state @ A_26 @ B_15 ) )
% 0.28/0.47 = ( semila179895820tate_o @ A_25 @ B_15 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_617_insert__inter__insert,axiom,
% 0.28/0.47 ! [A_24: pname,A_23: pname > $o,B_14: pname > $o] :
% 0.28/0.47 ( ( semila1673364395name_o @ ( insert_pname @ A_24 @ A_23 ) @ ( insert_pname @ A_24 @ B_14 ) )
% 0.28/0.47 = ( insert_pname @ A_24 @ ( semila1673364395name_o @ A_23 @ B_14 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_618_insert__inter__insert,axiom,
% 0.28/0.47 ! [A_24: hoare_1167836817_state,A_23: hoare_1167836817_state > $o,B_14: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ ( insert2134838167_state @ A_24 @ A_23 ) @ ( insert2134838167_state @ A_24 @ B_14 ) )
% 0.28/0.47 = ( insert2134838167_state @ A_24 @ ( semila179895820tate_o @ A_23 @ B_14 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_619_Int__insert__left,axiom,
% 0.28/0.47 ! [B_13: pname > $o,A_22: pname,C_4: pname > $o] :
% 0.28/0.47 ( ( ( member_pname @ A_22 @ C_4 )
% 0.28/0.47 => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_13 ) @ C_4 )
% 0.28/0.47 = ( insert_pname @ A_22 @ ( semila1673364395name_o @ B_13 @ C_4 ) ) ) )
% 0.28/0.47 & ( ~ ( member_pname @ A_22 @ C_4 )
% 0.28/0.47 => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_13 ) @ C_4 )
% 0.28/0.47 = ( semila1673364395name_o @ B_13 @ C_4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_620_Int__insert__left,axiom,
% 0.28/0.47 ! [B_13: hoare_1167836817_state > $o,A_22: hoare_1167836817_state,C_4: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ( member2058392318_state @ A_22 @ C_4 )
% 0.28/0.47 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_13 ) @ C_4 )
% 0.28/0.47 = ( insert2134838167_state @ A_22 @ ( semila179895820tate_o @ B_13 @ C_4 ) ) ) )
% 0.28/0.47 & ( ~ ( member2058392318_state @ A_22 @ C_4 )
% 0.28/0.47 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_13 ) @ C_4 )
% 0.28/0.47 = ( semila179895820tate_o @ B_13 @ C_4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_621_Int__insert__right,axiom,
% 0.28/0.47 ! [B_12: pname > $o,A_21: pname,A_20: pname > $o] :
% 0.28/0.47 ( ( ( member_pname @ A_21 @ A_20 )
% 0.28/0.47 => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_12 ) )
% 0.28/0.47 = ( insert_pname @ A_21 @ ( semila1673364395name_o @ A_20 @ B_12 ) ) ) )
% 0.28/0.47 & ( ~ ( member_pname @ A_21 @ A_20 )
% 0.28/0.47 => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_12 ) )
% 0.28/0.47 = ( semila1673364395name_o @ A_20 @ B_12 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_622_Int__insert__right,axiom,
% 0.28/0.47 ! [B_12: hoare_1167836817_state > $o,A_21: hoare_1167836817_state,A_20: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ( member2058392318_state @ A_21 @ A_20 )
% 0.28/0.47 => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_12 ) )
% 0.28/0.47 = ( insert2134838167_state @ A_21 @ ( semila179895820tate_o @ A_20 @ B_12 ) ) ) )
% 0.28/0.47 & ( ~ ( member2058392318_state @ A_21 @ A_20 )
% 0.28/0.47 => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_12 ) )
% 0.28/0.47 = ( semila179895820tate_o @ A_20 @ B_12 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_623_inf__sup__ord_I1_J,axiom,
% 0.28/0.47 ! [X_29: pname > $o,Y_20: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_29 @ Y_20 ) @ X_29 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_624_inf__sup__ord_I1_J,axiom,
% 0.28/0.47 ! [X_29: hoare_1167836817_state > $o,Y_20: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_29 @ Y_20 ) @ X_29 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_625_inf__le1,axiom,
% 0.28/0.47 ! [X_28: pname > $o,Y_19: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_28 @ Y_19 ) @ X_28 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_626_inf__le1,axiom,
% 0.28/0.47 ! [X_28: hoare_1167836817_state > $o,Y_19: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_28 @ Y_19 ) @ X_28 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_627_inf__sup__ord_I2_J,axiom,
% 0.28/0.47 ! [X_27: pname > $o,Y_18: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_27 @ Y_18 ) @ Y_18 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_628_inf__sup__ord_I2_J,axiom,
% 0.28/0.47 ! [X_27: hoare_1167836817_state > $o,Y_18: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_27 @ Y_18 ) @ Y_18 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_629_inf__le2,axiom,
% 0.28/0.47 ! [X_26: pname > $o,Y_17: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_26 @ Y_17 ) @ Y_17 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_630_inf__le2,axiom,
% 0.28/0.47 ! [X_26: hoare_1167836817_state > $o,Y_17: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_26 @ Y_17 ) @ Y_17 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_631_le__iff__inf,axiom,
% 0.28/0.47 ! [X_25: pname > $o,Y_16: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ X_25 @ Y_16 )
% 0.28/0.47 <=> ( ( semila1673364395name_o @ X_25 @ Y_16 )
% 0.28/0.47 = X_25 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_632_le__iff__inf,axiom,
% 0.28/0.47 ! [X_25: hoare_1167836817_state > $o,Y_16: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ X_25 @ Y_16 )
% 0.28/0.47 <=> ( ( semila179895820tate_o @ X_25 @ Y_16 )
% 0.28/0.47 = X_25 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_633_le__inf__iff,axiom,
% 0.28/0.47 ! [X_24: pname > $o,Y_15: pname > $o,Z_10: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ X_24 @ ( semila1673364395name_o @ Y_15 @ Z_10 ) )
% 0.28/0.47 <=> ( ( ord_less_eq_pname_o @ X_24 @ Y_15 )
% 0.28/0.47 & ( ord_less_eq_pname_o @ X_24 @ Z_10 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_634_le__inf__iff,axiom,
% 0.28/0.47 ! [X_24: hoare_1167836817_state > $o,Y_15: hoare_1167836817_state > $o,Z_10: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ X_24 @ ( semila179895820tate_o @ Y_15 @ Z_10 ) )
% 0.28/0.47 <=> ( ( ord_le827224136tate_o @ X_24 @ Y_15 )
% 0.28/0.47 & ( ord_le827224136tate_o @ X_24 @ Z_10 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_635_le__infI1,axiom,
% 0.28/0.47 ! [B_11: pname > $o,A_19: pname > $o,X_23: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ A_19 @ X_23 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_19 @ B_11 ) @ X_23 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_636_le__infI1,axiom,
% 0.28/0.47 ! [B_11: hoare_1167836817_state > $o,A_19: hoare_1167836817_state > $o,X_23: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ A_19 @ X_23 )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_19 @ B_11 ) @ X_23 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_637_le__infI2,axiom,
% 0.28/0.47 ! [A_18: pname > $o,B_10: pname > $o,X_22: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ B_10 @ X_22 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_18 @ B_10 ) @ X_22 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_638_le__infI2,axiom,
% 0.28/0.47 ! [A_18: hoare_1167836817_state > $o,B_10: hoare_1167836817_state > $o,X_22: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ B_10 @ X_22 )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_18 @ B_10 ) @ X_22 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_639_inf__absorb1,axiom,
% 0.28/0.47 ! [X_21: pname > $o,Y_14: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ X_21 @ Y_14 )
% 0.28/0.47 => ( ( semila1673364395name_o @ X_21 @ Y_14 )
% 0.28/0.47 = X_21 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_640_inf__absorb1,axiom,
% 0.28/0.47 ! [X_21: hoare_1167836817_state > $o,Y_14: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ X_21 @ Y_14 )
% 0.28/0.47 => ( ( semila179895820tate_o @ X_21 @ Y_14 )
% 0.28/0.47 = X_21 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_641_inf__absorb2,axiom,
% 0.28/0.47 ! [Y_13: pname > $o,X_20: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ Y_13 @ X_20 )
% 0.28/0.47 => ( ( semila1673364395name_o @ X_20 @ Y_13 )
% 0.28/0.47 = Y_13 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_642_inf__absorb2,axiom,
% 0.28/0.47 ! [Y_13: hoare_1167836817_state > $o,X_20: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ Y_13 @ X_20 )
% 0.28/0.47 => ( ( semila179895820tate_o @ X_20 @ Y_13 )
% 0.28/0.47 = Y_13 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_643_le__infI,axiom,
% 0.28/0.47 ! [B_9: pname > $o,X_19: pname > $o,A_17: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ X_19 @ A_17 )
% 0.28/0.47 => ( ( ord_less_eq_pname_o @ X_19 @ B_9 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ X_19 @ ( semila1673364395name_o @ A_17 @ B_9 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_644_le__infI,axiom,
% 0.28/0.47 ! [B_9: hoare_1167836817_state > $o,X_19: hoare_1167836817_state > $o,A_17: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ X_19 @ A_17 )
% 0.28/0.47 => ( ( ord_le827224136tate_o @ X_19 @ B_9 )
% 0.28/0.47 => ( ord_le827224136tate_o @ X_19 @ ( semila179895820tate_o @ A_17 @ B_9 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_645_inf__greatest,axiom,
% 0.28/0.47 ! [Z_9: pname > $o,X_18: pname > $o,Y_12: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ X_18 @ Y_12 )
% 0.28/0.47 => ( ( ord_less_eq_pname_o @ X_18 @ Z_9 )
% 0.28/0.47 => ( ord_less_eq_pname_o @ X_18 @ ( semila1673364395name_o @ Y_12 @ Z_9 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_646_inf__greatest,axiom,
% 0.28/0.47 ! [Z_9: hoare_1167836817_state > $o,X_18: hoare_1167836817_state > $o,Y_12: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ X_18 @ Y_12 )
% 0.28/0.47 => ( ( ord_le827224136tate_o @ X_18 @ Z_9 )
% 0.28/0.47 => ( ord_le827224136tate_o @ X_18 @ ( semila179895820tate_o @ Y_12 @ Z_9 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_647_inf__mono,axiom,
% 0.28/0.47 ! [B_8: pname > $o,D: pname > $o,A_16: pname > $o,C_3: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ A_16 @ C_3 )
% 0.28/0.47 => ( ( ord_less_eq_pname_o @ B_8 @ D )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_16 @ B_8 ) @ ( semila1673364395name_o @ C_3 @ D ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_648_inf__mono,axiom,
% 0.28/0.47 ! [B_8: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o,A_16: hoare_1167836817_state > $o,C_3: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ A_16 @ C_3 )
% 0.28/0.47 => ( ( ord_le827224136tate_o @ B_8 @ D )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_16 @ B_8 ) @ ( semila179895820tate_o @ C_3 @ D ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_649_le__infE,axiom,
% 0.28/0.47 ! [X_17: pname > $o,A_15: pname > $o,B_7: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ X_17 @ ( semila1673364395name_o @ A_15 @ B_7 ) )
% 0.28/0.47 => ~ ( ( ord_less_eq_pname_o @ X_17 @ A_15 )
% 0.28/0.47 => ~ ( ord_less_eq_pname_o @ X_17 @ B_7 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_650_le__infE,axiom,
% 0.28/0.47 ! [X_17: hoare_1167836817_state > $o,A_15: hoare_1167836817_state > $o,B_7: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ X_17 @ ( semila179895820tate_o @ A_15 @ B_7 ) )
% 0.28/0.47 => ~ ( ( ord_le827224136tate_o @ X_17 @ A_15 )
% 0.28/0.47 => ~ ( ord_le827224136tate_o @ X_17 @ B_7 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_651_inf__sup__absorb,axiom,
% 0.28/0.47 ! [X_16: hoare_1167836817_state > $o,Y_11: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ X_16 @ ( semila1172322802tate_o @ X_16 @ Y_11 ) )
% 0.28/0.47 = X_16 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_652_sup__inf__absorb,axiom,
% 0.28/0.47 ! [X_15: hoare_1167836817_state > $o,Y_10: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ X_15 @ ( semila179895820tate_o @ X_15 @ Y_10 ) )
% 0.28/0.47 = X_15 ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_653_inf__sup__distrib1,axiom,
% 0.28/0.47 ! [X_14: hoare_1167836817_state > $o,Y_9: hoare_1167836817_state > $o,Z_8: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ X_14 @ ( semila1172322802tate_o @ Y_9 @ Z_8 ) )
% 0.28/0.47 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_14 @ Y_9 ) @ ( semila179895820tate_o @ X_14 @ Z_8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_654_sup__inf__distrib1,axiom,
% 0.28/0.47 ! [X_13: hoare_1167836817_state > $o,Y_8: hoare_1167836817_state > $o,Z_7: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ X_13 @ ( semila179895820tate_o @ Y_8 @ Z_7 ) )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_13 @ Y_8 ) @ ( semila1172322802tate_o @ X_13 @ Z_7 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_655_inf__sup__distrib2,axiom,
% 0.28/0.47 ! [Y_7: hoare_1167836817_state > $o,Z_6: hoare_1167836817_state > $o,X_12: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_7 @ Z_6 ) @ X_12 )
% 0.28/0.47 = ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_7 @ X_12 ) @ ( semila179895820tate_o @ Z_6 @ X_12 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_656_sup__inf__distrib2,axiom,
% 0.28/0.47 ! [Y_6: hoare_1167836817_state > $o,Z_5: hoare_1167836817_state > $o,X_11: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_6 @ Z_5 ) @ X_11 )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_6 @ X_11 ) @ ( semila1172322802tate_o @ Z_5 @ X_11 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_657_inf__bot__right,axiom,
% 0.28/0.47 ! [X_10: pname > $o] :
% 0.28/0.47 ( ( semila1673364395name_o @ X_10 @ bot_bot_pname_o )
% 0.28/0.47 = bot_bot_pname_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_658_inf__bot__right,axiom,
% 0.28/0.47 ! [X_10: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ X_10 @ bot_bo70021908tate_o )
% 0.28/0.47 = bot_bo70021908tate_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_659_inf__bot__left,axiom,
% 0.28/0.47 ! [X_9: pname > $o] :
% 0.28/0.47 ( ( semila1673364395name_o @ bot_bot_pname_o @ X_9 )
% 0.28/0.47 = bot_bot_pname_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_660_inf__bot__left,axiom,
% 0.28/0.47 ! [X_9: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ bot_bo70021908tate_o @ X_9 )
% 0.28/0.47 = bot_bo70021908tate_o ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_661_distrib__sup__le,axiom,
% 0.28/0.47 ! [X_8: pname > $o,Y_5: pname > $o,Z_4: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_8 @ ( semila1673364395name_o @ Y_5 @ Z_4 ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ X_8 @ Y_5 ) @ ( semila1780557381name_o @ X_8 @ Z_4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_662_distrib__sup__le,axiom,
% 0.28/0.47 ! [X_8: hoare_1167836817_state > $o,Y_5: hoare_1167836817_state > $o,Z_4: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ X_8 @ ( semila179895820tate_o @ Y_5 @ Z_4 ) ) @ ( semila179895820tate_o @ ( semila1172322802tate_o @ X_8 @ Y_5 ) @ ( semila1172322802tate_o @ X_8 @ Z_4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_663_distrib__inf__le,axiom,
% 0.28/0.47 ! [X_7: pname > $o,Y_4: pname > $o,Z_3: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ X_7 @ Y_4 ) @ ( semila1673364395name_o @ X_7 @ Z_3 ) ) @ ( semila1673364395name_o @ X_7 @ ( semila1780557381name_o @ Y_4 @ Z_3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_664_distrib__inf__le,axiom,
% 0.28/0.47 ! [X_7: hoare_1167836817_state > $o,Y_4: hoare_1167836817_state > $o,Z_3: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ X_7 @ Y_4 ) @ ( semila179895820tate_o @ X_7 @ Z_3 ) ) @ ( semila179895820tate_o @ X_7 @ ( semila1172322802tate_o @ Y_4 @ Z_3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_665_image__Int__subset,axiom,
% 0.28/0.47 ! [F_6: pname > hoare_1167836817_state,A_14: pname > $o,B_6: pname > $o] : ( ord_le827224136tate_o @ ( image_575578384_state @ F_6 @ ( semila1673364395name_o @ A_14 @ B_6 ) ) @ ( semila179895820tate_o @ ( image_575578384_state @ F_6 @ A_14 ) @ ( image_575578384_state @ F_6 @ B_6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_666_Un__Int__assoc__eq,axiom,
% 0.28/0.47 ! [A_13: pname > $o,B_5: pname > $o,C_2: pname > $o] :
% 0.28/0.47 ( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A_13 @ B_5 ) @ C_2 )
% 0.28/0.47 = ( semila1673364395name_o @ A_13 @ ( semila1780557381name_o @ B_5 @ C_2 ) ) )
% 0.28/0.47 <=> ( ord_less_eq_pname_o @ C_2 @ A_13 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_667_Un__Int__assoc__eq,axiom,
% 0.28/0.47 ! [A_13: hoare_1167836817_state > $o,B_5: hoare_1167836817_state > $o,C_2: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ( semila1172322802tate_o @ ( semila179895820tate_o @ A_13 @ B_5 ) @ C_2 )
% 0.28/0.47 = ( semila179895820tate_o @ A_13 @ ( semila1172322802tate_o @ B_5 @ C_2 ) ) )
% 0.28/0.47 <=> ( ord_le827224136tate_o @ C_2 @ A_13 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_668_if__image__distrib,axiom,
% 0.28/0.47 ! [P_3: pname > $o,F_5: pname > hoare_1167836817_state,G_1: pname > hoare_1167836817_state,S: pname > $o] :
% 0.28/0.47 ( ( image_575578384_state
% 0.28/0.47 @ ^ [X_5: pname] : ( if_Hoa833675553_state @ ( P_3 @ X_5 ) @ ( F_5 @ X_5 ) @ ( G_1 @ X_5 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( semila1172322802tate_o @ ( image_575578384_state @ F_5 @ ( semila1673364395name_o @ S @ ( collect_pname @ P_3 ) ) )
% 0.28/0.47 @ ( image_575578384_state @ G_1
% 0.28/0.47 @ ( semila1673364395name_o @ S
% 0.28/0.47 @ ( collect_pname
% 0.28/0.47 @ ^ [X_5: pname] : ( (~) @ ( P_3 @ X_5 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_669_dom__if,axiom,
% 0.28/0.47 ! [P_2: pname > $o,F_4: pname > option_com,G: pname > option_com] :
% 0.28/0.47 ( ( dom_pname_com
% 0.28/0.47 @ ^ [X_5: pname] : ( if_option_com @ ( P_2 @ X_5 ) @ ( F_4 @ X_5 ) @ ( G @ X_5 ) ) )
% 0.28/0.47 = ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ F_4 ) @ ( collect_pname @ P_2 ) )
% 0.28/0.47 @ ( semila1673364395name_o @ ( dom_pname_com @ G )
% 0.28/0.47 @ ( collect_pname
% 0.28/0.47 @ ^ [X_5: pname] : ( (~) @ ( P_2 @ X_5 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_670_Int__Collect__mono,axiom,
% 0.28/0.47 ! [Q: pname > $o,P_1: pname > $o,A_12: pname > $o,B_4: pname > $o] :
% 0.28/0.47 ( ( ord_less_eq_pname_o @ A_12 @ B_4 )
% 0.28/0.47 => ( ! [X_5: pname] :
% 0.28/0.47 ( ( member_pname @ X_5 @ A_12 )
% 0.28/0.47 => ( ( P_1 @ X_5 )
% 0.28/0.47 => ( Q @ X_5 ) ) )
% 0.28/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_12 @ ( collect_pname @ P_1 ) ) @ ( semila1673364395name_o @ B_4 @ ( collect_pname @ Q ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_671_Int__Collect__mono,axiom,
% 0.28/0.47 ! [Q: hoare_1167836817_state > $o,P_1: hoare_1167836817_state > $o,A_12: hoare_1167836817_state > $o,B_4: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( ord_le827224136tate_o @ A_12 @ B_4 )
% 0.28/0.47 => ( ! [X_5: hoare_1167836817_state] :
% 0.28/0.47 ( ( member2058392318_state @ X_5 @ A_12 )
% 0.28/0.47 => ( ( P_1 @ X_5 )
% 0.28/0.47 => ( Q @ X_5 ) ) )
% 0.28/0.47 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_12 @ ( collec1027672124_state @ P_1 ) ) @ ( semila179895820tate_o @ B_4 @ ( collec1027672124_state @ Q ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_672_Int__Collect__mono,axiom,
% 0.28/0.47 ! [Q: ( pname > $o ) > $o,P_1: ( pname > $o ) > $o,A_12: ( pname > $o ) > $o,B_4: ( pname > $o ) > $o] :
% 0.28/0.47 ( ( ord_le1205211808me_o_o @ A_12 @ B_4 )
% 0.28/0.47 => ( ! [X_5: pname > $o] :
% 0.28/0.47 ( ( member_pname_o @ X_5 @ A_12 )
% 0.28/0.47 => ( ( P_1 @ X_5 )
% 0.28/0.47 => ( Q @ X_5 ) ) )
% 0.28/0.47 => ( ord_le1205211808me_o_o @ ( semila2013987940me_o_o @ A_12 @ ( collect_pname_o @ P_1 ) ) @ ( semila2013987940me_o_o @ B_4 @ ( collect_pname_o @ Q ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_673_Int__Collect__mono,axiom,
% 0.28/0.47 ! [Q: ( hoare_1167836817_state > $o ) > $o,P_1: ( hoare_1167836817_state > $o ) > $o,A_12: ( hoare_1167836817_state > $o ) > $o,B_4: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ( ord_le741939125te_o_o @ A_12 @ B_4 )
% 0.28/0.47 => ( ! [X_5: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member864234961tate_o @ X_5 @ A_12 )
% 0.28/0.47 => ( ( P_1 @ X_5 )
% 0.28/0.47 => ( Q @ X_5 ) ) )
% 0.28/0.47 => ( ord_le741939125te_o_o @ ( semila1758709489te_o_o @ A_12 @ ( collec269976083tate_o @ P_1 ) ) @ ( semila1758709489te_o_o @ B_4 @ ( collec269976083tate_o @ Q ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_674_distrib__imp1,axiom,
% 0.28/0.47 ! [X_6: hoare_1167836817_state > $o,Y_3: hoare_1167836817_state > $o,Z_2: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila179895820tate_o @ X_5 @ ( semila1172322802tate_o @ Y_2 @ Z_1 ) )
% 0.28/0.47 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_5 @ Y_2 ) @ ( semila179895820tate_o @ X_5 @ Z_1 ) ) )
% 0.28/0.47 => ( ( semila1172322802tate_o @ X_6 @ ( semila179895820tate_o @ Y_3 @ Z_2 ) )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_6 @ Y_3 ) @ ( semila1172322802tate_o @ X_6 @ Z_2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_675_distrib__imp2,axiom,
% 0.28/0.47 ! [X_4: hoare_1167836817_state > $o,Y_1: hoare_1167836817_state > $o,Z: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( semila1172322802tate_o @ X_5 @ ( semila179895820tate_o @ Y_2 @ Z_1 ) )
% 0.28/0.47 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_5 @ Y_2 ) @ ( semila1172322802tate_o @ X_5 @ Z_1 ) ) )
% 0.28/0.47 => ( ( semila179895820tate_o @ X_4 @ ( semila1172322802tate_o @ Y_1 @ Z ) )
% 0.28/0.47 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_4 @ Y_1 ) @ ( semila179895820tate_o @ X_4 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_676_folding__one_Oremove,axiom,
% 0.28/0.47 ! [X_3: pname,A_11: pname > $o,F_3: pname > pname > pname,F_2: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_3 @ F_2 )
% 0.28/0.47 => ( ( finite_finite_pname @ A_11 )
% 0.28/0.47 => ( ( member_pname @ X_3 @ A_11 )
% 0.28/0.47 => ( ( ( ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 0.28/0.47 = bot_bot_pname_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = X_3 ) )
% 0.28/0.47 & ( ( ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 0.28/0.47 != bot_bot_pname_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = ( F_3 @ X_3 @ ( F_2 @ ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_677_folding__one_Oremove,axiom,
% 0.28/0.47 ! [X_3: hoare_1167836817_state,A_11: hoare_1167836817_state > $o,F_3: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_2: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_3 @ F_2 )
% 0.28/0.47 => ( ( finite1084549118_state @ A_11 )
% 0.28/0.47 => ( ( member2058392318_state @ X_3 @ A_11 )
% 0.28/0.47 => ( ( ( ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) )
% 0.28/0.47 = bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = X_3 ) )
% 0.28/0.47 & ( ( ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) )
% 0.28/0.47 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = ( F_3 @ X_3 @ ( F_2 @ ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_678_folding__one_Oremove,axiom,
% 0.28/0.47 ! [X_3: pname > $o,A_11: ( pname > $o ) > $o,F_3: ( pname > $o ) > ( pname > $o ) > pname > $o,F_2: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.47 ( ( finite349908348name_o @ F_3 @ F_2 )
% 0.28/0.47 => ( ( finite297249702name_o @ A_11 )
% 0.28/0.47 => ( ( member_pname_o @ X_3 @ A_11 )
% 0.28/0.47 => ( ( ( ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 0.28/0.47 = bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = X_3 ) )
% 0.28/0.47 & ( ( ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 0.28/0.47 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = ( F_3 @ X_3 @ ( F_2 @ ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_679_folding__one_Oremove,axiom,
% 0.28/0.47 ! [X_3: hoare_1167836817_state > $o,A_11: ( hoare_1167836817_state > $o ) > $o,F_3: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_2: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite979047547tate_o @ F_3 @ F_2 )
% 0.28/0.47 => ( ( finite1380128977tate_o @ A_11 )
% 0.28/0.47 => ( ( member864234961tate_o @ X_3 @ A_11 )
% 0.28/0.47 => ( ( ( ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) )
% 0.28/0.47 = bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = X_3 ) )
% 0.28/0.47 & ( ( ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) )
% 0.28/0.47 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F_2 @ A_11 )
% 0.28/0.47 = ( F_3 @ X_3 @ ( F_2 @ ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_680_folding__one_Oinsert__remove,axiom,
% 0.28/0.47 ! [X_2: pname,A_10: pname > $o,F_1: pname > pname > pname,F: ( pname > $o ) > pname] :
% 0.28/0.47 ( ( finite1282449217_pname @ F_1 @ F )
% 0.28/0.47 => ( ( finite_finite_pname @ A_10 )
% 0.28/0.47 => ( ( ( ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) )
% 0.28/0.47 = bot_bot_pname_o )
% 0.28/0.47 => ( ( F @ ( insert_pname @ X_2 @ A_10 ) )
% 0.28/0.47 = X_2 ) )
% 0.28/0.47 & ( ( ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) )
% 0.28/0.47 != bot_bot_pname_o )
% 0.28/0.47 => ( ( F @ ( insert_pname @ X_2 @ A_10 ) )
% 0.28/0.47 = ( F_1 @ X_2 @ ( F @ ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_681_folding__one_Oinsert__remove,axiom,
% 0.28/0.47 ! [X_2: hoare_1167836817_state,A_10: hoare_1167836817_state > $o,F_1: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.28/0.47 ( ( finite1074406356_state @ F_1 @ F )
% 0.28/0.47 => ( ( finite1084549118_state @ A_10 )
% 0.28/0.47 => ( ( ( ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) )
% 0.28/0.47 = bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F @ ( insert2134838167_state @ X_2 @ A_10 ) )
% 0.28/0.47 = X_2 ) )
% 0.28/0.47 & ( ( ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) )
% 0.28/0.47 != bot_bo70021908tate_o )
% 0.28/0.47 => ( ( F @ ( insert2134838167_state @ X_2 @ A_10 ) )
% 0.28/0.47 = ( F_1 @ X_2 @ ( F @ ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_682_folding__one_Oinsert__remove,axiom,
% 0.28/0.47 ! [X_2: pname > $o,A_10: ( pname > $o ) > $o,F_1: ( pname > $o ) > ( pname > $o ) > pname > $o,F: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.28/0.47 ( ( finite349908348name_o @ F_1 @ F )
% 0.28/0.47 => ( ( finite297249702name_o @ A_10 )
% 0.28/0.47 => ( ( ( ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) )
% 0.28/0.47 = bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F @ ( insert_pname_o @ X_2 @ A_10 ) )
% 0.28/0.47 = X_2 ) )
% 0.28/0.47 & ( ( ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) )
% 0.28/0.47 != bot_bot_pname_o_o )
% 0.28/0.47 => ( ( F @ ( insert_pname_o @ X_2 @ A_10 ) )
% 0.28/0.47 = ( F_1 @ X_2 @ ( F @ ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_683_folding__one_Oinsert__remove,axiom,
% 0.28/0.47 ! [X_2: hoare_1167836817_state > $o,A_10: ( hoare_1167836817_state > $o ) > $o,F_1: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite979047547tate_o @ F_1 @ F )
% 0.28/0.47 => ( ( finite1380128977tate_o @ A_10 )
% 0.28/0.47 => ( ( ( ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) )
% 0.28/0.47 = bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F @ ( insert999278200tate_o @ X_2 @ A_10 ) )
% 0.28/0.47 = X_2 ) )
% 0.28/0.47 & ( ( ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) )
% 0.28/0.47 != bot_bo691907561te_o_o )
% 0.28/0.47 => ( ( F @ ( insert999278200tate_o @ X_2 @ A_10 ) )
% 0.28/0.47 = ( F_1 @ X_2 @ ( F @ ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_684_DiffI,axiom,
% 0.28/0.47 ! [B_3: pname > $o,C_1: pname,A_9: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C_1 @ A_9 )
% 0.28/0.47 => ( ~ ( member_pname @ C_1 @ B_3 )
% 0.28/0.47 => ( member_pname @ C_1 @ ( minus_minus_pname_o @ A_9 @ B_3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_685_DiffI,axiom,
% 0.28/0.47 ! [B_3: hoare_1167836817_state > $o,C_1: hoare_1167836817_state,A_9: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C_1 @ A_9 )
% 0.28/0.47 => ( ~ ( member2058392318_state @ C_1 @ B_3 )
% 0.28/0.47 => ( member2058392318_state @ C_1 @ ( minus_2107060239tate_o @ A_9 @ B_3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_686_DiffE,axiom,
% 0.28/0.47 ! [C: pname,A_8: pname > $o,B_2: pname > $o] :
% 0.28/0.47 ( ( member_pname @ C @ ( minus_minus_pname_o @ A_8 @ B_2 ) )
% 0.28/0.47 => ~ ( ( member_pname @ C @ A_8 )
% 0.28/0.47 => ( member_pname @ C @ B_2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_687_DiffE,axiom,
% 0.28/0.47 ! [C: hoare_1167836817_state,A_8: hoare_1167836817_state > $o,B_2: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ C @ ( minus_2107060239tate_o @ A_8 @ B_2 ) )
% 0.28/0.47 => ~ ( ( member2058392318_state @ C @ A_8 )
% 0.28/0.47 => ( member2058392318_state @ C @ B_2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_688_finite__Diff,axiom,
% 0.28/0.47 ! [B_1: ( pname > $o ) > $o,A_7: ( pname > $o ) > $o] :
% 0.28/0.47 ( ( finite297249702name_o @ A_7 )
% 0.28/0.47 => ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_7 @ B_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_689_finite__Diff,axiom,
% 0.28/0.47 ! [B_1: ( hoare_1167836817_state > $o ) > $o,A_7: ( hoare_1167836817_state > $o ) > $o] :
% 0.28/0.47 ( ( finite1380128977tate_o @ A_7 )
% 0.28/0.47 => ( finite1380128977tate_o @ ( minus_1708687022te_o_o @ A_7 @ B_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_690_finite__Diff,axiom,
% 0.28/0.47 ! [B_1: pname > $o,A_7: pname > $o] :
% 0.28/0.47 ( ( finite_finite_pname @ A_7 )
% 0.28/0.47 => ( finite_finite_pname @ ( minus_minus_pname_o @ A_7 @ B_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_691_finite__Diff,axiom,
% 0.28/0.47 ! [B_1: hoare_1167836817_state > $o,A_7: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( finite1084549118_state @ A_7 )
% 0.28/0.47 => ( finite1084549118_state @ ( minus_2107060239tate_o @ A_7 @ B_1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_692_insert__Diff,axiom,
% 0.28/0.47 ! [A_6: pname,A_5: pname > $o] :
% 0.28/0.47 ( ( member_pname @ A_6 @ A_5 )
% 0.28/0.47 => ( ( insert_pname @ A_6 @ ( minus_minus_pname_o @ A_5 @ ( insert_pname @ A_6 @ bot_bot_pname_o ) ) )
% 0.28/0.47 = A_5 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_693_insert__Diff,axiom,
% 0.28/0.47 ! [A_6: hoare_1167836817_state,A_5: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( member2058392318_state @ A_6 @ A_5 )
% 0.28/0.47 => ( ( insert2134838167_state @ A_6 @ ( minus_2107060239tate_o @ A_5 @ ( insert2134838167_state @ A_6 @ bot_bo70021908tate_o ) ) )
% 0.28/0.47 = A_5 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_694_Diff__insert__absorb,axiom,
% 0.28/0.47 ! [X_1: pname,A_4: pname > $o] :
% 0.28/0.47 ( ~ ( member_pname @ X_1 @ A_4 )
% 0.28/0.47 => ( ( minus_minus_pname_o @ ( insert_pname @ X_1 @ A_4 ) @ ( insert_pname @ X_1 @ bot_bot_pname_o ) )
% 0.28/0.47 = A_4 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_695_Diff__insert__absorb,axiom,
% 0.28/0.47 ! [X_1: hoare_1167836817_state,A_4: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ~ ( member2058392318_state @ X_1 @ A_4 )
% 0.28/0.47 => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_1 @ A_4 ) @ ( insert2134838167_state @ X_1 @ bot_bo70021908tate_o ) )
% 0.28/0.47 = A_4 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_696_insert__Diff__single,axiom,
% 0.28/0.47 ! [A_3: pname,A_2: pname > $o] :
% 0.28/0.47 ( ( insert_pname @ A_3 @ ( minus_minus_pname_o @ A_2 @ ( insert_pname @ A_3 @ bot_bot_pname_o ) ) )
% 0.28/0.47 = ( insert_pname @ A_3 @ A_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_697_insert__Diff__single,axiom,
% 0.28/0.47 ! [A_3: hoare_1167836817_state,A_2: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( insert2134838167_state @ A_3 @ ( minus_2107060239tate_o @ A_2 @ ( insert2134838167_state @ A_3 @ bot_bo70021908tate_o ) ) )
% 0.28/0.47 = ( insert2134838167_state @ A_3 @ A_2 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(fact_698_Diff__insert2,axiom,
% 0.28/0.47 ! [A_1: hoare_1167836817_state > $o,A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( minus_2107060239tate_o @ A_1 @ ( insert2134838167_state @ A @ B ) )
% 0.28/0.47 = ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A_1 @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 %----Helper facts (16)
% 0.28/0.47 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.28/0.47 ! [X: pname,Y: pname] :
% 0.28/0.47 ( ~ ( fequal_pname @ X @ Y )
% 0.28/0.47 | ( X = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.28/0.47 ! [X: pname,Y: pname] :
% 0.28/0.47 ( ( X != Y )
% 0.28/0.47 | ( fequal_pname @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.28/0.47 ! [X: state,Y: state] :
% 0.28/0.47 ( ~ ( fequal_state @ X @ Y )
% 0.28/0.47 | ( X = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.28/0.47 ! [X: state,Y: state] :
% 0.28/0.47 ( ( X != Y )
% 0.28/0.47 | ( fequal_state @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.28/0.47 ! [X: pname > $o,Y: pname > $o] :
% 0.28/0.47 ( ~ ( fequal_pname_o @ X @ Y )
% 0.28/0.47 | ( X = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.28/0.47 ! [X: pname > $o,Y: pname > $o] :
% 0.28/0.47 ( ( X != Y )
% 0.28/0.47 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 0.28/0.47 ! [X: option_com,Y: option_com] :
% 0.28/0.47 ( ( if_option_com @ $true @ X @ Y )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 0.28/0.47 ! [X: option_com,Y: option_com] :
% 0.28/0.47 ( ( if_option_com @ $false @ X @ Y )
% 0.28/0.47 = Y ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 0.28/0.47 ! [P: $o] :
% 0.28/0.47 ( ( P = $true )
% 0.28/0.47 | ( P = $false ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 0.28/0.47 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.28/0.47 ( ( if_Hoa833675553_state @ $true @ X @ Y )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 0.28/0.47 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.28/0.47 ( ( if_Hoa833675553_state @ $false @ X @ Y )
% 0.28/0.47 = Y ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 0.28/0.47 ! [P: $o] :
% 0.28/0.47 ( ( P = $true )
% 0.28/0.47 | ( P = $false ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,
% 0.28/0.47 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.28/0.47 ( ~ ( fequal1831255762_state @ X @ Y )
% 0.28/0.47 | ( X = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,
% 0.28/0.47 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.28/0.47 ( ( X != Y )
% 0.28/0.47 | ( fequal1831255762_state @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It,axiom,
% 0.28/0.47 ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ~ ( fequal1486222077tate_o @ X @ Y )
% 0.28/0.47 | ( X = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It,axiom,
% 0.28/0.47 ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.28/0.47 ( ( X != Y )
% 0.28/0.47 | ( fequal1486222077tate_o @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 %----Conjectures (8)
% 0.28/0.47 thf(conj_0,hypothesis,
% 0.28/0.47 hoare_1201148605gleton ).
% 0.28/0.47
% 0.28/0.47 thf(conj_1,hypothesis,
% 0.28/0.47 wT_bodies ).
% 0.28/0.47
% 0.28/0.47 thf(conj_2,hypothesis,
% 0.28/0.47 finite1084549118_state @ fa ).
% 0.28/0.47
% 0.28/0.47 thf(conj_3,hypothesis,
% 0.28/0.47 ~ ( member2058392318_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_4,hypothesis,
% 0.28/0.47 ( ord_le827224136tate_o @ fa
% 0.28/0.47 @ ( image_575578384_state
% 0.28/0.47 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 0.28/0.47 @ ( dom_pname_com @ body ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_5,hypothesis,
% 0.28/0.47 ( ( body @ pn )
% 0.28/0.47 = ( some_com @ y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_6,hypothesis,
% 0.28/0.47 ( hoare_123228589_state
% 0.28/0.47 @ ( image_575578384_state
% 0.28/0.47 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.28/0.47 @ ( dom_pname_com @ body ) )
% 0.28/0.47 @ fa ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_7,conjecture,
% 0.28/0.47 ( hoare_123228589_state
% 0.28/0.47 @ ( image_575578384_state
% 0.28/0.47 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.28/0.47 @ ( dom_pname_com @ body ) )
% 0.28/0.47 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 3.21/1.63 ---- Embedded in THF ---
% 3.21/1.63 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.21/1.63 %%% Generated on Tue Feb 24 13:40:58 EST 2026
% 3.21/1.63 %%% using '$$dhol' embedding, version 1.3.0.
% 3.21/1.63 %%% Logic specification used:
% 3.21/1.63 %%% thf(spec, logic, $$dhol).
% 3.21/1.63
% 3.21/1.63 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2DTF3263.p
% See solution above
% 3.21/1.63 ------------------------
% 3.28/1.75 ---- Cleaned THF ---
% 3.28/1.75 thf(ty_ty_tc__Com__Ocom,type,
% 3.28/1.75 com: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(ty_ty_tc__Com__Opname,type,
% 3.28/1.75 pname: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(ty_ty_tc__Com__Ostate,type,
% 3.28/1.75 state: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 3.28/1.75 hoare_1167836817_state: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.28/1.75 option_com: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(ty_ty_tc__Option__Ooption_Itc__Com__Opname_J,type,
% 3.28/1.75 option_pname: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,
% 3.28/1.75 option1574264306_state: $tType ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_OWT,type,
% 3.28/1.75 wt: com > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_OWT__bodies,type,
% 3.28/1.75 wT_bodies: $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_Obody,type,
% 3.28/1.75 body: pname > option_com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_Ocom_OBODY,type,
% 3.28/1.75 body_1: pname > com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_Ocom_OSKIP,type,
% 3.28/1.75 skip: com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_Ocom_OSemi,type,
% 3.28/1.75 semi: com > com > com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Com_Ocom_OWhile,type,
% 3.28/1.75 while: ( state > $o ) > com > com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.28/1.75 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 3.28/1.75 finite33115244te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 3.28/1.75 finite1380128977tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 3.28/1.75 finite_finite_pname: ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C,type,
% 3.28/1.75 finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 3.28/1.75 finite979047547tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 3.28/1.75 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 3.28/1.75 finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____srushsum,type,
% 3.28/1.75 finite671847800tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 3.28/1.75 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 3.28/1.75 finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.28/1.75 minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____srushs,type,
% 3.28/1.75 minus_1708687022te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__,type,
% 3.28/1.75 minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_HOL_OThe_000tc__Com__Opname,type,
% 3.28/1.75 the_pname: ( pname > $o ) > pname ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_,type,
% 3.28/1.75 the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Hoare__Mirabelle__srushsumbx_OMGT,type,
% 3.28/1.75 hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate,type,
% 3.28/1.75 hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate,type,
% 3.28/1.75 hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ostate__not__singleton,type,
% 3.28/1.75 hoare_1201148605gleton: $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate,type,
% 3.28/1.75 hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 3.28/1.75 if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.28/1.75 if_option_com: $o > option_com > option_com > option_com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 3.28/1.75 semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,
% 3.28/1.75 semila1758709489te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s,type,
% 3.28/1.75 semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 3.28/1.75 semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,
% 3.28/1.75 semila866907787te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s,type,
% 3.28/1.75 semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,
% 3.28/1.75 semila10642723_sup_o: $o > $o > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
% 3.28/1.75 dom_pname_com: ( pname > option_com ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Natural_Oevalc,type,
% 3.28/1.75 evalc: com > state > state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,
% 3.28/1.75 some_com: com > option_com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Ooption_OSome_000tc__Com__Opname,type,
% 3.28/1.75 some_pname: pname > option_pname ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__,type,
% 3.28/1.75 some_H1433514562_state: hoare_1167836817_state > option1574264306_state ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Oset_000tc__Com__Ocom,type,
% 3.28/1.75 set_com: option_com > com > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Oset_000tc__Com__Opname,type,
% 3.28/1.75 set_pname: option_pname > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Oset_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,
% 3.28/1.75 set_Ho2131684873_state: option1574264306_state > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 3.28/1.75 the_com: option_com > com ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.28/1.75 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu,type,
% 3.28/1.75 bot_bo691907561te_o_o: ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 3.28/1.75 bot_bot_com_o: com > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 bot_bot_pname_o: pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,
% 3.28/1.75 bot_bo70021908tate_o: hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 3.28/1.75 bot_bot_o: $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 3.28/1.75 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____sr,type,
% 3.28/1.75 ord_le741939125te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____srushsum,type,
% 3.28/1.75 ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 3.28/1.75 ord_less_eq_o: $o > $o > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.28/1.75 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_I,type,
% 3.28/1.75 collec1218656682te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,
% 3.28/1.75 collec269976083tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 3.28/1.75 collect_pname: ( pname > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 3.28/1.75 collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 3.28/1.75 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____sru,type,
% 3.28/1.75 image_1381916541_state: ( ( pname > $o ) > hoare_1167836817_state ) > ( ( pname > $o ) > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_,type,
% 3.28/1.75 image_1488525317tate_o: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__001,type,
% 3.28/1.75 image_980295115_pname: ( ( hoare_1167836817_state > $o ) > pname ) > ( ( hoare_1167836817_state > $o ) > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__002,type,
% 3.28/1.75 image_635813834_state: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____srushsumbx,type,
% 3.28/1.75 image_475339327tate_o: ( pname > hoare_1167836817_state > $o ) > ( pname > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 3.28/1.75 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri,type,
% 3.28/1.75 image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat,type,
% 3.28/1.75 image_2066861949name_o: ( hoare_1167836817_state > pname > $o ) > ( hoare_1167836817_state > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_003,type,
% 3.28/1.75 image_1745649338tate_o: ( hoare_1167836817_state > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_004,type,
% 3.28/1.75 image_8178176_pname: ( hoare_1167836817_state > pname ) > ( hoare_1167836817_state > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_005,type,
% 3.28/1.75 image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,type,
% 3.28/1.75 insert999278200tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oinsert_000tc__Com__Ocom,type,
% 3.28/1.75 insert_com: com > ( com > $o ) > com > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 3.28/1.75 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,
% 3.28/1.75 insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Othe__elem_000tc__Com__Opname,type,
% 3.28/1.75 the_elem_pname: ( pname > $o ) > pname ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O,type,
% 3.28/1.75 the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 3.28/1.75 fequal1486222077tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_fequal_000tc__Com__Opname,type,
% 3.28/1.75 fequal_pname: pname > pname > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_fequal_000tc__Com__Ostate,type,
% 3.28/1.75 fequal_state: state > state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 3.28/1.75 fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.28/1.75 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 3.28/1.75 member864234961tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_member_000tc__Com__Ocom,type,
% 3.28/1.75 member_com: com > ( com > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_member_000tc__Com__Opname,type,
% 3.28/1.75 member_pname: pname > ( pname > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 3.28/1.75 member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_v_Fa,type,
% 3.28/1.75 fa: hoare_1167836817_state > $o ).
% 3.28/1.75
% 3.28/1.75 thf(sy_v_pn,type,
% 3.28/1.75 pn: pname ).
% 3.28/1.75
% 3.28/1.75 thf(sy_v_y,type,
% 3.28/1.75 y: com ).
% 3.28/1.75
% 3.28/1.75 thf(fact_0_empty,axiom,
% 3.28/1.75 ! [G_3: hoare_1167836817_state > $o] : ( hoare_123228589_state @ G_3 @ bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_1_asm,axiom,
% 3.28/1.75 ! [Ts_7: hoare_1167836817_state > $o,G_35: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Ts_7 @ G_35 )
% 3.28/1.75 => ( hoare_123228589_state @ G_35 @ Ts_7 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_2_weaken,axiom,
% 3.28/1.75 ! [Ts_6: hoare_1167836817_state > $o,G_34: hoare_1167836817_state > $o,Ts_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_34 @ Ts_5 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ Ts_6 @ Ts_5 )
% 3.28/1.75 => ( hoare_123228589_state @ G_34 @ Ts_6 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_3_thin,axiom,
% 3.28/1.75 ! [G_33: hoare_1167836817_state > $o,G_32: hoare_1167836817_state > $o,Ts_4: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_32 @ Ts_4 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ G_32 @ G_33 )
% 3.28/1.75 => ( hoare_123228589_state @ G_33 @ Ts_4 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_4_cut,axiom,
% 3.28/1.75 ! [G_31: hoare_1167836817_state > $o,G_30: hoare_1167836817_state > $o,Ts_3: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_30 @ Ts_3 )
% 3.28/1.75 => ( ( hoare_123228589_state @ G_31 @ G_30 )
% 3.28/1.75 => ( hoare_123228589_state @ G_31 @ Ts_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 3.28/1.75 ! [Ts_2: hoare_1167836817_state > $o,G_29: hoare_1167836817_state > $o,T_3: hoare_1167836817_state] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_29 @ ( insert2134838167_state @ T_3 @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ( hoare_123228589_state @ G_29 @ Ts_2 )
% 3.28/1.75 => ( hoare_123228589_state @ G_29 @ ( insert2134838167_state @ T_3 @ Ts_2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_6_derivs__insertD,axiom,
% 3.28/1.75 ! [G_28: hoare_1167836817_state > $o,T_2: hoare_1167836817_state,Ts_1: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_28 @ ( insert2134838167_state @ T_2 @ Ts_1 ) )
% 3.28/1.75 => ( ( hoare_123228589_state @ G_28 @ ( insert2134838167_state @ T_2 @ bot_bo70021908tate_o ) )
% 3.28/1.75 & ( hoare_123228589_state @ G_28 @ Ts_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_7_MGT__BodyN,axiom,
% 3.28/1.75 ! [Pn_1: pname,G_3: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G_3 ) @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_8_finite__Collect__subsets,axiom,
% 3.28/1.75 ! [A_201: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ A_201 )
% 3.28/1.75 => ( finite1066544169me_o_o
% 3.28/1.75 @ ( collect_pname_o_o
% 3.28/1.75 @ ^ [B_43: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_43 @ A_201 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_9_finite__Collect__subsets,axiom,
% 3.28/1.75 ! [A_201: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ A_201 )
% 3.28/1.75 => ( finite33115244te_o_o
% 3.28/1.75 @ ( collec1218656682te_o_o
% 3.28/1.75 @ ^ [B_43: ( hoare_1167836817_state > $o ) > $o] : ( ord_le741939125te_o_o @ B_43 @ A_201 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_10_finite__Collect__subsets,axiom,
% 3.28/1.75 ! [A_201: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_201 )
% 3.28/1.75 => ( finite1380128977tate_o
% 3.28/1.75 @ ( collec269976083tate_o
% 3.28/1.75 @ ^ [B_43: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ B_43 @ A_201 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_11_finite__Collect__subsets,axiom,
% 3.28/1.75 ! [A_201: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_201 )
% 3.28/1.75 => ( finite297249702name_o
% 3.28/1.75 @ ( collect_pname_o
% 3.28/1.75 @ ^ [B_43: pname > $o] : ( ord_less_eq_pname_o @ B_43 @ A_201 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_12_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: hoare_1167836817_state > pname > $o,F_61: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_61 )
% 3.28/1.75 => ( finite297249702name_o @ ( image_2066861949name_o @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_13_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: hoare_1167836817_state > hoare_1167836817_state > $o,F_61: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_61 )
% 3.28/1.75 => ( finite1380128977tate_o @ ( image_1745649338tate_o @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_14_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: pname > pname > $o,F_61: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_61 )
% 3.28/1.75 => ( finite297249702name_o @ ( image_pname_pname_o @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_15_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: pname > hoare_1167836817_state > $o,F_61: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_61 )
% 3.28/1.75 => ( finite1380128977tate_o @ ( image_475339327tate_o @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_16_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: ( pname > $o ) > hoare_1167836817_state,F_61: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_61 )
% 3.28/1.75 => ( finite1084549118_state @ ( image_1381916541_state @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_17_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,F_61: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_61 )
% 3.28/1.75 => ( finite1084549118_state @ ( image_635813834_state @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_18_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: ( pname > $o ) > pname,F_61: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_61 )
% 3.28/1.75 => ( finite_finite_pname @ ( image_pname_o_pname @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_19_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: ( hoare_1167836817_state > $o ) > pname,F_61: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_61 )
% 3.28/1.75 => ( finite_finite_pname @ ( image_980295115_pname @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_20_finite__imageI,axiom,
% 3.28/1.75 ! [H_1: pname > hoare_1167836817_state,F_61: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_61 )
% 3.28/1.75 => ( finite1084549118_state @ ( image_575578384_state @ H_1 @ F_61 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_21_empty__subsetI,axiom,
% 3.28/1.75 ! [A_200: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_200 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_22_empty__subsetI,axiom,
% 3.28/1.75 ! [A_200: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_200 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_23_finite_OinsertI,axiom,
% 3.28/1.75 ! [A_199: pname > $o,A_198: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ A_198 )
% 3.28/1.75 => ( finite297249702name_o @ ( insert_pname_o @ A_199 @ A_198 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_24_finite_OinsertI,axiom,
% 3.28/1.75 ! [A_199: hoare_1167836817_state > $o,A_198: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ A_198 )
% 3.28/1.75 => ( finite1380128977tate_o @ ( insert999278200tate_o @ A_199 @ A_198 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_25_finite_OinsertI,axiom,
% 3.28/1.75 ! [A_199: pname,A_198: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_198 )
% 3.28/1.75 => ( finite_finite_pname @ ( insert_pname @ A_199 @ A_198 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_26_finite_OinsertI,axiom,
% 3.28/1.75 ! [A_199: hoare_1167836817_state,A_198: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_198 )
% 3.28/1.75 => ( finite1084549118_state @ ( insert2134838167_state @ A_199 @ A_198 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_27_finite_OemptyI,axiom,
% 3.28/1.75 finite297249702name_o @ bot_bot_pname_o_o ).
% 3.28/1.75
% 3.28/1.75 thf(fact_28_finite_OemptyI,axiom,
% 3.28/1.75 finite1380128977tate_o @ bot_bo691907561te_o_o ).
% 3.28/1.75
% 3.28/1.75 thf(fact_29_finite_OemptyI,axiom,
% 3.28/1.75 finite1084549118_state @ bot_bo70021908tate_o ).
% 3.28/1.75
% 3.28/1.75 thf(fact_30_finite_OemptyI,axiom,
% 3.28/1.75 finite_finite_pname @ bot_bot_pname_o ).
% 3.28/1.75
% 3.28/1.75 thf(fact_31_finite__Collect__conjI,axiom,
% 3.28/1.75 ! [Q_24: ( pname > $o ) > $o,P_42: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_42 ) )
% 3.28/1.75 | ( finite297249702name_o @ ( collect_pname_o @ Q_24 ) ) )
% 3.28/1.75 => ( finite297249702name_o
% 3.28/1.75 @ ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_32_finite__Collect__conjI,axiom,
% 3.28/1.75 ! [Q_24: ( hoare_1167836817_state > $o ) > $o,P_42: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ( finite1380128977tate_o @ ( collec269976083tate_o @ P_42 ) )
% 3.28/1.75 | ( finite1380128977tate_o @ ( collec269976083tate_o @ Q_24 ) ) )
% 3.28/1.75 => ( finite1380128977tate_o
% 3.28/1.75 @ ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_33_finite__Collect__conjI,axiom,
% 3.28/1.75 ! [Q_24: hoare_1167836817_state > $o,P_42: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( finite1084549118_state @ ( collec1027672124_state @ P_42 ) )
% 3.28/1.75 | ( finite1084549118_state @ ( collec1027672124_state @ Q_24 ) ) )
% 3.28/1.75 => ( finite1084549118_state
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_34_finite__Collect__conjI,axiom,
% 3.28/1.75 ! [Q_24: pname > $o,P_42: pname > $o] :
% 3.28/1.75 ( ( ( finite_finite_pname @ ( collect_pname @ P_42 ) )
% 3.28/1.75 | ( finite_finite_pname @ ( collect_pname @ Q_24 ) ) )
% 3.28/1.75 => ( finite_finite_pname
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_35_image__constant__conv,axiom,
% 3.28/1.75 ! [C_54: pname,A_197: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( A_197 = bot_bo70021908tate_o )
% 3.28/1.75 => ( ( image_8178176_pname
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : C_54
% 3.28/1.75 @ A_197 )
% 3.28/1.75 = bot_bot_pname_o ) )
% 3.28/1.75 & ( ( A_197 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( image_8178176_pname
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : C_54
% 3.28/1.75 @ A_197 )
% 3.28/1.75 = ( insert_pname @ C_54 @ bot_bot_pname_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_36_image__constant__conv,axiom,
% 3.28/1.75 ! [C_54: hoare_1167836817_state,A_197: pname > $o] :
% 3.28/1.75 ( ( ( A_197 = bot_bot_pname_o )
% 3.28/1.75 => ( ( image_575578384_state
% 3.28/1.75 @ ^ [X_5: pname] : C_54
% 3.28/1.75 @ A_197 )
% 3.28/1.75 = bot_bo70021908tate_o ) )
% 3.28/1.75 & ( ( A_197 != bot_bot_pname_o )
% 3.28/1.75 => ( ( image_575578384_state
% 3.28/1.75 @ ^ [X_5: pname] : C_54
% 3.28/1.75 @ A_197 )
% 3.28/1.75 = ( insert2134838167_state @ C_54 @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_37_image__constant,axiom,
% 3.28/1.75 ! [C_53: pname,X_101: hoare_1167836817_state,A_196: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_101 @ A_196 )
% 3.28/1.75 => ( ( image_8178176_pname
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : C_53
% 3.28/1.75 @ A_196 )
% 3.28/1.75 = ( insert_pname @ C_53 @ bot_bot_pname_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_38_image__constant,axiom,
% 3.28/1.75 ! [C_53: hoare_1167836817_state,X_101: pname,A_196: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_101 @ A_196 )
% 3.28/1.75 => ( ( image_575578384_state
% 3.28/1.75 @ ^ [X_5: pname] : C_53
% 3.28/1.75 @ A_196 )
% 3.28/1.75 = ( insert2134838167_state @ C_53 @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_39_insert__dom,axiom,
% 3.28/1.75 ! [F_60: pname > option_com,X_100: pname,Y_49: com] :
% 3.28/1.75 ( ( ( F_60 @ X_100 )
% 3.28/1.75 = ( some_com @ Y_49 ) )
% 3.28/1.75 => ( ( insert_pname @ X_100 @ ( dom_pname_com @ F_60 ) )
% 3.28/1.75 = ( dom_pname_com @ F_60 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_40_finite__surj,axiom,
% 3.28/1.75 ! [B_130: ( pname > $o ) > $o,F_59: hoare_1167836817_state > pname > $o,A_195: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_195 )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ B_130 @ ( image_2066861949name_o @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite297249702name_o @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_41_finite__surj,axiom,
% 3.28/1.75 ! [B_130: ( hoare_1167836817_state > $o ) > $o,F_59: hoare_1167836817_state > hoare_1167836817_state > $o,A_195: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_195 )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ B_130 @ ( image_1745649338tate_o @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite1380128977tate_o @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_42_finite__surj,axiom,
% 3.28/1.75 ! [B_130: pname > $o,F_59: hoare_1167836817_state > pname,A_195: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_195 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_8178176_pname @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite_finite_pname @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_43_finite__surj,axiom,
% 3.28/1.75 ! [B_130: ( pname > $o ) > $o,F_59: pname > pname > $o,A_195: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_195 )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ B_130 @ ( image_pname_pname_o @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite297249702name_o @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_44_finite__surj,axiom,
% 3.28/1.75 ! [B_130: ( hoare_1167836817_state > $o ) > $o,F_59: pname > hoare_1167836817_state > $o,A_195: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_195 )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ B_130 @ ( image_475339327tate_o @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite1380128977tate_o @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_45_finite__surj,axiom,
% 3.28/1.75 ! [B_130: pname > $o,F_59: pname > pname,A_195: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_195 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_pname_pname @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite_finite_pname @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_46_finite__surj,axiom,
% 3.28/1.75 ! [B_130: hoare_1167836817_state > $o,F_59: ( pname > $o ) > hoare_1167836817_state,A_195: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ A_195 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_130 @ ( image_1381916541_state @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite1084549118_state @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_47_finite__surj,axiom,
% 3.28/1.75 ! [B_130: hoare_1167836817_state > $o,F_59: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_195: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ A_195 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_130 @ ( image_635813834_state @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite1084549118_state @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_48_finite__surj,axiom,
% 3.28/1.75 ! [B_130: pname > $o,F_59: ( pname > $o ) > pname,A_195: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ A_195 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_pname_o_pname @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite_finite_pname @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_49_finite__surj,axiom,
% 3.28/1.75 ! [B_130: pname > $o,F_59: ( hoare_1167836817_state > $o ) > pname,A_195: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ A_195 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_130 @ ( image_980295115_pname @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite_finite_pname @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_50_finite__surj,axiom,
% 3.28/1.75 ! [B_130: hoare_1167836817_state > $o,F_59: pname > hoare_1167836817_state,A_195: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_195 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_130 @ ( image_575578384_state @ F_59 @ A_195 ) )
% 3.28/1.75 => ( finite1084549118_state @ B_130 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_51_subset__singletonD,axiom,
% 3.28/1.75 ! [A_194: pname > $o,X_99: pname] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_194 @ ( insert_pname @ X_99 @ bot_bot_pname_o ) )
% 3.28/1.75 => ( ( A_194 = bot_bot_pname_o )
% 3.28/1.75 | ( A_194
% 3.28/1.75 = ( insert_pname @ X_99 @ bot_bot_pname_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_52_subset__singletonD,axiom,
% 3.28/1.75 ! [A_194: hoare_1167836817_state > $o,X_99: hoare_1167836817_state] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_194 @ ( insert2134838167_state @ X_99 @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ( A_194 = bot_bo70021908tate_o )
% 3.28/1.75 | ( A_194
% 3.28/1.75 = ( insert2134838167_state @ X_99 @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_53_MGF,axiom,
% 3.28/1.75 ! [C_21: com] :
% 3.28/1.75 ( hoare_1201148605gleton
% 3.28/1.75 => ( wT_bodies
% 3.28/1.75 => ( ( wt @ C_21 )
% 3.28/1.75 => ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_54_emptyE,axiom,
% 3.28/1.75 ! [A_193: pname] :
% 3.28/1.75 ~ ( member_pname @ A_193 @ bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_55_emptyE,axiom,
% 3.28/1.75 ! [A_193: hoare_1167836817_state] :
% 3.28/1.75 ~ ( member2058392318_state @ A_193 @ bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_56_insertCI,axiom,
% 3.28/1.75 ! [B_129: pname,A_192: pname,B_128: pname > $o] :
% 3.28/1.75 ( ( ~ ( member_pname @ A_192 @ B_128 )
% 3.28/1.75 => ( A_192 = B_129 ) )
% 3.28/1.75 => ( member_pname @ A_192 @ ( insert_pname @ B_129 @ B_128 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_57_insertCI,axiom,
% 3.28/1.75 ! [B_129: hoare_1167836817_state,A_192: hoare_1167836817_state,B_128: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ~ ( member2058392318_state @ A_192 @ B_128 )
% 3.28/1.75 => ( A_192 = B_129 ) )
% 3.28/1.75 => ( member2058392318_state @ A_192 @ ( insert2134838167_state @ B_129 @ B_128 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_58_insertE,axiom,
% 3.28/1.75 ! [A_191: pname,B_127: pname,A_190: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_191 @ ( insert_pname @ B_127 @ A_190 ) )
% 3.28/1.75 => ( ( A_191 != B_127 )
% 3.28/1.75 => ( member_pname @ A_191 @ A_190 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_59_insertE,axiom,
% 3.28/1.75 ! [A_191: hoare_1167836817_state,B_127: hoare_1167836817_state,A_190: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_191 @ ( insert2134838167_state @ B_127 @ A_190 ) )
% 3.28/1.75 => ( ( A_191 != B_127 )
% 3.28/1.75 => ( member2058392318_state @ A_191 @ A_190 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_60_equalityI,axiom,
% 3.28/1.75 ! [A_189: pname > $o,B_126: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_189 @ B_126 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_126 @ A_189 )
% 3.28/1.75 => ( A_189 = B_126 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_61_equalityI,axiom,
% 3.28/1.75 ! [A_189: hoare_1167836817_state > $o,B_126: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_189 @ B_126 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_126 @ A_189 )
% 3.28/1.75 => ( A_189 = B_126 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_62_subsetD,axiom,
% 3.28/1.75 ! [C_52: pname,A_188: pname > $o,B_125: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_188 @ B_125 )
% 3.28/1.75 => ( ( member_pname @ C_52 @ A_188 )
% 3.28/1.75 => ( member_pname @ C_52 @ B_125 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_63_subsetD,axiom,
% 3.28/1.75 ! [C_52: hoare_1167836817_state,A_188: hoare_1167836817_state > $o,B_125: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_188 @ B_125 )
% 3.28/1.75 => ( ( member2058392318_state @ C_52 @ A_188 )
% 3.28/1.75 => ( member2058392318_state @ C_52 @ B_125 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_64_image__eqI,axiom,
% 3.28/1.75 ! [A_187: hoare_1167836817_state > $o,B_124: pname,F_58: hoare_1167836817_state > pname,X_98: hoare_1167836817_state] :
% 3.28/1.75 ( ( B_124
% 3.28/1.75 = ( F_58 @ X_98 ) )
% 3.28/1.75 => ( ( member2058392318_state @ X_98 @ A_187 )
% 3.28/1.75 => ( member_pname @ B_124 @ ( image_8178176_pname @ F_58 @ A_187 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_65_image__eqI,axiom,
% 3.28/1.75 ! [A_187: pname > $o,B_124: hoare_1167836817_state,F_58: pname > hoare_1167836817_state,X_98: pname] :
% 3.28/1.75 ( ( B_124
% 3.28/1.75 = ( F_58 @ X_98 ) )
% 3.28/1.75 => ( ( member_pname @ X_98 @ A_187 )
% 3.28/1.75 => ( member2058392318_state @ B_124 @ ( image_575578384_state @ F_58 @ A_187 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_66_equals0D,axiom,
% 3.28/1.75 ! [A_186: pname,A_185: pname > $o] :
% 3.28/1.75 ( ( A_185 = bot_bot_pname_o )
% 3.28/1.75 => ~ ( member_pname @ A_186 @ A_185 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_67_equals0D,axiom,
% 3.28/1.75 ! [A_186: hoare_1167836817_state,A_185: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_185 = bot_bo70021908tate_o )
% 3.28/1.75 => ~ ( member2058392318_state @ A_186 @ A_185 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_68_Collect__empty__eq,axiom,
% 3.28/1.75 ! [P_41: pname > $o] :
% 3.28/1.75 ( ( ( collect_pname @ P_41 )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 <=> ! [X_5: pname] :
% 3.28/1.75 ~ ( P_41 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_69_Collect__empty__eq,axiom,
% 3.28/1.75 ! [P_41: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ( collect_pname_o @ P_41 )
% 3.28/1.75 = bot_bot_pname_o_o )
% 3.28/1.75 <=> ! [X_5: pname > $o] :
% 3.28/1.75 ~ ( P_41 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_70_Collect__empty__eq,axiom,
% 3.28/1.75 ! [P_41: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ( collec269976083tate_o @ P_41 )
% 3.28/1.75 = bot_bo691907561te_o_o )
% 3.28/1.75 <=> ! [X_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ~ ( P_41 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_71_Collect__empty__eq,axiom,
% 3.28/1.75 ! [P_41: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( collec1027672124_state @ P_41 )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 <=> ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ~ ( P_41 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_72_empty__iff,axiom,
% 3.28/1.75 ! [C_51: pname] :
% 3.28/1.75 ~ ( member_pname @ C_51 @ bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_73_empty__iff,axiom,
% 3.28/1.75 ! [C_51: hoare_1167836817_state] :
% 3.28/1.75 ~ ( member2058392318_state @ C_51 @ bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_74_empty__Collect__eq,axiom,
% 3.28/1.75 ! [P_40: pname > $o] :
% 3.28/1.75 ( ( bot_bot_pname_o
% 3.28/1.75 = ( collect_pname @ P_40 ) )
% 3.28/1.75 <=> ! [X_5: pname] :
% 3.28/1.75 ~ ( P_40 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_75_empty__Collect__eq,axiom,
% 3.28/1.75 ! [P_40: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( bot_bot_pname_o_o
% 3.28/1.75 = ( collect_pname_o @ P_40 ) )
% 3.28/1.75 <=> ! [X_5: pname > $o] :
% 3.28/1.75 ~ ( P_40 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_76_empty__Collect__eq,axiom,
% 3.28/1.75 ! [P_40: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( bot_bo691907561te_o_o
% 3.28/1.75 = ( collec269976083tate_o @ P_40 ) )
% 3.28/1.75 <=> ! [X_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ~ ( P_40 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_77_empty__Collect__eq,axiom,
% 3.28/1.75 ! [P_40: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( bot_bo70021908tate_o
% 3.28/1.75 = ( collec1027672124_state @ P_40 ) )
% 3.28/1.75 <=> ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ~ ( P_40 @ X_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_78_ex__in__conv,axiom,
% 3.28/1.75 ! [A_184: pname > $o] :
% 3.28/1.75 ( ? [X_5: pname] : ( member_pname @ X_5 @ A_184 )
% 3.28/1.75 <=> ( A_184 != bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_79_ex__in__conv,axiom,
% 3.28/1.75 ! [A_184: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ? [X_5: hoare_1167836817_state] : ( member2058392318_state @ X_5 @ A_184 )
% 3.28/1.75 <=> ( A_184 != bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_80_all__not__in__conv,axiom,
% 3.28/1.75 ! [A_183: pname > $o] :
% 3.28/1.75 ( ! [X_5: pname] :
% 3.28/1.75 ~ ( member_pname @ X_5 @ A_183 )
% 3.28/1.75 <=> ( A_183 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_81_all__not__in__conv,axiom,
% 3.28/1.75 ! [A_183: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ~ ( member2058392318_state @ X_5 @ A_183 )
% 3.28/1.75 <=> ( A_183 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_82_empty__def,axiom,
% 3.28/1.75 ( bot_bot_pname_o
% 3.28/1.75 = ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : $false ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_83_empty__def,axiom,
% 3.28/1.75 ( bot_bot_pname_o_o
% 3.28/1.75 = ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : $false ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_84_empty__def,axiom,
% 3.28/1.75 ( bot_bo691907561te_o_o
% 3.28/1.75 = ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : $false ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_85_empty__def,axiom,
% 3.28/1.75 ( bot_bo70021908tate_o
% 3.28/1.75 = ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : $false ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_86_insert__absorb,axiom,
% 3.28/1.75 ! [A_182: pname,A_181: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_182 @ A_181 )
% 3.28/1.75 => ( ( insert_pname @ A_182 @ A_181 )
% 3.28/1.75 = A_181 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_87_insert__absorb,axiom,
% 3.28/1.75 ! [A_182: hoare_1167836817_state,A_181: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_182 @ A_181 )
% 3.28/1.75 => ( ( insert2134838167_state @ A_182 @ A_181 )
% 3.28/1.75 = A_181 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_88_insertI2,axiom,
% 3.28/1.75 ! [B_123: pname,A_180: pname,B_122: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_180 @ B_122 )
% 3.28/1.75 => ( member_pname @ A_180 @ ( insert_pname @ B_123 @ B_122 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_89_insertI2,axiom,
% 3.28/1.75 ! [B_123: hoare_1167836817_state,A_180: hoare_1167836817_state,B_122: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_180 @ B_122 )
% 3.28/1.75 => ( member2058392318_state @ A_180 @ ( insert2134838167_state @ B_123 @ B_122 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_90_insert__ident,axiom,
% 3.28/1.75 ! [B_121: pname > $o,X_97: pname,A_179: pname > $o] :
% 3.28/1.75 ( ~ ( member_pname @ X_97 @ A_179 )
% 3.28/1.75 => ( ~ ( member_pname @ X_97 @ B_121 )
% 3.28/1.75 => ( ( ( insert_pname @ X_97 @ A_179 )
% 3.28/1.75 = ( insert_pname @ X_97 @ B_121 ) )
% 3.28/1.75 <=> ( A_179 = B_121 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_91_insert__ident,axiom,
% 3.28/1.75 ! [B_121: hoare_1167836817_state > $o,X_97: hoare_1167836817_state,A_179: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( member2058392318_state @ X_97 @ A_179 )
% 3.28/1.75 => ( ~ ( member2058392318_state @ X_97 @ B_121 )
% 3.28/1.75 => ( ( ( insert2134838167_state @ X_97 @ A_179 )
% 3.28/1.75 = ( insert2134838167_state @ X_97 @ B_121 ) )
% 3.28/1.75 <=> ( A_179 = B_121 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_92_insert__code,axiom,
% 3.28/1.75 ! [Y_48: pname,A_178: pname > $o,X_96: pname] :
% 3.28/1.75 ( ( insert_pname @ Y_48 @ A_178 @ X_96 )
% 3.28/1.75 <=> ( ( Y_48 = X_96 )
% 3.28/1.75 | ( A_178 @ X_96 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_93_insert__code,axiom,
% 3.28/1.75 ! [Y_48: hoare_1167836817_state,A_178: hoare_1167836817_state > $o,X_96: hoare_1167836817_state] :
% 3.28/1.75 ( ( insert2134838167_state @ Y_48 @ A_178 @ X_96 )
% 3.28/1.75 <=> ( ( Y_48 = X_96 )
% 3.28/1.75 | ( A_178 @ X_96 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_94_insert__iff,axiom,
% 3.28/1.75 ! [A_177: pname,B_120: pname,A_176: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_177 @ ( insert_pname @ B_120 @ A_176 ) )
% 3.28/1.75 <=> ( ( A_177 = B_120 )
% 3.28/1.75 | ( member_pname @ A_177 @ A_176 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_95_insert__iff,axiom,
% 3.28/1.75 ! [A_177: hoare_1167836817_state,B_120: hoare_1167836817_state,A_176: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_177 @ ( insert2134838167_state @ B_120 @ A_176 ) )
% 3.28/1.75 <=> ( ( A_177 = B_120 )
% 3.28/1.75 | ( member2058392318_state @ A_177 @ A_176 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_96_insert__commute,axiom,
% 3.28/1.75 ! [X_95: pname,Y_47: pname,A_175: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ X_95 @ ( insert_pname @ Y_47 @ A_175 ) )
% 3.28/1.75 = ( insert_pname @ Y_47 @ ( insert_pname @ X_95 @ A_175 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_97_insert__commute,axiom,
% 3.28/1.75 ! [X_95: hoare_1167836817_state,Y_47: hoare_1167836817_state,A_175: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ X_95 @ ( insert2134838167_state @ Y_47 @ A_175 ) )
% 3.28/1.75 = ( insert2134838167_state @ Y_47 @ ( insert2134838167_state @ X_95 @ A_175 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_98_insert__absorb2,axiom,
% 3.28/1.75 ! [X_94: pname,A_174: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ X_94 @ ( insert_pname @ X_94 @ A_174 ) )
% 3.28/1.75 = ( insert_pname @ X_94 @ A_174 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_99_insert__absorb2,axiom,
% 3.28/1.75 ! [X_94: hoare_1167836817_state,A_174: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ X_94 @ ( insert2134838167_state @ X_94 @ A_174 ) )
% 3.28/1.75 = ( insert2134838167_state @ X_94 @ A_174 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_100_insert__Collect,axiom,
% 3.28/1.75 ! [A_173: pname,P_39: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ A_173 @ ( collect_pname @ P_39 ) )
% 3.28/1.75 = ( collect_pname
% 3.28/1.75 @ ^ [U_2: pname] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_101_insert__Collect,axiom,
% 3.28/1.75 ! [A_173: pname > $o,P_39: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( insert_pname_o @ A_173 @ ( collect_pname_o @ P_39 ) )
% 3.28/1.75 = ( collect_pname_o
% 3.28/1.75 @ ^ [U_2: pname > $o] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_102_insert__Collect,axiom,
% 3.28/1.75 ! [A_173: hoare_1167836817_state > $o,P_39: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( insert999278200tate_o @ A_173 @ ( collec269976083tate_o @ P_39 ) )
% 3.28/1.75 = ( collec269976083tate_o
% 3.28/1.75 @ ^ [U_2: hoare_1167836817_state > $o] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_103_insert__Collect,axiom,
% 3.28/1.75 ! [A_173: hoare_1167836817_state,P_39: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ A_173 @ ( collec1027672124_state @ P_39 ) )
% 3.28/1.75 = ( collec1027672124_state
% 3.28/1.75 @ ^ [U_2: hoare_1167836817_state] : ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_104_insert__compr,axiom,
% 3.28/1.75 ! [A_172: pname,B_119: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ A_172 @ B_119 )
% 3.28/1.75 = ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (|) @ ( X_5 = A_172 ) @ ( member_pname @ X_5 @ B_119 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_105_insert__compr,axiom,
% 3.28/1.75 ! [A_172: pname > $o,B_119: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( insert_pname_o @ A_172 @ B_119 )
% 3.28/1.75 = ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (|) @ ( X_5 = A_172 ) @ ( member_pname_o @ X_5 @ B_119 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_106_insert__compr,axiom,
% 3.28/1.75 ! [A_172: hoare_1167836817_state > $o,B_119: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( insert999278200tate_o @ A_172 @ B_119 )
% 3.28/1.75 = ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( X_5 = A_172 ) @ ( member864234961tate_o @ X_5 @ B_119 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_107_insert__compr,axiom,
% 3.28/1.75 ! [A_172: hoare_1167836817_state,B_119: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ A_172 @ B_119 )
% 3.28/1.75 = ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( X_5 = A_172 ) @ ( member2058392318_state @ X_5 @ B_119 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_108_insertI1,axiom,
% 3.28/1.75 ! [A_171: pname,B_118: pname > $o] : ( member_pname @ A_171 @ ( insert_pname @ A_171 @ B_118 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_109_insertI1,axiom,
% 3.28/1.75 ! [A_171: hoare_1167836817_state,B_118: hoare_1167836817_state > $o] : ( member2058392318_state @ A_171 @ ( insert2134838167_state @ A_171 @ B_118 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_110_equalityE,axiom,
% 3.28/1.75 ! [A_170: pname > $o,B_117: pname > $o] :
% 3.28/1.75 ( ( A_170 = B_117 )
% 3.28/1.75 => ~ ( ( ord_less_eq_pname_o @ A_170 @ B_117 )
% 3.28/1.75 => ~ ( ord_less_eq_pname_o @ B_117 @ A_170 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_111_equalityE,axiom,
% 3.28/1.75 ! [A_170: hoare_1167836817_state > $o,B_117: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_170 = B_117 )
% 3.28/1.75 => ~ ( ( ord_le827224136tate_o @ A_170 @ B_117 )
% 3.28/1.75 => ~ ( ord_le827224136tate_o @ B_117 @ A_170 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_112_subset__trans,axiom,
% 3.28/1.75 ! [C_50: pname > $o,A_169: pname > $o,B_116: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_169 @ B_116 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_116 @ C_50 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ A_169 @ C_50 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_113_subset__trans,axiom,
% 3.28/1.75 ! [C_50: hoare_1167836817_state > $o,A_169: hoare_1167836817_state > $o,B_116: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_169 @ B_116 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_116 @ C_50 )
% 3.28/1.75 => ( ord_le827224136tate_o @ A_169 @ C_50 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_114_set__mp,axiom,
% 3.28/1.75 ! [X_93: pname,A_168: pname > $o,B_115: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_168 @ B_115 )
% 3.28/1.75 => ( ( member_pname @ X_93 @ A_168 )
% 3.28/1.75 => ( member_pname @ X_93 @ B_115 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_115_set__mp,axiom,
% 3.28/1.75 ! [X_93: hoare_1167836817_state,A_168: hoare_1167836817_state > $o,B_115: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_168 @ B_115 )
% 3.28/1.75 => ( ( member2058392318_state @ X_93 @ A_168 )
% 3.28/1.75 => ( member2058392318_state @ X_93 @ B_115 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_116_set__rev__mp,axiom,
% 3.28/1.75 ! [B_114: pname > $o,X_92: pname,A_167: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_92 @ A_167 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ A_167 @ B_114 )
% 3.28/1.75 => ( member_pname @ X_92 @ B_114 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_117_set__rev__mp,axiom,
% 3.28/1.75 ! [B_114: hoare_1167836817_state > $o,X_92: hoare_1167836817_state,A_167: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_92 @ A_167 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ A_167 @ B_114 )
% 3.28/1.75 => ( member2058392318_state @ X_92 @ B_114 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_118_in__mono,axiom,
% 3.28/1.75 ! [X_91: pname,A_166: pname > $o,B_113: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_166 @ B_113 )
% 3.28/1.75 => ( ( member_pname @ X_91 @ A_166 )
% 3.28/1.75 => ( member_pname @ X_91 @ B_113 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_119_in__mono,axiom,
% 3.28/1.75 ! [X_91: hoare_1167836817_state,A_166: hoare_1167836817_state > $o,B_113: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_166 @ B_113 )
% 3.28/1.75 => ( ( member2058392318_state @ X_91 @ A_166 )
% 3.28/1.75 => ( member2058392318_state @ X_91 @ B_113 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_120_equalityD2,axiom,
% 3.28/1.75 ! [A_165: pname > $o,B_112: pname > $o] :
% 3.28/1.75 ( ( A_165 = B_112 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ B_112 @ A_165 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_121_equalityD2,axiom,
% 3.28/1.75 ! [A_165: hoare_1167836817_state > $o,B_112: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_165 = B_112 )
% 3.28/1.75 => ( ord_le827224136tate_o @ B_112 @ A_165 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_122_equalityD1,axiom,
% 3.28/1.75 ! [A_164: pname > $o,B_111: pname > $o] :
% 3.28/1.75 ( ( A_164 = B_111 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ A_164 @ B_111 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_123_equalityD1,axiom,
% 3.28/1.75 ! [A_164: hoare_1167836817_state > $o,B_111: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_164 = B_111 )
% 3.28/1.75 => ( ord_le827224136tate_o @ A_164 @ B_111 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_124_set__eq__subset,axiom,
% 3.28/1.75 ! [A_163: pname > $o,B_110: pname > $o] :
% 3.28/1.75 ( ( A_163 = B_110 )
% 3.28/1.75 <=> ( ( ord_less_eq_pname_o @ A_163 @ B_110 )
% 3.28/1.75 & ( ord_less_eq_pname_o @ B_110 @ A_163 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_125_set__eq__subset,axiom,
% 3.28/1.75 ! [A_163: hoare_1167836817_state > $o,B_110: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_163 = B_110 )
% 3.28/1.75 <=> ( ( ord_le827224136tate_o @ A_163 @ B_110 )
% 3.28/1.75 & ( ord_le827224136tate_o @ B_110 @ A_163 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_126_subset__refl,axiom,
% 3.28/1.75 ! [A_162: pname > $o] : ( ord_less_eq_pname_o @ A_162 @ A_162 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_127_subset__refl,axiom,
% 3.28/1.75 ! [A_162: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A_162 @ A_162 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_128_rev__image__eqI,axiom,
% 3.28/1.75 ! [B_109: pname,F_57: hoare_1167836817_state > pname,X_90: hoare_1167836817_state,A_161: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_90 @ A_161 )
% 3.28/1.75 => ( ( B_109
% 3.28/1.75 = ( F_57 @ X_90 ) )
% 3.28/1.75 => ( member_pname @ B_109 @ ( image_8178176_pname @ F_57 @ A_161 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_129_rev__image__eqI,axiom,
% 3.28/1.75 ! [B_109: hoare_1167836817_state,F_57: pname > hoare_1167836817_state,X_90: pname,A_161: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_90 @ A_161 )
% 3.28/1.75 => ( ( B_109
% 3.28/1.75 = ( F_57 @ X_90 ) )
% 3.28/1.75 => ( member2058392318_state @ B_109 @ ( image_575578384_state @ F_57 @ A_161 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_130_imageI,axiom,
% 3.28/1.75 ! [F_56: hoare_1167836817_state > pname,X_89: hoare_1167836817_state,A_160: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_89 @ A_160 )
% 3.28/1.75 => ( member_pname @ ( F_56 @ X_89 ) @ ( image_8178176_pname @ F_56 @ A_160 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_131_imageI,axiom,
% 3.28/1.75 ! [F_56: pname > hoare_1167836817_state,X_89: pname,A_160: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_89 @ A_160 )
% 3.28/1.75 => ( member2058392318_state @ ( F_56 @ X_89 ) @ ( image_575578384_state @ F_56 @ A_160 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_132_image__iff,axiom,
% 3.28/1.75 ! [Z_21: hoare_1167836817_state,F_55: pname > hoare_1167836817_state,A_159: pname > $o] :
% 3.28/1.75 ( ( member2058392318_state @ Z_21 @ ( image_575578384_state @ F_55 @ A_159 ) )
% 3.28/1.75 <=> ? [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_159 )
% 3.28/1.75 & ( Z_21
% 3.28/1.75 = ( F_55 @ X_5 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_133_finite__Collect__disjI,axiom,
% 3.28/1.75 ! [P_38: ( pname > $o ) > $o,Q_23: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o
% 3.28/1.75 @ ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 3.28/1.75 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_38 ) )
% 3.28/1.75 & ( finite297249702name_o @ ( collect_pname_o @ Q_23 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_134_finite__Collect__disjI,axiom,
% 3.28/1.75 ! [P_38: ( hoare_1167836817_state > $o ) > $o,Q_23: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o
% 3.28/1.75 @ ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 3.28/1.75 <=> ( ( finite1380128977tate_o @ ( collec269976083tate_o @ P_38 ) )
% 3.28/1.75 & ( finite1380128977tate_o @ ( collec269976083tate_o @ Q_23 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_135_finite__Collect__disjI,axiom,
% 3.28/1.75 ! [P_38: hoare_1167836817_state > $o,Q_23: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 3.28/1.75 <=> ( ( finite1084549118_state @ ( collec1027672124_state @ P_38 ) )
% 3.28/1.75 & ( finite1084549118_state @ ( collec1027672124_state @ Q_23 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_136_finite__Collect__disjI,axiom,
% 3.28/1.75 ! [P_38: pname > $o,Q_23: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
% 3.28/1.75 <=> ( ( finite_finite_pname @ ( collect_pname @ P_38 ) )
% 3.28/1.75 & ( finite_finite_pname @ ( collect_pname @ Q_23 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_137_insert__compr__raw,axiom,
% 3.28/1.75 ! [X_5: pname,Xa: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ X_5 @ Xa )
% 3.28/1.75 = ( collect_pname
% 3.28/1.75 @ ^ [Y_2: pname] : ( (|) @ ( Y_2 = X_5 ) @ ( member_pname @ Y_2 @ Xa ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_138_insert__compr__raw,axiom,
% 3.28/1.75 ! [X_5: pname > $o,Xa: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( insert_pname_o @ X_5 @ Xa )
% 3.28/1.75 = ( collect_pname_o
% 3.28/1.75 @ ^ [Y_2: pname > $o] : ( (|) @ ( Y_2 = X_5 ) @ ( member_pname_o @ Y_2 @ Xa ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_139_insert__compr__raw,axiom,
% 3.28/1.75 ! [X_5: hoare_1167836817_state > $o,Xa: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( insert999278200tate_o @ X_5 @ Xa )
% 3.28/1.75 = ( collec269976083tate_o
% 3.28/1.75 @ ^ [Y_2: hoare_1167836817_state > $o] : ( (|) @ ( Y_2 = X_5 ) @ ( member864234961tate_o @ Y_2 @ Xa ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_140_insert__compr__raw,axiom,
% 3.28/1.75 ! [X_5: hoare_1167836817_state,Xa: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ X_5 @ Xa )
% 3.28/1.75 = ( collec1027672124_state
% 3.28/1.75 @ ^ [Y_2: hoare_1167836817_state] : ( (|) @ ( Y_2 = X_5 ) @ ( member2058392318_state @ Y_2 @ Xa ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_141_singleton__inject,axiom,
% 3.28/1.75 ! [A_158: pname,B_108: pname] :
% 3.28/1.75 ( ( ( insert_pname @ A_158 @ bot_bot_pname_o )
% 3.28/1.75 = ( insert_pname @ B_108 @ bot_bot_pname_o ) )
% 3.28/1.75 => ( A_158 = B_108 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_142_singleton__inject,axiom,
% 3.28/1.75 ! [A_158: hoare_1167836817_state,B_108: hoare_1167836817_state] :
% 3.28/1.75 ( ( ( insert2134838167_state @ A_158 @ bot_bo70021908tate_o )
% 3.28/1.75 = ( insert2134838167_state @ B_108 @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( A_158 = B_108 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_143_singletonE,axiom,
% 3.28/1.75 ! [B_107: pname,A_157: pname] :
% 3.28/1.75 ( ( member_pname @ B_107 @ ( insert_pname @ A_157 @ bot_bot_pname_o ) )
% 3.28/1.75 => ( B_107 = A_157 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_144_singletonE,axiom,
% 3.28/1.75 ! [B_107: hoare_1167836817_state,A_157: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ B_107 @ ( insert2134838167_state @ A_157 @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( B_107 = A_157 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_145_doubleton__eq__iff,axiom,
% 3.28/1.75 ! [A_156: pname,B_106: pname,C_49: pname,D_6: pname] :
% 3.28/1.75 ( ( ( insert_pname @ A_156 @ ( insert_pname @ B_106 @ bot_bot_pname_o ) )
% 3.28/1.75 = ( insert_pname @ C_49 @ ( insert_pname @ D_6 @ bot_bot_pname_o ) ) )
% 3.28/1.75 <=> ( ( ( A_156 = C_49 )
% 3.28/1.75 & ( B_106 = D_6 ) )
% 3.28/1.75 | ( ( A_156 = D_6 )
% 3.28/1.75 & ( B_106 = C_49 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_146_doubleton__eq__iff,axiom,
% 3.28/1.75 ! [A_156: hoare_1167836817_state,B_106: hoare_1167836817_state,C_49: hoare_1167836817_state,D_6: hoare_1167836817_state] :
% 3.28/1.75 ( ( ( insert2134838167_state @ A_156 @ ( insert2134838167_state @ B_106 @ bot_bo70021908tate_o ) )
% 3.28/1.75 = ( insert2134838167_state @ C_49 @ ( insert2134838167_state @ D_6 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 <=> ( ( ( A_156 = C_49 )
% 3.28/1.75 & ( B_106 = D_6 ) )
% 3.28/1.75 | ( ( A_156 = D_6 )
% 3.28/1.75 & ( B_106 = C_49 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_147_singleton__iff,axiom,
% 3.28/1.75 ! [B_105: pname,A_155: pname] :
% 3.28/1.75 ( ( member_pname @ B_105 @ ( insert_pname @ A_155 @ bot_bot_pname_o ) )
% 3.28/1.75 <=> ( B_105 = A_155 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_148_singleton__iff,axiom,
% 3.28/1.75 ! [B_105: hoare_1167836817_state,A_155: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ B_105 @ ( insert2134838167_state @ A_155 @ bot_bo70021908tate_o ) )
% 3.28/1.75 <=> ( B_105 = A_155 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_149_insert__not__empty,axiom,
% 3.28/1.75 ! [A_154: pname,A_153: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ A_154 @ A_153 )
% 3.28/1.75 != bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_150_insert__not__empty,axiom,
% 3.28/1.75 ! [A_154: hoare_1167836817_state,A_153: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ A_154 @ A_153 )
% 3.28/1.75 != bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_151_empty__not__insert,axiom,
% 3.28/1.75 ! [A_152: pname,A_151: pname > $o] :
% 3.28/1.75 ( bot_bot_pname_o
% 3.28/1.75 != ( insert_pname @ A_152 @ A_151 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_152_empty__not__insert,axiom,
% 3.28/1.75 ! [A_152: hoare_1167836817_state,A_151: hoare_1167836817_state > $o] :
% 3.28/1.75 ( bot_bo70021908tate_o
% 3.28/1.75 != ( insert2134838167_state @ A_152 @ A_151 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_153_finite__insert,axiom,
% 3.28/1.75 ! [A_150: pname > $o,A_149: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ ( insert_pname_o @ A_150 @ A_149 ) )
% 3.28/1.75 <=> ( finite297249702name_o @ A_149 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_154_finite__insert,axiom,
% 3.28/1.75 ! [A_150: hoare_1167836817_state > $o,A_149: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ ( insert999278200tate_o @ A_150 @ A_149 ) )
% 3.28/1.75 <=> ( finite1380128977tate_o @ A_149 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_155_finite__insert,axiom,
% 3.28/1.75 ! [A_150: pname,A_149: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ ( insert_pname @ A_150 @ A_149 ) )
% 3.28/1.75 <=> ( finite_finite_pname @ A_149 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_156_finite__insert,axiom,
% 3.28/1.75 ! [A_150: hoare_1167836817_state,A_149: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ ( insert2134838167_state @ A_150 @ A_149 ) )
% 3.28/1.75 <=> ( finite1084549118_state @ A_149 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_157_subset__empty,axiom,
% 3.28/1.75 ! [A_148: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_148 @ bot_bot_pname_o )
% 3.28/1.75 <=> ( A_148 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_158_subset__empty,axiom,
% 3.28/1.75 ! [A_148: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_148 @ bot_bo70021908tate_o )
% 3.28/1.75 <=> ( A_148 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_159_image__is__empty,axiom,
% 3.28/1.75 ! [F_54: hoare_1167836817_state > pname,A_147: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( image_8178176_pname @ F_54 @ A_147 )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 <=> ( A_147 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_160_image__is__empty,axiom,
% 3.28/1.75 ! [F_54: pname > hoare_1167836817_state,A_147: pname > $o] :
% 3.28/1.75 ( ( ( image_575578384_state @ F_54 @ A_147 )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 <=> ( A_147 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_161_image__empty,axiom,
% 3.28/1.75 ! [F_53: hoare_1167836817_state > pname] :
% 3.28/1.75 ( ( image_8178176_pname @ F_53 @ bot_bo70021908tate_o )
% 3.28/1.75 = bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_162_image__empty,axiom,
% 3.28/1.75 ! [F_53: pname > hoare_1167836817_state] :
% 3.28/1.75 ( ( image_575578384_state @ F_53 @ bot_bot_pname_o )
% 3.28/1.75 = bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_163_empty__is__image,axiom,
% 3.28/1.75 ! [F_52: hoare_1167836817_state > pname,A_146: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( bot_bot_pname_o
% 3.28/1.75 = ( image_8178176_pname @ F_52 @ A_146 ) )
% 3.28/1.75 <=> ( A_146 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_164_empty__is__image,axiom,
% 3.28/1.75 ! [F_52: pname > hoare_1167836817_state,A_146: pname > $o] :
% 3.28/1.75 ( ( bot_bo70021908tate_o
% 3.28/1.75 = ( image_575578384_state @ F_52 @ A_146 ) )
% 3.28/1.75 <=> ( A_146 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_165_finite__subset,axiom,
% 3.28/1.75 ! [A_145: ( pname > $o ) > $o,B_104: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ord_le1205211808me_o_o @ A_145 @ B_104 )
% 3.28/1.75 => ( ( finite297249702name_o @ B_104 )
% 3.28/1.75 => ( finite297249702name_o @ A_145 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_166_finite__subset,axiom,
% 3.28/1.75 ! [A_145: ( hoare_1167836817_state > $o ) > $o,B_104: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ord_le741939125te_o_o @ A_145 @ B_104 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ B_104 )
% 3.28/1.75 => ( finite1380128977tate_o @ A_145 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_167_finite__subset,axiom,
% 3.28/1.75 ! [A_145: hoare_1167836817_state > $o,B_104: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_145 @ B_104 )
% 3.28/1.75 => ( ( finite1084549118_state @ B_104 )
% 3.28/1.75 => ( finite1084549118_state @ A_145 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_168_finite__subset,axiom,
% 3.28/1.75 ! [A_145: pname > $o,B_104: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_145 @ B_104 )
% 3.28/1.75 => ( ( finite_finite_pname @ B_104 )
% 3.28/1.75 => ( finite_finite_pname @ A_145 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_169_rev__finite__subset,axiom,
% 3.28/1.75 ! [A_144: ( pname > $o ) > $o,B_103: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ B_103 )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ A_144 @ B_103 )
% 3.28/1.75 => ( finite297249702name_o @ A_144 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_170_rev__finite__subset,axiom,
% 3.28/1.75 ! [A_144: ( hoare_1167836817_state > $o ) > $o,B_103: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ B_103 )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ A_144 @ B_103 )
% 3.28/1.75 => ( finite1380128977tate_o @ A_144 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_171_rev__finite__subset,axiom,
% 3.28/1.75 ! [A_144: hoare_1167836817_state > $o,B_103: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ B_103 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ A_144 @ B_103 )
% 3.28/1.75 => ( finite1084549118_state @ A_144 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_172_rev__finite__subset,axiom,
% 3.28/1.75 ! [A_144: pname > $o,B_103: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ B_103 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ A_144 @ B_103 )
% 3.28/1.75 => ( finite_finite_pname @ A_144 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_173_insert__mono,axiom,
% 3.28/1.75 ! [A_143: pname,C_48: pname > $o,D_5: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ C_48 @ D_5 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( insert_pname @ A_143 @ C_48 ) @ ( insert_pname @ A_143 @ D_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_174_insert__mono,axiom,
% 3.28/1.75 ! [A_143: hoare_1167836817_state,C_48: hoare_1167836817_state > $o,D_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ C_48 @ D_5 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( insert2134838167_state @ A_143 @ C_48 ) @ ( insert2134838167_state @ A_143 @ D_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_175_mem__def,axiom,
% 3.28/1.75 ! [X_88: pname,A_142: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_88 @ A_142 )
% 3.28/1.75 <=> ( A_142 @ X_88 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_176_mem__def,axiom,
% 3.28/1.75 ! [X_88: hoare_1167836817_state,A_142: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_88 @ A_142 )
% 3.28/1.75 <=> ( A_142 @ X_88 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_177_Collect__def,axiom,
% 3.28/1.75 ! [P_37: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( collec1027672124_state @ P_37 )
% 3.28/1.75 = P_37 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_178_Collect__def,axiom,
% 3.28/1.75 ! [P_37: pname > $o] :
% 3.28/1.75 ( ( collect_pname @ P_37 )
% 3.28/1.75 = P_37 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_179_Collect__def,axiom,
% 3.28/1.75 ! [P_37: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( collect_pname_o @ P_37 )
% 3.28/1.75 = P_37 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_180_Collect__def,axiom,
% 3.28/1.75 ! [P_37: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( collec269976083tate_o @ P_37 )
% 3.28/1.75 = P_37 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_181_subset__insertI2,axiom,
% 3.28/1.75 ! [B_102: pname,A_141: pname > $o,B_101: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_141 @ B_101 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ A_141 @ ( insert_pname @ B_102 @ B_101 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_182_subset__insertI2,axiom,
% 3.28/1.75 ! [B_102: hoare_1167836817_state,A_141: hoare_1167836817_state > $o,B_101: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_141 @ B_101 )
% 3.28/1.75 => ( ord_le827224136tate_o @ A_141 @ ( insert2134838167_state @ B_102 @ B_101 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_183_subset__insert,axiom,
% 3.28/1.75 ! [B_100: pname > $o,X_87: pname,A_140: pname > $o] :
% 3.28/1.75 ( ~ ( member_pname @ X_87 @ A_140 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ A_140 @ ( insert_pname @ X_87 @ B_100 ) )
% 3.28/1.75 <=> ( ord_less_eq_pname_o @ A_140 @ B_100 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_184_subset__insert,axiom,
% 3.28/1.75 ! [B_100: hoare_1167836817_state > $o,X_87: hoare_1167836817_state,A_140: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( member2058392318_state @ X_87 @ A_140 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ A_140 @ ( insert2134838167_state @ X_87 @ B_100 ) )
% 3.28/1.75 <=> ( ord_le827224136tate_o @ A_140 @ B_100 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_185_insert__subset,axiom,
% 3.28/1.75 ! [X_86: pname,A_139: pname > $o,B_99: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_86 @ A_139 ) @ B_99 )
% 3.28/1.75 <=> ( ( member_pname @ X_86 @ B_99 )
% 3.28/1.75 & ( ord_less_eq_pname_o @ A_139 @ B_99 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_186_insert__subset,axiom,
% 3.28/1.75 ! [X_86: hoare_1167836817_state,A_139: hoare_1167836817_state > $o,B_99: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ ( insert2134838167_state @ X_86 @ A_139 ) @ B_99 )
% 3.28/1.75 <=> ( ( member2058392318_state @ X_86 @ B_99 )
% 3.28/1.75 & ( ord_le827224136tate_o @ A_139 @ B_99 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_187_subset__insertI,axiom,
% 3.28/1.75 ! [B_98: pname > $o,A_138: pname] : ( ord_less_eq_pname_o @ B_98 @ ( insert_pname @ A_138 @ B_98 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_188_subset__insertI,axiom,
% 3.28/1.75 ! [B_98: hoare_1167836817_state > $o,A_138: hoare_1167836817_state] : ( ord_le827224136tate_o @ B_98 @ ( insert2134838167_state @ A_138 @ B_98 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_189_insert__image,axiom,
% 3.28/1.75 ! [F_51: hoare_1167836817_state > pname,X_85: hoare_1167836817_state,A_137: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_85 @ A_137 )
% 3.28/1.75 => ( ( insert_pname @ ( F_51 @ X_85 ) @ ( image_8178176_pname @ F_51 @ A_137 ) )
% 3.28/1.75 = ( image_8178176_pname @ F_51 @ A_137 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_190_insert__image,axiom,
% 3.28/1.75 ! [F_51: pname > hoare_1167836817_state,X_85: pname,A_137: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_85 @ A_137 )
% 3.28/1.75 => ( ( insert2134838167_state @ ( F_51 @ X_85 ) @ ( image_575578384_state @ F_51 @ A_137 ) )
% 3.28/1.75 = ( image_575578384_state @ F_51 @ A_137 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_191_image__insert,axiom,
% 3.28/1.75 ! [F_50: hoare_1167836817_state > pname,A_136: hoare_1167836817_state,B_97: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( image_8178176_pname @ F_50 @ ( insert2134838167_state @ A_136 @ B_97 ) )
% 3.28/1.75 = ( insert_pname @ ( F_50 @ A_136 ) @ ( image_8178176_pname @ F_50 @ B_97 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_192_image__insert,axiom,
% 3.28/1.75 ! [F_50: pname > hoare_1167836817_state,A_136: pname,B_97: pname > $o] :
% 3.28/1.75 ( ( image_575578384_state @ F_50 @ ( insert_pname @ A_136 @ B_97 ) )
% 3.28/1.75 = ( insert2134838167_state @ ( F_50 @ A_136 ) @ ( image_575578384_state @ F_50 @ B_97 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_193_image__mono,axiom,
% 3.28/1.75 ! [F_49: hoare_1167836817_state > pname,A_135: hoare_1167836817_state > $o,B_96: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_135 @ B_96 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( image_8178176_pname @ F_49 @ A_135 ) @ ( image_8178176_pname @ F_49 @ B_96 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_194_image__mono,axiom,
% 3.28/1.75 ! [F_49: pname > hoare_1167836817_state,A_135: pname > $o,B_96: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_135 @ B_96 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( image_575578384_state @ F_49 @ A_135 ) @ ( image_575578384_state @ F_49 @ B_96 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_195_subset__image__iff,axiom,
% 3.28/1.75 ! [B_95: pname > $o,F_48: hoare_1167836817_state > pname,A_134: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ B_95 @ ( image_8178176_pname @ F_48 @ A_134 ) )
% 3.28/1.75 <=> ? [AA: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ AA @ A_134 )
% 3.28/1.75 & ( B_95
% 3.28/1.75 = ( image_8178176_pname @ F_48 @ AA ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_196_subset__image__iff,axiom,
% 3.28/1.75 ! [B_95: hoare_1167836817_state > $o,F_48: pname > hoare_1167836817_state,A_134: pname > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ B_95 @ ( image_575578384_state @ F_48 @ A_134 ) )
% 3.28/1.75 <=> ? [AA: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ AA @ A_134 )
% 3.28/1.75 & ( B_95
% 3.28/1.75 = ( image_575578384_state @ F_48 @ AA ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_197_domI,axiom,
% 3.28/1.75 ! [M_2: pname > option_com,A_133: pname,B_94: com] :
% 3.28/1.75 ( ( ( M_2 @ A_133 )
% 3.28/1.75 = ( some_com @ B_94 ) )
% 3.28/1.75 => ( member_pname @ A_133 @ ( dom_pname_com @ M_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_198_Collect__conv__if,axiom,
% 3.28/1.75 ! [P_36: pname > $o,A_132: pname] :
% 3.28/1.75 ( ( ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = ( insert_pname @ A_132 @ bot_bot_pname_o ) ) )
% 3.28/1.75 & ( ~ ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = bot_bot_pname_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_199_Collect__conv__if,axiom,
% 3.28/1.75 ! [P_36: ( pname > $o ) > $o,A_132: pname > $o] :
% 3.28/1.75 ( ( ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = ( insert_pname_o @ A_132 @ bot_bot_pname_o_o ) ) )
% 3.28/1.75 & ( ~ ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = bot_bot_pname_o_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_200_Collect__conv__if,axiom,
% 3.28/1.75 ! [P_36: ( hoare_1167836817_state > $o ) > $o,A_132: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = ( insert999278200tate_o @ A_132 @ bot_bo691907561te_o_o ) ) )
% 3.28/1.75 & ( ~ ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = bot_bo691907561te_o_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_201_Collect__conv__if,axiom,
% 3.28/1.75 ! [P_36: hoare_1167836817_state > $o,A_132: hoare_1167836817_state] :
% 3.28/1.75 ( ( ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = ( insert2134838167_state @ A_132 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 & ( ~ ( P_36 @ A_132 )
% 3.28/1.75 => ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
% 3.28/1.75 = bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_202_Collect__conv__if2,axiom,
% 3.28/1.75 ! [P_35: pname > $o,A_131: pname] :
% 3.28/1.75 ( ( ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = ( insert_pname @ A_131 @ bot_bot_pname_o ) ) )
% 3.28/1.75 & ( ~ ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = bot_bot_pname_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_203_Collect__conv__if2,axiom,
% 3.28/1.75 ! [P_35: ( pname > $o ) > $o,A_131: pname > $o] :
% 3.28/1.75 ( ( ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = ( insert_pname_o @ A_131 @ bot_bot_pname_o_o ) ) )
% 3.28/1.75 & ( ~ ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = bot_bot_pname_o_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_204_Collect__conv__if2,axiom,
% 3.28/1.75 ! [P_35: ( hoare_1167836817_state > $o ) > $o,A_131: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = ( insert999278200tate_o @ A_131 @ bot_bo691907561te_o_o ) ) )
% 3.28/1.75 & ( ~ ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = bot_bo691907561te_o_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_205_Collect__conv__if2,axiom,
% 3.28/1.75 ! [P_35: hoare_1167836817_state > $o,A_131: hoare_1167836817_state] :
% 3.28/1.75 ( ( ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = ( insert2134838167_state @ A_131 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 & ( ~ ( P_35 @ A_131 )
% 3.28/1.75 => ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
% 3.28/1.75 = bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_206_singleton__conv,axiom,
% 3.28/1.75 ! [A_130: pname] :
% 3.28/1.75 ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( X_5 = A_130 ) )
% 3.28/1.75 = ( insert_pname @ A_130 @ bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_207_singleton__conv,axiom,
% 3.28/1.75 ! [A_130: pname > $o] :
% 3.28/1.75 ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( X_5 = A_130 ) )
% 3.28/1.75 = ( insert_pname_o @ A_130 @ bot_bot_pname_o_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_208_singleton__conv,axiom,
% 3.28/1.75 ! [A_130: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( X_5 = A_130 ) )
% 3.28/1.75 = ( insert999278200tate_o @ A_130 @ bot_bo691907561te_o_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_209_singleton__conv,axiom,
% 3.28/1.75 ! [A_130: hoare_1167836817_state] :
% 3.28/1.75 ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( X_5 = A_130 ) )
% 3.28/1.75 = ( insert2134838167_state @ A_130 @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_210_singleton__conv2,axiom,
% 3.28/1.75 ! [A_129: pname] :
% 3.28/1.75 ( ( collect_pname @ ( fequal_pname @ A_129 ) )
% 3.28/1.75 = ( insert_pname @ A_129 @ bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_211_singleton__conv2,axiom,
% 3.28/1.75 ! [A_129: pname > $o] :
% 3.28/1.75 ( ( collect_pname_o @ ( fequal_pname_o @ A_129 ) )
% 3.28/1.75 = ( insert_pname_o @ A_129 @ bot_bot_pname_o_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_212_singleton__conv2,axiom,
% 3.28/1.75 ! [A_129: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( collec269976083tate_o @ ( fequal1486222077tate_o @ A_129 ) )
% 3.28/1.75 = ( insert999278200tate_o @ A_129 @ bot_bo691907561te_o_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_213_singleton__conv2,axiom,
% 3.28/1.75 ! [A_129: hoare_1167836817_state] :
% 3.28/1.75 ( ( collec1027672124_state @ ( fequal1831255762_state @ A_129 ) )
% 3.28/1.75 = ( insert2134838167_state @ A_129 @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_214_MGF__lemma1,axiom,
% 3.28/1.75 ! [C_21: com,G_3: hoare_1167836817_state > $o] :
% 3.28/1.75 ( hoare_1201148605gleton
% 3.28/1.75 => ( ! [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ ( dom_pname_com @ body ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_5 ) ) @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 => ( ( wt @ C_21 )
% 3.28/1.75 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_215_WT__bodiesD,axiom,
% 3.28/1.75 ! [Pn_1: pname,B_42: com] :
% 3.28/1.75 ( wT_bodies
% 3.28/1.75 => ( ( ( body @ Pn_1 )
% 3.28/1.75 = ( some_com @ B_42 ) )
% 3.28/1.75 => ( wt @ B_42 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_216_imageE,axiom,
% 3.28/1.75 ! [B_93: pname,F_47: hoare_1167836817_state > pname,A_128: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member_pname @ B_93 @ ( image_8178176_pname @ F_47 @ A_128 ) )
% 3.28/1.75 => ~ ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( B_93
% 3.28/1.75 = ( F_47 @ X_5 ) )
% 3.28/1.75 => ~ ( member2058392318_state @ X_5 @ A_128 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_217_imageE,axiom,
% 3.28/1.75 ! [B_93: hoare_1167836817_state,F_47: pname > hoare_1167836817_state,A_128: pname > $o] :
% 3.28/1.75 ( ( member2058392318_state @ B_93 @ ( image_575578384_state @ F_47 @ A_128 ) )
% 3.28/1.75 => ~ ! [X_5: pname] :
% 3.28/1.75 ( ( B_93
% 3.28/1.75 = ( F_47 @ X_5 ) )
% 3.28/1.75 => ~ ( member_pname @ X_5 @ A_128 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_218_finite__subset__induct,axiom,
% 3.28/1.75 ! [P_34: ( ( pname > $o ) > $o ) > $o,A_127: ( pname > $o ) > $o,F_46: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_46 )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ F_46 @ A_127 )
% 3.28/1.75 => ( ( P_34 @ bot_bot_pname_o_o )
% 3.28/1.75 => ( ! [A_122: pname > $o,F_26: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_26 )
% 3.28/1.75 => ( ( member_pname_o @ A_122 @ A_127 )
% 3.28/1.75 => ( ~ ( member_pname_o @ A_122 @ F_26 )
% 3.28/1.75 => ( ( P_34 @ F_26 )
% 3.28/1.75 => ( P_34 @ ( insert_pname_o @ A_122 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_34 @ F_46 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_219_finite__subset__induct,axiom,
% 3.28/1.75 ! [P_34: ( ( hoare_1167836817_state > $o ) > $o ) > $o,A_127: ( hoare_1167836817_state > $o ) > $o,F_46: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_46 )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ F_46 @ A_127 )
% 3.28/1.75 => ( ( P_34 @ bot_bo691907561te_o_o )
% 3.28/1.75 => ( ! [A_122: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_26 )
% 3.28/1.75 => ( ( member864234961tate_o @ A_122 @ A_127 )
% 3.28/1.75 => ( ~ ( member864234961tate_o @ A_122 @ F_26 )
% 3.28/1.75 => ( ( P_34 @ F_26 )
% 3.28/1.75 => ( P_34 @ ( insert999278200tate_o @ A_122 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_34 @ F_46 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_220_finite__subset__induct,axiom,
% 3.28/1.75 ! [P_34: ( pname > $o ) > $o,A_127: pname > $o,F_46: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_46 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ F_46 @ A_127 )
% 3.28/1.75 => ( ( P_34 @ bot_bot_pname_o )
% 3.28/1.75 => ( ! [A_122: pname,F_26: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_26 )
% 3.28/1.75 => ( ( member_pname @ A_122 @ A_127 )
% 3.28/1.75 => ( ~ ( member_pname @ A_122 @ F_26 )
% 3.28/1.75 => ( ( P_34 @ F_26 )
% 3.28/1.75 => ( P_34 @ ( insert_pname @ A_122 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_34 @ F_46 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_221_finite__subset__induct,axiom,
% 3.28/1.75 ! [P_34: ( hoare_1167836817_state > $o ) > $o,A_127: hoare_1167836817_state > $o,F_46: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_46 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ F_46 @ A_127 )
% 3.28/1.75 => ( ( P_34 @ bot_bo70021908tate_o )
% 3.28/1.75 => ( ! [A_122: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_26 )
% 3.28/1.75 => ( ( member2058392318_state @ A_122 @ A_127 )
% 3.28/1.75 => ( ~ ( member2058392318_state @ A_122 @ F_26 )
% 3.28/1.75 => ( ( P_34 @ F_26 )
% 3.28/1.75 => ( P_34 @ ( insert2134838167_state @ A_122 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_34 @ F_46 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_222_WTs__elim__cases_I7_J,axiom,
% 3.28/1.75 ! [P: pname] :
% 3.28/1.75 ( ( wt @ ( body_1 @ P ) )
% 3.28/1.75 => ~ ! [Y_2: com] :
% 3.28/1.75 ( ( body @ P )
% 3.28/1.75 != ( some_com @ Y_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_223_subsetI,axiom,
% 3.28/1.75 ! [B_92: pname > $o,A_126: pname > $o] :
% 3.28/1.75 ( ! [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_126 )
% 3.28/1.75 => ( member_pname @ X_5 @ B_92 ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ A_126 @ B_92 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_224_subsetI,axiom,
% 3.28/1.75 ! [B_92: hoare_1167836817_state > $o,A_126: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_126 )
% 3.28/1.75 => ( member2058392318_state @ X_5 @ B_92 ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ A_126 @ B_92 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_225_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: ( pname > $o ) > hoare_1167836817_state,A_125: ( pname > $o ) > $o,B_91: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ B_91 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_91 @ ( image_1381916541_state @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ord_le1205211808me_o_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite297249702name_o @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_1381916541_state @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_226_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_125: ( hoare_1167836817_state > $o ) > $o,B_91: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ B_91 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_91 @ ( image_635813834_state @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ord_le741939125te_o_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite1380128977tate_o @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_635813834_state @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_227_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: ( pname > $o ) > pname,A_125: ( pname > $o ) > $o,B_91: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ B_91 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_pname_o_pname @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ord_le1205211808me_o_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite297249702name_o @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_pname_o_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_228_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: ( hoare_1167836817_state > $o ) > pname,A_125: ( hoare_1167836817_state > $o ) > $o,B_91: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ B_91 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_980295115_pname @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ord_le741939125te_o_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite1380128977tate_o @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_980295115_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_229_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: hoare_1167836817_state > pname > $o,A_125: hoare_1167836817_state > $o,B_91: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ B_91 )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ B_91 @ ( image_2066861949name_o @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite1084549118_state @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_2066861949name_o @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_230_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: hoare_1167836817_state > hoare_1167836817_state > $o,A_125: hoare_1167836817_state > $o,B_91: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ B_91 )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ B_91 @ ( image_1745649338tate_o @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite1084549118_state @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_1745649338tate_o @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_231_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: hoare_1167836817_state > pname,A_125: hoare_1167836817_state > $o,B_91: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ B_91 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_8178176_pname @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite1084549118_state @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_8178176_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_232_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: pname > pname > $o,A_125: pname > $o,B_91: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ B_91 )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ B_91 @ ( image_pname_pname_o @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite_finite_pname @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_pname_pname_o @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_233_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: pname > hoare_1167836817_state > $o,A_125: pname > $o,B_91: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ B_91 )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ B_91 @ ( image_475339327tate_o @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite_finite_pname @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_475339327tate_o @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_234_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: pname > pname,A_125: pname > $o,B_91: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ B_91 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_91 @ ( image_pname_pname @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite_finite_pname @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_pname_pname @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_235_finite__subset__image,axiom,
% 3.28/1.75 ! [F_45: pname > hoare_1167836817_state,A_125: pname > $o,B_91: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ B_91 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_91 @ ( image_575578384_state @ F_45 @ A_125 ) )
% 3.28/1.75 => ? [C_47: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
% 3.28/1.75 & ( finite_finite_pname @ C_47 )
% 3.28/1.75 & ( B_91
% 3.28/1.75 = ( image_575578384_state @ F_45 @ C_47 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_236_finite__dom__body,axiom,
% 3.28/1.75 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_237_finite__induct,axiom,
% 3.28/1.75 ! [P_33: ( ( pname > $o ) > $o ) > $o,F_44: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_44 )
% 3.28/1.75 => ( ( P_33 @ bot_bot_pname_o_o )
% 3.28/1.75 => ( ! [X_5: pname > $o,F_26: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_26 )
% 3.28/1.75 => ( ~ ( member_pname_o @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_33 @ F_26 )
% 3.28/1.75 => ( P_33 @ ( insert_pname_o @ X_5 @ F_26 ) ) ) ) )
% 3.28/1.75 => ( P_33 @ F_44 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_238_finite__induct,axiom,
% 3.28/1.75 ! [P_33: ( ( hoare_1167836817_state > $o ) > $o ) > $o,F_44: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_44 )
% 3.28/1.75 => ( ( P_33 @ bot_bo691907561te_o_o )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_26 )
% 3.28/1.75 => ( ~ ( member864234961tate_o @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_33 @ F_26 )
% 3.28/1.75 => ( P_33 @ ( insert999278200tate_o @ X_5 @ F_26 ) ) ) ) )
% 3.28/1.75 => ( P_33 @ F_44 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_239_finite__induct,axiom,
% 3.28/1.75 ! [P_33: ( pname > $o ) > $o,F_44: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_44 )
% 3.28/1.75 => ( ( P_33 @ bot_bot_pname_o )
% 3.28/1.75 => ( ! [X_5: pname,F_26: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_26 )
% 3.28/1.75 => ( ~ ( member_pname @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_33 @ F_26 )
% 3.28/1.75 => ( P_33 @ ( insert_pname @ X_5 @ F_26 ) ) ) ) )
% 3.28/1.75 => ( P_33 @ F_44 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_240_finite__induct,axiom,
% 3.28/1.75 ! [P_33: ( hoare_1167836817_state > $o ) > $o,F_44: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_44 )
% 3.28/1.75 => ( ( P_33 @ bot_bo70021908tate_o )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_26 )
% 3.28/1.75 => ( ~ ( member2058392318_state @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_33 @ F_26 )
% 3.28/1.75 => ( P_33 @ ( insert2134838167_state @ X_5 @ F_26 ) ) ) ) )
% 3.28/1.75 => ( P_33 @ F_44 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_241_finite_Osimps,axiom,
% 3.28/1.75 ! [A_123: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ A_123 )
% 3.28/1.75 <=> ( ( A_123 = bot_bot_pname_o_o )
% 3.28/1.75 | ? [A_124: ( pname > $o ) > $o,A_122: pname > $o] :
% 3.28/1.75 ( ( A_123
% 3.28/1.75 = ( insert_pname_o @ A_122 @ A_124 ) )
% 3.28/1.75 & ( finite297249702name_o @ A_124 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_242_finite_Osimps,axiom,
% 3.28/1.75 ! [A_123: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ A_123 )
% 3.28/1.75 <=> ( ( A_123 = bot_bo691907561te_o_o )
% 3.28/1.75 | ? [A_124: ( hoare_1167836817_state > $o ) > $o,A_122: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_123
% 3.28/1.75 = ( insert999278200tate_o @ A_122 @ A_124 ) )
% 3.28/1.75 & ( finite1380128977tate_o @ A_124 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_243_finite_Osimps,axiom,
% 3.28/1.75 ! [A_123: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_123 )
% 3.28/1.75 <=> ( ( A_123 = bot_bot_pname_o )
% 3.28/1.75 | ? [A_124: pname > $o,A_122: pname] :
% 3.28/1.75 ( ( A_123
% 3.28/1.75 = ( insert_pname @ A_122 @ A_124 ) )
% 3.28/1.75 & ( finite_finite_pname @ A_124 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_244_finite_Osimps,axiom,
% 3.28/1.75 ! [A_123: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_123 )
% 3.28/1.75 <=> ( ( A_123 = bot_bo70021908tate_o )
% 3.28/1.75 | ? [A_124: hoare_1167836817_state > $o,A_122: hoare_1167836817_state] :
% 3.28/1.75 ( ( A_123
% 3.28/1.75 = ( insert2134838167_state @ A_122 @ A_124 ) )
% 3.28/1.75 & ( finite1084549118_state @ A_124 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_245_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: pname > pname > $o,A_121: pname > $o] :
% 3.28/1.75 ( ~ ( finite_finite_pname @ A_121 )
% 3.28/1.75 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite_finite_pname
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [A_122: pname] :
% 3.28/1.75 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_246_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: pname > hoare_1167836817_state > $o,A_121: pname > $o] :
% 3.28/1.75 ( ~ ( finite_finite_pname @ A_121 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ ( image_475339327tate_o @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite_finite_pname
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [A_122: pname] :
% 3.28/1.75 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_247_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: hoare_1167836817_state > hoare_1167836817_state,A_121: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( finite1084549118_state @ A_121 )
% 3.28/1.75 => ( ( finite1084549118_state @ ( image_31595733_state @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite1084549118_state
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [A_122: hoare_1167836817_state] :
% 3.28/1.75 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_248_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: ( pname > $o ) > hoare_1167836817_state,A_121: ( pname > $o ) > $o] :
% 3.28/1.75 ( ~ ( finite297249702name_o @ A_121 )
% 3.28/1.75 => ( ( finite1084549118_state @ ( image_1381916541_state @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: pname > $o] :
% 3.28/1.75 ( ( member_pname_o @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite297249702name_o
% 3.28/1.75 @ ( collect_pname_o
% 3.28/1.75 @ ^ [A_122: pname > $o] :
% 3.28/1.75 ( (&) @ ( member_pname_o @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_249_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_121: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ~ ( finite1380128977tate_o @ A_121 )
% 3.28/1.75 => ( ( finite1084549118_state @ ( image_635813834_state @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member864234961tate_o @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite1380128977tate_o
% 3.28/1.75 @ ( collec269976083tate_o
% 3.28/1.75 @ ^ [A_122: hoare_1167836817_state > $o] :
% 3.28/1.75 ( (&) @ ( member864234961tate_o @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_250_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: pname > pname,A_121: pname > $o] :
% 3.28/1.75 ( ~ ( finite_finite_pname @ A_121 )
% 3.28/1.75 => ( ( finite_finite_pname @ ( image_pname_pname @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite_finite_pname
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [A_122: pname] :
% 3.28/1.75 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_251_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: hoare_1167836817_state > pname,A_121: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( finite1084549118_state @ A_121 )
% 3.28/1.75 => ( ( finite_finite_pname @ ( image_8178176_pname @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite1084549118_state
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [A_122: hoare_1167836817_state] :
% 3.28/1.75 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_252_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: ( pname > $o ) > pname,A_121: ( pname > $o ) > $o] :
% 3.28/1.75 ( ~ ( finite297249702name_o @ A_121 )
% 3.28/1.75 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: pname > $o] :
% 3.28/1.75 ( ( member_pname_o @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite297249702name_o
% 3.28/1.75 @ ( collect_pname_o
% 3.28/1.75 @ ^ [A_122: pname > $o] :
% 3.28/1.75 ( (&) @ ( member_pname_o @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_253_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: ( hoare_1167836817_state > $o ) > pname,A_121: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ~ ( finite1380128977tate_o @ A_121 )
% 3.28/1.75 => ( ( finite_finite_pname @ ( image_980295115_pname @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member864234961tate_o @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite1380128977tate_o
% 3.28/1.75 @ ( collec269976083tate_o
% 3.28/1.75 @ ^ [A_122: hoare_1167836817_state > $o] :
% 3.28/1.75 ( (&) @ ( member864234961tate_o @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_254_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: hoare_1167836817_state > pname > $o,A_121: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( finite1084549118_state @ A_121 )
% 3.28/1.75 => ( ( finite297249702name_o @ ( image_2066861949name_o @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite1084549118_state
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [A_122: hoare_1167836817_state] :
% 3.28/1.75 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_255_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: hoare_1167836817_state > hoare_1167836817_state > $o,A_121: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( finite1084549118_state @ A_121 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ ( image_1745649338tate_o @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite1084549118_state
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [A_122: hoare_1167836817_state] :
% 3.28/1.75 ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_256_pigeonhole__infinite,axiom,
% 3.28/1.75 ! [F_43: pname > hoare_1167836817_state,A_121: pname > $o] :
% 3.28/1.75 ( ~ ( finite_finite_pname @ A_121 )
% 3.28/1.75 => ( ( finite1084549118_state @ ( image_575578384_state @ F_43 @ A_121 ) )
% 3.28/1.75 => ? [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_121 )
% 3.28/1.75 & ~ ( finite_finite_pname
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [A_122: pname] :
% 3.28/1.75 ( (&) @ ( member_pname @ A_122 @ A_121 )
% 3.28/1.75 @ ( ( F_43 @ A_122 )
% 3.28/1.75 = ( F_43 @ X_5 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_257_com_Osimps_I6_J,axiom,
% 3.28/1.75 ! [Pname_1: pname,Pname: pname] :
% 3.28/1.75 ( ( ( body_1 @ Pname_1 )
% 3.28/1.75 = ( body_1 @ Pname ) )
% 3.28/1.75 <=> ( Pname_1 = Pname ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_258_MGT__Body,axiom,
% 3.28/1.75 ! [G_3: hoare_1167836817_state > $o,Procs_3: pname > $o] :
% 3.28/1.75 ( ( hoare_123228589_state
% 3.28/1.75 @ ( semila1172322802tate_o @ G_3
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.28/1.75 @ Procs_3 ) )
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 3.28/1.75 @ Procs_3 ) )
% 3.28/1.75 => ( ( finite_finite_pname @ Procs_3 )
% 3.28/1.75 => ( hoare_123228589_state @ G_3
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.28/1.75 @ Procs_3 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_259_domD,axiom,
% 3.28/1.75 ! [A_120: pname,M_1: pname > option_com] :
% 3.28/1.75 ( ( member_pname @ A_120 @ ( dom_pname_com @ M_1 ) )
% 3.28/1.75 => ? [B_90: com] :
% 3.28/1.75 ( ( M_1 @ A_120 )
% 3.28/1.75 = ( some_com @ B_90 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_260_the__elem__eq,axiom,
% 3.28/1.75 ! [X_84: pname] :
% 3.28/1.75 ( ( the_elem_pname @ ( insert_pname @ X_84 @ bot_bot_pname_o ) )
% 3.28/1.75 = X_84 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_261_the__elem__eq,axiom,
% 3.28/1.75 ! [X_84: hoare_1167836817_state] :
% 3.28/1.75 ( ( the_el323660082_state @ ( insert2134838167_state @ X_84 @ bot_bo70021908tate_o ) )
% 3.28/1.75 = X_84 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_262_image__subsetI,axiom,
% 3.28/1.75 ! [F_42: hoare_1167836817_state > pname,B_89: pname > $o,A_119: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_119 )
% 3.28/1.75 => ( member_pname @ ( F_42 @ X_5 ) @ B_89 ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( image_8178176_pname @ F_42 @ A_119 ) @ B_89 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_263_image__subsetI,axiom,
% 3.28/1.75 ! [F_42: pname > hoare_1167836817_state,B_89: hoare_1167836817_state > $o,A_119: pname > $o] :
% 3.28/1.75 ( ! [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_119 )
% 3.28/1.75 => ( member2058392318_state @ ( F_42 @ X_5 ) @ B_89 ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( image_575578384_state @ F_42 @ A_119 ) @ B_89 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_264_order__refl,axiom,
% 3.28/1.75 ! [X_83: pname > $o] : ( ord_less_eq_pname_o @ X_83 @ X_83 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_265_order__refl,axiom,
% 3.28/1.75 ! [X_83: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_83 @ X_83 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_266_nonempty__iff,axiom,
% 3.28/1.75 ! [A_118: pname > $o] :
% 3.28/1.75 ( ( A_118 != bot_bot_pname_o )
% 3.28/1.75 <=> ? [X_5: pname,B_43: pname > $o] :
% 3.28/1.75 ( ( A_118
% 3.28/1.75 = ( insert_pname @ X_5 @ B_43 ) )
% 3.28/1.75 & ~ ( member_pname @ X_5 @ B_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_267_nonempty__iff,axiom,
% 3.28/1.75 ! [A_118: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_118 != bot_bo70021908tate_o )
% 3.28/1.75 <=> ? [X_5: hoare_1167836817_state,B_43: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_118
% 3.28/1.75 = ( insert2134838167_state @ X_5 @ B_43 ) )
% 3.28/1.75 & ~ ( member2058392318_state @ X_5 @ B_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_268_the_Osimps,axiom,
% 3.28/1.75 ! [X_82: com] :
% 3.28/1.75 ( ( the_com @ ( some_com @ X_82 ) )
% 3.28/1.75 = X_82 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_269_weak__Body,axiom,
% 3.28/1.75 ! [G_27: hoare_1167836817_state > $o,P_32: state > state > $o,Pn_4: pname,Q_22: state > state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_27 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_32 @ ( the_com @ ( body @ Pn_4 ) ) @ Q_22 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_27 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_32 @ ( body_1 @ Pn_4 ) @ Q_22 ) @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_270_UnCI,axiom,
% 3.28/1.75 ! [A_117: pname > $o,C_46: pname,B_88: pname > $o] :
% 3.28/1.75 ( ( ~ ( member_pname @ C_46 @ B_88 )
% 3.28/1.75 => ( member_pname @ C_46 @ A_117 ) )
% 3.28/1.75 => ( member_pname @ C_46 @ ( semila1780557381name_o @ A_117 @ B_88 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_271_UnCI,axiom,
% 3.28/1.75 ! [A_117: hoare_1167836817_state > $o,C_46: hoare_1167836817_state,B_88: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ~ ( member2058392318_state @ C_46 @ B_88 )
% 3.28/1.75 => ( member2058392318_state @ C_46 @ A_117 ) )
% 3.28/1.75 => ( member2058392318_state @ C_46 @ ( semila1172322802tate_o @ A_117 @ B_88 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_272_UnE,axiom,
% 3.28/1.75 ! [C_45: pname,A_116: pname > $o,B_87: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_45 @ ( semila1780557381name_o @ A_116 @ B_87 ) )
% 3.28/1.75 => ( ~ ( member_pname @ C_45 @ A_116 )
% 3.28/1.75 => ( member_pname @ C_45 @ B_87 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_273_UnE,axiom,
% 3.28/1.75 ! [C_45: hoare_1167836817_state,A_116: hoare_1167836817_state > $o,B_87: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_45 @ ( semila1172322802tate_o @ A_116 @ B_87 ) )
% 3.28/1.75 => ( ~ ( member2058392318_state @ C_45 @ A_116 )
% 3.28/1.75 => ( member2058392318_state @ C_45 @ B_87 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_274_Collect__disj__eq,axiom,
% 3.28/1.75 ! [P_31: pname > $o,Q_21: pname > $o] :
% 3.28/1.75 ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 3.28/1.75 = ( semila1780557381name_o @ ( collect_pname @ P_31 ) @ ( collect_pname @ Q_21 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_275_Collect__disj__eq,axiom,
% 3.28/1.75 ! [P_31: ( pname > $o ) > $o,Q_21: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 3.28/1.75 = ( semila181081674me_o_o @ ( collect_pname_o @ P_31 ) @ ( collect_pname_o @ Q_21 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_276_Collect__disj__eq,axiom,
% 3.28/1.75 ! [P_31: ( hoare_1167836817_state > $o ) > $o,Q_21: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 3.28/1.75 = ( semila866907787te_o_o @ ( collec269976083tate_o @ P_31 ) @ ( collec269976083tate_o @ Q_21 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_277_Collect__disj__eq,axiom,
% 3.28/1.75 ! [P_31: hoare_1167836817_state > $o,Q_21: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
% 3.28/1.75 = ( semila1172322802tate_o @ ( collec1027672124_state @ P_31 ) @ ( collec1027672124_state @ Q_21 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_278_triple_Oinject,axiom,
% 3.28/1.75 ! [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] :
% 3.28/1.75 ( ( ( hoare_908217195_state @ Fun1_2 @ Com_4 @ Fun2_2 )
% 3.28/1.75 = ( hoare_908217195_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 3.28/1.75 <=> ( ( Fun1_2 = Fun1_1 )
% 3.28/1.75 & ( Com_4 = Com_3 )
% 3.28/1.75 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_279_UnI2,axiom,
% 3.28/1.75 ! [A_115: pname > $o,C_44: pname,B_86: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_44 @ B_86 )
% 3.28/1.75 => ( member_pname @ C_44 @ ( semila1780557381name_o @ A_115 @ B_86 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_280_UnI2,axiom,
% 3.28/1.75 ! [A_115: hoare_1167836817_state > $o,C_44: hoare_1167836817_state,B_86: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_44 @ B_86 )
% 3.28/1.75 => ( member2058392318_state @ C_44 @ ( semila1172322802tate_o @ A_115 @ B_86 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_281_UnI1,axiom,
% 3.28/1.75 ! [B_85: pname > $o,C_43: pname,A_114: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_43 @ A_114 )
% 3.28/1.75 => ( member_pname @ C_43 @ ( semila1780557381name_o @ A_114 @ B_85 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_282_UnI1,axiom,
% 3.28/1.75 ! [B_85: hoare_1167836817_state > $o,C_43: hoare_1167836817_state,A_114: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_43 @ A_114 )
% 3.28/1.75 => ( member2058392318_state @ C_43 @ ( semila1172322802tate_o @ A_114 @ B_85 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_283_ball__Un,axiom,
% 3.28/1.75 ! [P_30: hoare_1167836817_state > $o,A_113: hoare_1167836817_state > $o,B_84: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ A_113 @ B_84 ) )
% 3.28/1.75 => ( P_30 @ X_5 ) )
% 3.28/1.75 <=> ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_113 )
% 3.28/1.75 => ( P_30 @ X_5 ) )
% 3.28/1.75 & ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ B_84 )
% 3.28/1.75 => ( P_30 @ X_5 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_284_bex__Un,axiom,
% 3.28/1.75 ! [P_29: hoare_1167836817_state > $o,A_112: hoare_1167836817_state > $o,B_83: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ A_112 @ B_83 ) )
% 3.28/1.75 & ( P_29 @ X_5 ) )
% 3.28/1.75 <=> ( ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_112 )
% 3.28/1.75 & ( P_29 @ X_5 ) )
% 3.28/1.75 | ? [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ B_83 )
% 3.28/1.75 & ( P_29 @ X_5 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_285_Un__assoc,axiom,
% 3.28/1.75 ! [A_111: hoare_1167836817_state > $o,B_82: hoare_1167836817_state > $o,C_42: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_111 @ B_82 ) @ C_42 )
% 3.28/1.75 = ( semila1172322802tate_o @ A_111 @ ( semila1172322802tate_o @ B_82 @ C_42 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_286_Un__iff,axiom,
% 3.28/1.75 ! [C_41: pname,A_110: pname > $o,B_81: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_41 @ ( semila1780557381name_o @ A_110 @ B_81 ) )
% 3.28/1.75 <=> ( ( member_pname @ C_41 @ A_110 )
% 3.28/1.75 | ( member_pname @ C_41 @ B_81 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_287_Un__iff,axiom,
% 3.28/1.75 ! [C_41: hoare_1167836817_state,A_110: hoare_1167836817_state > $o,B_81: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_41 @ ( semila1172322802tate_o @ A_110 @ B_81 ) )
% 3.28/1.75 <=> ( ( member2058392318_state @ C_41 @ A_110 )
% 3.28/1.75 | ( member2058392318_state @ C_41 @ B_81 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_288_Un__left__commute,axiom,
% 3.28/1.75 ! [A_109: hoare_1167836817_state > $o,B_80: hoare_1167836817_state > $o,C_40: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_109 @ ( semila1172322802tate_o @ B_80 @ C_40 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ B_80 @ ( semila1172322802tate_o @ A_109 @ C_40 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_289_Un__left__absorb,axiom,
% 3.28/1.75 ! [A_108: hoare_1167836817_state > $o,B_79: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_108 @ ( semila1172322802tate_o @ A_108 @ B_79 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ A_108 @ B_79 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_290_Un__commute,axiom,
% 3.28/1.75 ! [A_107: hoare_1167836817_state > $o,B_78: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_107 @ B_78 )
% 3.28/1.75 = ( semila1172322802tate_o @ B_78 @ A_107 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_291_Un__def,axiom,
% 3.28/1.75 ! [A_106: pname > $o,B_77: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ A_106 @ B_77 )
% 3.28/1.75 = ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (|) @ ( member_pname @ X_5 @ A_106 ) @ ( member_pname @ X_5 @ B_77 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_292_Un__def,axiom,
% 3.28/1.75 ! [A_106: ( pname > $o ) > $o,B_77: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( semila181081674me_o_o @ A_106 @ B_77 )
% 3.28/1.75 = ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (|) @ ( member_pname_o @ X_5 @ A_106 ) @ ( member_pname_o @ X_5 @ B_77 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_293_Un__def,axiom,
% 3.28/1.75 ! [A_106: ( hoare_1167836817_state > $o ) > $o,B_77: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( semila866907787te_o_o @ A_106 @ B_77 )
% 3.28/1.75 = ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (|) @ ( member864234961tate_o @ X_5 @ A_106 ) @ ( member864234961tate_o @ X_5 @ B_77 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_294_Un__def,axiom,
% 3.28/1.75 ! [A_106: hoare_1167836817_state > $o,B_77: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_106 @ B_77 )
% 3.28/1.75 = ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (|) @ ( member2058392318_state @ X_5 @ A_106 ) @ ( member2058392318_state @ X_5 @ B_77 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_295_Un__absorb,axiom,
% 3.28/1.75 ! [A_105: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_105 @ A_105 )
% 3.28/1.75 = A_105 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_296_Un__empty,axiom,
% 3.28/1.75 ! [A_104: pname > $o,B_76: pname > $o] :
% 3.28/1.75 ( ( ( semila1780557381name_o @ A_104 @ B_76 )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 <=> ( ( A_104 = bot_bot_pname_o )
% 3.28/1.75 & ( B_76 = bot_bot_pname_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_297_Un__empty,axiom,
% 3.28/1.75 ! [A_104: hoare_1167836817_state > $o,B_76: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( semila1172322802tate_o @ A_104 @ B_76 )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 <=> ( ( A_104 = bot_bo70021908tate_o )
% 3.28/1.75 & ( B_76 = bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_298_Un__empty__right,axiom,
% 3.28/1.75 ! [A_103: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ A_103 @ bot_bot_pname_o )
% 3.28/1.75 = A_103 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_299_Un__empty__right,axiom,
% 3.28/1.75 ! [A_103: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_103 @ bot_bo70021908tate_o )
% 3.28/1.75 = A_103 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_300_Un__empty__left,axiom,
% 3.28/1.75 ! [B_75: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ bot_bot_pname_o @ B_75 )
% 3.28/1.75 = B_75 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_301_Un__empty__left,axiom,
% 3.28/1.75 ! [B_75: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ B_75 )
% 3.28/1.75 = B_75 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_302_finite__UnI,axiom,
% 3.28/1.75 ! [G_26: ( pname > $o ) > $o,F_41: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_41 )
% 3.28/1.75 => ( ( finite297249702name_o @ G_26 )
% 3.28/1.75 => ( finite297249702name_o @ ( semila181081674me_o_o @ F_41 @ G_26 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_303_finite__UnI,axiom,
% 3.28/1.75 ! [G_26: ( hoare_1167836817_state > $o ) > $o,F_41: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_41 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ G_26 )
% 3.28/1.75 => ( finite1380128977tate_o @ ( semila866907787te_o_o @ F_41 @ G_26 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_304_finite__UnI,axiom,
% 3.28/1.75 ! [G_26: pname > $o,F_41: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_41 )
% 3.28/1.75 => ( ( finite_finite_pname @ G_26 )
% 3.28/1.75 => ( finite_finite_pname @ ( semila1780557381name_o @ F_41 @ G_26 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_305_finite__UnI,axiom,
% 3.28/1.75 ! [G_26: hoare_1167836817_state > $o,F_41: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_41 )
% 3.28/1.75 => ( ( finite1084549118_state @ G_26 )
% 3.28/1.75 => ( finite1084549118_state @ ( semila1172322802tate_o @ F_41 @ G_26 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_306_finite__Un,axiom,
% 3.28/1.75 ! [F_40: ( pname > $o ) > $o,G_25: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ ( semila181081674me_o_o @ F_40 @ G_25 ) )
% 3.28/1.75 <=> ( ( finite297249702name_o @ F_40 )
% 3.28/1.75 & ( finite297249702name_o @ G_25 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_307_finite__Un,axiom,
% 3.28/1.75 ! [F_40: ( hoare_1167836817_state > $o ) > $o,G_25: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ ( semila866907787te_o_o @ F_40 @ G_25 ) )
% 3.28/1.75 <=> ( ( finite1380128977tate_o @ F_40 )
% 3.28/1.75 & ( finite1380128977tate_o @ G_25 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_308_finite__Un,axiom,
% 3.28/1.75 ! [F_40: pname > $o,G_25: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ ( semila1780557381name_o @ F_40 @ G_25 ) )
% 3.28/1.75 <=> ( ( finite_finite_pname @ F_40 )
% 3.28/1.75 & ( finite_finite_pname @ G_25 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_309_finite__Un,axiom,
% 3.28/1.75 ! [F_40: hoare_1167836817_state > $o,G_25: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ ( semila1172322802tate_o @ F_40 @ G_25 ) )
% 3.28/1.75 <=> ( ( finite1084549118_state @ F_40 )
% 3.28/1.75 & ( finite1084549118_state @ G_25 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_310_Un__insert__left,axiom,
% 3.28/1.75 ! [A_102: pname,B_74: pname > $o,C_39: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ ( insert_pname @ A_102 @ B_74 ) @ C_39 )
% 3.28/1.75 = ( insert_pname @ A_102 @ ( semila1780557381name_o @ B_74 @ C_39 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_311_Un__insert__left,axiom,
% 3.28/1.75 ! [A_102: hoare_1167836817_state,B_74: hoare_1167836817_state > $o,C_39: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( insert2134838167_state @ A_102 @ B_74 ) @ C_39 )
% 3.28/1.75 = ( insert2134838167_state @ A_102 @ ( semila1172322802tate_o @ B_74 @ C_39 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_312_Un__insert__right,axiom,
% 3.28/1.75 ! [A_101: pname > $o,A_100: pname,B_73: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ A_101 @ ( insert_pname @ A_100 @ B_73 ) )
% 3.28/1.75 = ( insert_pname @ A_100 @ ( semila1780557381name_o @ A_101 @ B_73 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_313_Un__insert__right,axiom,
% 3.28/1.75 ! [A_101: hoare_1167836817_state > $o,A_100: hoare_1167836817_state,B_73: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_101 @ ( insert2134838167_state @ A_100 @ B_73 ) )
% 3.28/1.75 = ( insert2134838167_state @ A_100 @ ( semila1172322802tate_o @ A_101 @ B_73 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_314_Un__mono,axiom,
% 3.28/1.75 ! [B_72: pname > $o,D_4: pname > $o,A_99: pname > $o,C_38: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_99 @ C_38 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_72 @ D_4 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_99 @ B_72 ) @ ( semila1780557381name_o @ C_38 @ D_4 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_315_Un__mono,axiom,
% 3.28/1.75 ! [B_72: hoare_1167836817_state > $o,D_4: hoare_1167836817_state > $o,A_99: hoare_1167836817_state > $o,C_38: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_99 @ C_38 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_72 @ D_4 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_99 @ B_72 ) @ ( semila1172322802tate_o @ C_38 @ D_4 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_316_Un__least,axiom,
% 3.28/1.75 ! [B_71: pname > $o,A_98: pname > $o,C_37: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_98 @ C_37 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_71 @ C_37 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_98 @ B_71 ) @ C_37 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_317_Un__least,axiom,
% 3.28/1.75 ! [B_71: hoare_1167836817_state > $o,A_98: hoare_1167836817_state > $o,C_37: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_98 @ C_37 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_71 @ C_37 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_98 @ B_71 ) @ C_37 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_318_Un__absorb2,axiom,
% 3.28/1.75 ! [B_70: pname > $o,A_97: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ B_70 @ A_97 )
% 3.28/1.75 => ( ( semila1780557381name_o @ A_97 @ B_70 )
% 3.28/1.75 = A_97 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_319_Un__absorb2,axiom,
% 3.28/1.75 ! [B_70: hoare_1167836817_state > $o,A_97: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ B_70 @ A_97 )
% 3.28/1.75 => ( ( semila1172322802tate_o @ A_97 @ B_70 )
% 3.28/1.75 = A_97 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_320_Un__absorb1,axiom,
% 3.28/1.75 ! [A_96: pname > $o,B_69: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_96 @ B_69 )
% 3.28/1.75 => ( ( semila1780557381name_o @ A_96 @ B_69 )
% 3.28/1.75 = B_69 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_321_Un__absorb1,axiom,
% 3.28/1.75 ! [A_96: hoare_1167836817_state > $o,B_69: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_96 @ B_69 )
% 3.28/1.75 => ( ( semila1172322802tate_o @ A_96 @ B_69 )
% 3.28/1.75 = B_69 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_322_subset__Un__eq,axiom,
% 3.28/1.75 ! [A_95: pname > $o,B_68: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_95 @ B_68 )
% 3.28/1.75 <=> ( ( semila1780557381name_o @ A_95 @ B_68 )
% 3.28/1.75 = B_68 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_323_subset__Un__eq,axiom,
% 3.28/1.75 ! [A_95: hoare_1167836817_state > $o,B_68: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_95 @ B_68 )
% 3.28/1.75 <=> ( ( semila1172322802tate_o @ A_95 @ B_68 )
% 3.28/1.75 = B_68 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_324_Un__upper2,axiom,
% 3.28/1.75 ! [B_67: pname > $o,A_94: pname > $o] : ( ord_less_eq_pname_o @ B_67 @ ( semila1780557381name_o @ A_94 @ B_67 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_325_Un__upper2,axiom,
% 3.28/1.75 ! [B_67: hoare_1167836817_state > $o,A_94: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ B_67 @ ( semila1172322802tate_o @ A_94 @ B_67 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_326_Un__upper1,axiom,
% 3.28/1.75 ! [A_93: pname > $o,B_66: pname > $o] : ( ord_less_eq_pname_o @ A_93 @ ( semila1780557381name_o @ A_93 @ B_66 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_327_Un__upper1,axiom,
% 3.28/1.75 ! [A_93: hoare_1167836817_state > $o,B_66: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A_93 @ ( semila1172322802tate_o @ A_93 @ B_66 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_328_image__Un,axiom,
% 3.28/1.75 ! [F_39: pname > hoare_1167836817_state,A_92: pname > $o,B_65: pname > $o] :
% 3.28/1.75 ( ( image_575578384_state @ F_39 @ ( semila1780557381name_o @ A_92 @ B_65 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ ( image_575578384_state @ F_39 @ A_92 ) @ ( image_575578384_state @ F_39 @ B_65 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_329_insert__def,axiom,
% 3.28/1.75 ! [A_91: pname,B_64: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ A_91 @ B_64 )
% 3.28/1.75 = ( semila1780557381name_o
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( X_5 = A_91 ) )
% 3.28/1.75 @ B_64 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_330_insert__def,axiom,
% 3.28/1.75 ! [A_91: hoare_1167836817_state,B_64: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ A_91 @ B_64 )
% 3.28/1.75 = ( semila1172322802tate_o
% 3.28/1.75 @ ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( X_5 = A_91 ) )
% 3.28/1.75 @ B_64 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_331_insert__def,axiom,
% 3.28/1.75 ! [A_91: pname > $o,B_64: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( insert_pname_o @ A_91 @ B_64 )
% 3.28/1.75 = ( semila181081674me_o_o
% 3.28/1.75 @ ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( X_5 = A_91 ) )
% 3.28/1.75 @ B_64 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_332_insert__def,axiom,
% 3.28/1.75 ! [A_91: hoare_1167836817_state > $o,B_64: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( insert999278200tate_o @ A_91 @ B_64 )
% 3.28/1.75 = ( semila866907787te_o_o
% 3.28/1.75 @ ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( X_5 = A_91 ) )
% 3.28/1.75 @ B_64 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_333_insert__is__Un,axiom,
% 3.28/1.75 ! [A_90: pname,A_89: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ A_90 @ A_89 )
% 3.28/1.75 = ( semila1780557381name_o @ ( insert_pname @ A_90 @ bot_bot_pname_o ) @ A_89 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_334_insert__is__Un,axiom,
% 3.28/1.75 ! [A_90: hoare_1167836817_state,A_89: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ A_90 @ A_89 )
% 3.28/1.75 = ( semila1172322802tate_o @ ( insert2134838167_state @ A_90 @ bot_bo70021908tate_o ) @ A_89 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_335_hoare__derivs_OBody,axiom,
% 3.28/1.75 ! [G_24: hoare_1167836817_state > $o,P_28: pname > state > state > $o,Q_20: pname > state > state > $o,Procs_2: pname > $o] :
% 3.28/1.75 ( ( hoare_123228589_state
% 3.28/1.75 @ ( semila1172322802tate_o @ G_24
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_20 @ P_24 ) )
% 3.28/1.75 @ Procs_2 ) )
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( the_com @ ( body @ P_24 ) ) @ ( Q_20 @ P_24 ) )
% 3.28/1.75 @ Procs_2 ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_24
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_20 @ P_24 ) )
% 3.28/1.75 @ Procs_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_336_xt1_I6_J,axiom,
% 3.28/1.75 ! [Z_20: pname > $o,Y_46: pname > $o,X_81: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_46 @ X_81 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ Z_20 @ Y_46 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ Z_20 @ X_81 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_337_xt1_I6_J,axiom,
% 3.28/1.75 ! [Z_20: hoare_1167836817_state > $o,Y_46: hoare_1167836817_state > $o,X_81: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_46 @ X_81 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ Z_20 @ Y_46 )
% 3.28/1.75 => ( ord_le827224136tate_o @ Z_20 @ X_81 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_338_xt1_I5_J,axiom,
% 3.28/1.75 ! [Y_45: pname > $o,X_80: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_45 @ X_80 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ X_80 @ Y_45 )
% 3.28/1.75 => ( X_80 = Y_45 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_339_xt1_I5_J,axiom,
% 3.28/1.75 ! [Y_45: hoare_1167836817_state > $o,X_80: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_45 @ X_80 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ X_80 @ Y_45 )
% 3.28/1.75 => ( X_80 = Y_45 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_340_order__trans,axiom,
% 3.28/1.75 ! [Z_19: pname > $o,X_79: pname > $o,Y_44: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_79 @ Y_44 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ Y_44 @ Z_19 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ X_79 @ Z_19 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_341_order__trans,axiom,
% 3.28/1.75 ! [Z_19: hoare_1167836817_state > $o,X_79: hoare_1167836817_state > $o,Y_44: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_79 @ Y_44 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ Y_44 @ Z_19 )
% 3.28/1.75 => ( ord_le827224136tate_o @ X_79 @ Z_19 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_342_order__antisym,axiom,
% 3.28/1.75 ! [X_78: pname > $o,Y_43: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_78 @ Y_43 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ Y_43 @ X_78 )
% 3.28/1.75 => ( X_78 = Y_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_343_order__antisym,axiom,
% 3.28/1.75 ! [X_78: hoare_1167836817_state > $o,Y_43: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_78 @ Y_43 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ Y_43 @ X_78 )
% 3.28/1.75 => ( X_78 = Y_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_344_xt1_I4_J,axiom,
% 3.28/1.75 ! [C_36: pname > $o,B_63: pname > $o,A_88: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ B_63 @ A_88 )
% 3.28/1.75 => ( ( B_63 = C_36 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ C_36 @ A_88 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_345_xt1_I4_J,axiom,
% 3.28/1.75 ! [C_36: hoare_1167836817_state > $o,B_63: hoare_1167836817_state > $o,A_88: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ B_63 @ A_88 )
% 3.28/1.75 => ( ( B_63 = C_36 )
% 3.28/1.75 => ( ord_le827224136tate_o @ C_36 @ A_88 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_346_ord__le__eq__trans,axiom,
% 3.28/1.75 ! [C_35: pname > $o,A_87: pname > $o,B_62: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_87 @ B_62 )
% 3.28/1.75 => ( ( B_62 = C_35 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ A_87 @ C_35 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_347_ord__le__eq__trans,axiom,
% 3.28/1.75 ! [C_35: hoare_1167836817_state > $o,A_87: hoare_1167836817_state > $o,B_62: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_87 @ B_62 )
% 3.28/1.75 => ( ( B_62 = C_35 )
% 3.28/1.75 => ( ord_le827224136tate_o @ A_87 @ C_35 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_348_xt1_I3_J,axiom,
% 3.28/1.75 ! [C_34: pname > $o,A_86: pname > $o,B_61: pname > $o] :
% 3.28/1.75 ( ( A_86 = B_61 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ C_34 @ B_61 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ C_34 @ A_86 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_349_xt1_I3_J,axiom,
% 3.28/1.75 ! [C_34: hoare_1167836817_state > $o,A_86: hoare_1167836817_state > $o,B_61: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_86 = B_61 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ C_34 @ B_61 )
% 3.28/1.75 => ( ord_le827224136tate_o @ C_34 @ A_86 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_350_ord__eq__le__trans,axiom,
% 3.28/1.75 ! [C_33: pname > $o,A_85: pname > $o,B_60: pname > $o] :
% 3.28/1.75 ( ( A_85 = B_60 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_60 @ C_33 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ A_85 @ C_33 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_351_ord__eq__le__trans,axiom,
% 3.28/1.75 ! [C_33: hoare_1167836817_state > $o,A_85: hoare_1167836817_state > $o,B_60: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_85 = B_60 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_60 @ C_33 )
% 3.28/1.75 => ( ord_le827224136tate_o @ A_85 @ C_33 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_352_order__antisym__conv,axiom,
% 3.28/1.75 ! [Y_42: pname > $o,X_77: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_42 @ X_77 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ X_77 @ Y_42 )
% 3.28/1.75 <=> ( X_77 = Y_42 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_353_order__antisym__conv,axiom,
% 3.28/1.75 ! [Y_42: hoare_1167836817_state > $o,X_77: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_42 @ X_77 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ X_77 @ Y_42 )
% 3.28/1.75 <=> ( X_77 = Y_42 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_354_order__eq__refl,axiom,
% 3.28/1.75 ! [X_76: pname > $o,Y_41: pname > $o] :
% 3.28/1.75 ( ( X_76 = Y_41 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ X_76 @ Y_41 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_355_order__eq__refl,axiom,
% 3.28/1.75 ! [X_76: hoare_1167836817_state > $o,Y_41: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( X_76 = Y_41 )
% 3.28/1.75 => ( ord_le827224136tate_o @ X_76 @ Y_41 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_356_order__eq__iff,axiom,
% 3.28/1.75 ! [X_75: pname > $o,Y_40: pname > $o] :
% 3.28/1.75 ( ( X_75 = Y_40 )
% 3.28/1.75 <=> ( ( ord_less_eq_pname_o @ X_75 @ Y_40 )
% 3.28/1.75 & ( ord_less_eq_pname_o @ Y_40 @ X_75 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_357_order__eq__iff,axiom,
% 3.28/1.75 ! [X_75: hoare_1167836817_state > $o,Y_40: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( X_75 = Y_40 )
% 3.28/1.75 <=> ( ( ord_le827224136tate_o @ X_75 @ Y_40 )
% 3.28/1.75 & ( ord_le827224136tate_o @ Y_40 @ X_75 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_358_option_Oinject,axiom,
% 3.28/1.75 ! [A_84: com,A_83: com] :
% 3.28/1.75 ( ( ( some_com @ A_84 )
% 3.28/1.75 = ( some_com @ A_83 ) )
% 3.28/1.75 <=> ( A_84 = A_83 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_359_constant,axiom,
% 3.28/1.75 ! [G_23: hoare_1167836817_state > $o,P_27: state > state > $o,C_32: com,Q_19: state > state > $o,C_31: $o] :
% 3.28/1.75 ( ( C_31
% 3.28/1.75 => ( hoare_123228589_state @ G_23 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_27 @ C_32 @ Q_19 ) @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_23
% 3.28/1.75 @ ( insert2134838167_state
% 3.28/1.75 @ ( hoare_908217195_state
% 3.28/1.75 @ ^ [Z_11: state,S_3: state] : ( (&) @ ( P_27 @ Z_11 @ S_3 ) @ C_31 )
% 3.28/1.75 @ C_32
% 3.28/1.75 @ Q_19 )
% 3.28/1.75 @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_360_Body1,axiom,
% 3.28/1.75 ! [Pn_3: pname,G_22: hoare_1167836817_state > $o,P_26: pname > state > state > $o,Q_18: pname > state > state > $o,Procs_1: pname > $o] :
% 3.28/1.75 ( ( hoare_123228589_state
% 3.28/1.75 @ ( semila1172322802tate_o @ G_22
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_26 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_18 @ P_24 ) )
% 3.28/1.75 @ Procs_1 ) )
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_26 @ P_24 ) @ ( the_com @ ( body @ P_24 ) ) @ ( Q_18 @ P_24 ) )
% 3.28/1.75 @ Procs_1 ) )
% 3.28/1.75 => ( ( member_pname @ Pn_3 @ Procs_1 )
% 3.28/1.75 => ( hoare_123228589_state @ G_22 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_26 @ Pn_3 ) @ ( body_1 @ Pn_3 ) @ ( Q_18 @ Pn_3 ) ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_361_le__bot,axiom,
% 3.28/1.75 ! [A_82: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_82 @ bot_bot_pname_o )
% 3.28/1.75 => ( A_82 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_362_le__bot,axiom,
% 3.28/1.75 ! [A_82: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_82 @ bot_bo70021908tate_o )
% 3.28/1.75 => ( A_82 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_363_bot__unique,axiom,
% 3.28/1.75 ! [A_81: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_81 @ bot_bot_pname_o )
% 3.28/1.75 <=> ( A_81 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_364_bot__unique,axiom,
% 3.28/1.75 ! [A_81: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_81 @ bot_bo70021908tate_o )
% 3.28/1.75 <=> ( A_81 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_365_bot__least,axiom,
% 3.28/1.75 ! [A_80: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_80 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_366_bot__least,axiom,
% 3.28/1.75 ! [A_80: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_80 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_367_le__funE,axiom,
% 3.28/1.75 ! [X_74: pname,F_38: pname > $o,G_21: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ F_38 @ G_21 )
% 3.28/1.75 => ( ord_less_eq_o @ ( F_38 @ X_74 ) @ ( G_21 @ X_74 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_368_le__funE,axiom,
% 3.28/1.75 ! [X_74: hoare_1167836817_state,F_38: hoare_1167836817_state > $o,G_21: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ F_38 @ G_21 )
% 3.28/1.75 => ( ord_less_eq_o @ ( F_38 @ X_74 ) @ ( G_21 @ X_74 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_369_le__funD,axiom,
% 3.28/1.75 ! [X_73: pname,F_37: pname > $o,G_20: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ F_37 @ G_20 )
% 3.28/1.75 => ( ord_less_eq_o @ ( F_37 @ X_73 ) @ ( G_20 @ X_73 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_370_le__funD,axiom,
% 3.28/1.75 ! [X_73: hoare_1167836817_state,F_37: hoare_1167836817_state > $o,G_20: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ F_37 @ G_20 )
% 3.28/1.75 => ( ord_less_eq_o @ ( F_37 @ X_73 ) @ ( G_20 @ X_73 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_371_le__fun__def,axiom,
% 3.28/1.75 ! [F_36: pname > $o,G_19: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ F_36 @ G_19 )
% 3.28/1.75 <=> ! [X_5: pname] : ( ord_less_eq_o @ ( F_36 @ X_5 ) @ ( G_19 @ X_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_372_le__fun__def,axiom,
% 3.28/1.75 ! [F_36: hoare_1167836817_state > $o,G_19: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ F_36 @ G_19 )
% 3.28/1.75 <=> ! [X_5: hoare_1167836817_state] : ( ord_less_eq_o @ ( F_36 @ X_5 ) @ ( G_19 @ X_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_373_bot__apply,axiom,
% 3.28/1.75 ! [X_72: pname] :
% 3.28/1.75 ( ( bot_bot_pname_o @ X_72 )
% 3.28/1.75 <=> bot_bot_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_374_bot__apply,axiom,
% 3.28/1.75 ! [X_72: hoare_1167836817_state] :
% 3.28/1.75 ( ( bot_bo70021908tate_o @ X_72 )
% 3.28/1.75 <=> bot_bot_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_375_bot__fun__def,axiom,
% 3.28/1.75 ! [X_5: pname] :
% 3.28/1.75 ( ( bot_bot_pname_o @ X_5 )
% 3.28/1.75 <=> bot_bot_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_376_bot__fun__def,axiom,
% 3.28/1.75 ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( bot_bo70021908tate_o @ X_5 )
% 3.28/1.75 <=> bot_bot_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_377_BodyN,axiom,
% 3.28/1.75 ! [P_25: state > state > $o,Pn_2: pname,Q_17: state > state > $o,G_18: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( body_1 @ Pn_2 ) @ Q_17 ) @ G_18 ) @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( the_com @ ( body @ Pn_2 ) ) @ Q_17 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_18 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( body_1 @ Pn_2 ) @ Q_17 ) @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_378_finite__pointwise,axiom,
% 3.28/1.75 ! [P_23: pname > state > state > $o,Q_16: pname > state > state > $o,G_17: hoare_1167836817_state > $o,P_22: pname > state > state > $o,C0_1: pname > com,Q_15: pname > state > state > $o,U_1: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ U_1 )
% 3.28/1.75 => ( ! [P_24: pname] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_17 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_22 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_15 @ P_24 ) ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_17 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_23 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_16 @ P_24 ) ) @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 => ( ( hoare_123228589_state @ G_17
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_22 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_15 @ P_24 ) )
% 3.28/1.75 @ U_1 ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_17
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [P_24: pname] : ( hoare_908217195_state @ ( P_23 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_16 @ P_24 ) )
% 3.28/1.75 @ U_1 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_379_escape,axiom,
% 3.28/1.75 ! [G_16: hoare_1167836817_state > $o,C_30: com,Q_14: state > state > $o,P_21: state > state > $o] :
% 3.28/1.75 ( ! [Z_11: state,S_3: state] :
% 3.28/1.75 ( ( P_21 @ Z_11 @ S_3 )
% 3.28/1.75 => ( hoare_123228589_state @ G_16
% 3.28/1.75 @ ( insert2134838167_state
% 3.28/1.75 @ ( hoare_908217195_state
% 3.28/1.75 @ ^ [Za: state,S_4: state] : ( S_4 = S_3 )
% 3.28/1.75 @ C_30
% 3.28/1.75 @ ^ [Z_18: state] : ( Q_14 @ Z_11 ) )
% 3.28/1.75 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_16 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ C_30 @ Q_14 ) @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_380_Body__sound__lemma,axiom,
% 3.28/1.75 ! [G_15: hoare_1167836817_state > $o,P_20: pname > state > state > $o,Q_13: pname > state > state > $o,Procs: pname > $o] :
% 3.28/1.75 ( ( hoare_529639851_state
% 3.28/1.75 @ ( semila1172322802tate_o @ G_15
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_13 @ Pn ) )
% 3.28/1.75 @ Procs ) )
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( the_com @ ( body @ Pn ) ) @ ( Q_13 @ Pn ) )
% 3.28/1.75 @ Procs ) )
% 3.28/1.75 => ( hoare_529639851_state @ G_15
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_13 @ Pn ) )
% 3.28/1.75 @ Procs ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_381_conseq1,axiom,
% 3.28/1.75 ! [P_19: state > state > $o,G_14: hoare_1167836817_state > $o,P_18: state > state > $o,C_29: com,Q_12: state > state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_18 @ C_29 @ Q_12 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ! [Z_11: state,S_3: state] :
% 3.28/1.75 ( ( P_19 @ Z_11 @ S_3 )
% 3.28/1.75 => ( P_18 @ Z_11 @ S_3 ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_19 @ C_29 @ Q_12 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_382_conseq2,axiom,
% 3.28/1.75 ! [Q_11: state > state > $o,G_13: hoare_1167836817_state > $o,P_17: state > state > $o,C_28: com,Q_10: state > state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_13 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_28 @ Q_10 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ! [Z_11: state,S_3: state] :
% 3.28/1.75 ( ( Q_10 @ Z_11 @ S_3 )
% 3.28/1.75 => ( Q_11 @ Z_11 @ S_3 ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_13 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_28 @ Q_11 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_383_MGF__complete,axiom,
% 3.28/1.75 ! [P: state > state > $o,Q_9: state > state > $o,C_21: com] :
% 3.28/1.75 ( ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ( hoare_529639851_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ P @ C_21 @ Q_9 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ P @ C_21 @ Q_9 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_384_sup1E,axiom,
% 3.28/1.75 ! [A_79: hoare_1167836817_state > $o,B_59: hoare_1167836817_state > $o,X_71: hoare_1167836817_state] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_79 @ B_59 @ X_71 )
% 3.28/1.75 => ( ~ ( A_79 @ X_71 )
% 3.28/1.75 => ( B_59 @ X_71 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_385_sup1CI,axiom,
% 3.28/1.75 ! [A_78: hoare_1167836817_state > $o,B_58: hoare_1167836817_state > $o,X_70: hoare_1167836817_state] :
% 3.28/1.75 ( ( ~ ( B_58 @ X_70 )
% 3.28/1.75 => ( A_78 @ X_70 ) )
% 3.28/1.75 => ( semila1172322802tate_o @ A_78 @ B_58 @ X_70 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_386_hoare__sound,axiom,
% 3.28/1.75 ! [G_12: hoare_1167836817_state > $o,Ts: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_12 @ Ts )
% 3.28/1.75 => ( hoare_529639851_state @ G_12 @ Ts ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_387_bot__empty__eq,axiom,
% 3.28/1.75 ! [X_5: pname] :
% 3.28/1.75 ( ( bot_bot_pname_o @ X_5 )
% 3.28/1.75 <=> ( member_pname @ X_5 @ bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_388_bot__empty__eq,axiom,
% 3.28/1.75 ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( bot_bo70021908tate_o @ X_5 )
% 3.28/1.75 <=> ( member2058392318_state @ X_5 @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_389_rev__predicate1D,axiom,
% 3.28/1.75 ! [Q_8: pname > $o,P_16: pname > $o,X_69: pname] :
% 3.28/1.75 ( ( P_16 @ X_69 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ P_16 @ Q_8 )
% 3.28/1.75 => ( Q_8 @ X_69 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_390_rev__predicate1D,axiom,
% 3.28/1.75 ! [Q_8: hoare_1167836817_state > $o,P_16: hoare_1167836817_state > $o,X_69: hoare_1167836817_state] :
% 3.28/1.75 ( ( P_16 @ X_69 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ P_16 @ Q_8 )
% 3.28/1.75 => ( Q_8 @ X_69 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_391_predicate1D,axiom,
% 3.28/1.75 ! [X_68: pname,P_15: pname > $o,Q_7: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ P_15 @ Q_7 )
% 3.28/1.75 => ( ( P_15 @ X_68 )
% 3.28/1.75 => ( Q_7 @ X_68 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_392_predicate1D,axiom,
% 3.28/1.75 ! [X_68: hoare_1167836817_state,P_15: hoare_1167836817_state > $o,Q_7: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ P_15 @ Q_7 )
% 3.28/1.75 => ( ( P_15 @ X_68 )
% 3.28/1.75 => ( Q_7 @ X_68 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_393_sup1I2,axiom,
% 3.28/1.75 ! [A_77: hoare_1167836817_state > $o,B_57: hoare_1167836817_state > $o,X_67: hoare_1167836817_state] :
% 3.28/1.75 ( ( B_57 @ X_67 )
% 3.28/1.75 => ( semila1172322802tate_o @ A_77 @ B_57 @ X_67 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_394_sup1I1,axiom,
% 3.28/1.75 ! [B_56: hoare_1167836817_state > $o,A_76: hoare_1167836817_state > $o,X_66: hoare_1167836817_state] :
% 3.28/1.75 ( ( A_76 @ X_66 )
% 3.28/1.75 => ( semila1172322802tate_o @ A_76 @ B_56 @ X_66 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_395_pred__subset__eq,axiom,
% 3.28/1.75 ! [R_3: pname > $o,S_6: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o
% 3.28/1.75 @ ^ [X_5: pname] : ( member_pname @ X_5 @ R_3 )
% 3.28/1.75 @ ^ [X_5: pname] : ( member_pname @ X_5 @ S_6 ) )
% 3.28/1.75 <=> ( ord_less_eq_pname_o @ R_3 @ S_6 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_396_pred__subset__eq,axiom,
% 3.28/1.75 ! [R_3: hoare_1167836817_state > $o,S_6: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( member2058392318_state @ X_5 @ R_3 )
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( member2058392318_state @ X_5 @ S_6 ) )
% 3.28/1.75 <=> ( ord_le827224136tate_o @ R_3 @ S_6 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_397_sup__Un__eq,axiom,
% 3.28/1.75 ! [R_2: pname > $o,S_5: pname > $o,X_5: pname] :
% 3.28/1.75 ( ( semila1780557381name_o
% 3.28/1.75 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ R_2 )
% 3.28/1.75 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ S_5 )
% 3.28/1.75 @ X_5 )
% 3.28/1.75 <=> ( member_pname @ X_5 @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_398_sup__Un__eq,axiom,
% 3.28/1.75 ! [R_2: hoare_1167836817_state > $o,S_5: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( semila1172322802tate_o
% 3.28/1.75 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ R_2 )
% 3.28/1.75 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ S_5 )
% 3.28/1.75 @ X_5 )
% 3.28/1.75 <=> ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ R_2 @ S_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_399_conseq12,axiom,
% 3.28/1.75 ! [Q_6: state > state > $o,P_14: state > state > $o,G_11: hoare_1167836817_state > $o,P_13: state > state > $o,C_27: com,Q_5: state > state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_13 @ C_27 @ Q_5 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ! [Z_11: state,S_3: state] :
% 3.28/1.75 ( ( P_14 @ Z_11 @ S_3 )
% 3.28/1.75 => ! [S_4: state] :
% 3.28/1.75 ( ! [Z_18: state] :
% 3.28/1.75 ( ( P_13 @ Z_18 @ S_3 )
% 3.28/1.75 => ( Q_5 @ Z_18 @ S_4 ) )
% 3.28/1.75 => ( Q_6 @ Z_11 @ S_4 ) ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_14 @ C_27 @ Q_6 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_400_le__funI,axiom,
% 3.28/1.75 ! [F_35: pname > $o,G_10: pname > $o] :
% 3.28/1.75 ( ! [X_5: pname] : ( ord_less_eq_o @ ( F_35 @ X_5 ) @ ( G_10 @ X_5 ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ F_35 @ G_10 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_401_le__funI,axiom,
% 3.28/1.75 ! [F_35: hoare_1167836817_state > $o,G_10: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] : ( ord_less_eq_o @ ( F_35 @ X_5 ) @ ( G_10 @ X_5 ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ F_35 @ G_10 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_402_Option_Oset_Osimps_I2_J,axiom,
% 3.28/1.75 ! [X_65: pname] :
% 3.28/1.75 ( ( set_pname @ ( some_pname @ X_65 ) )
% 3.28/1.75 = ( insert_pname @ X_65 @ bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_403_Option_Oset_Osimps_I2_J,axiom,
% 3.28/1.75 ! [X_65: hoare_1167836817_state] :
% 3.28/1.75 ( ( set_Ho2131684873_state @ ( some_H1433514562_state @ X_65 ) )
% 3.28/1.75 = ( insert2134838167_state @ X_65 @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_404_Option_Oset_Osimps_I2_J,axiom,
% 3.28/1.75 ! [X_65: com] :
% 3.28/1.75 ( ( set_com @ ( some_com @ X_65 ) )
% 3.28/1.75 = ( insert_com @ X_65 @ bot_bot_com_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_405_elem__set,axiom,
% 3.28/1.75 ! [X_64: pname,Xo: option_pname] :
% 3.28/1.75 ( ( member_pname @ X_64 @ ( set_pname @ Xo ) )
% 3.28/1.75 <=> ( Xo
% 3.28/1.75 = ( some_pname @ X_64 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_406_elem__set,axiom,
% 3.28/1.75 ! [X_64: hoare_1167836817_state,Xo: option1574264306_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_64 @ ( set_Ho2131684873_state @ Xo ) )
% 3.28/1.75 <=> ( Xo
% 3.28/1.75 = ( some_H1433514562_state @ X_64 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_407_elem__set,axiom,
% 3.28/1.75 ! [X_64: com,Xo: option_com] :
% 3.28/1.75 ( ( member_com @ X_64 @ ( set_com @ Xo ) )
% 3.28/1.75 <=> ( Xo
% 3.28/1.75 = ( some_com @ X_64 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_408_ospec,axiom,
% 3.28/1.75 ! [X_63: com,P_12: com > $o,A_75: option_com] :
% 3.28/1.75 ( ! [X_5: com] :
% 3.28/1.75 ( ( member_com @ X_5 @ ( set_com @ A_75 ) )
% 3.28/1.75 => ( P_12 @ X_5 ) )
% 3.28/1.75 => ( ( A_75
% 3.28/1.75 = ( some_com @ X_63 ) )
% 3.28/1.75 => ( P_12 @ X_63 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_409_sup__fun__def,axiom,
% 3.28/1.75 ! [F_34: hoare_1167836817_state > $o,G_9: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( semila1172322802tate_o @ F_34 @ G_9 @ X_5 )
% 3.28/1.75 <=> ( semila10642723_sup_o @ ( F_34 @ X_5 ) @ ( G_9 @ X_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_410_sup__apply,axiom,
% 3.28/1.75 ! [F_33: hoare_1167836817_state > $o,G_8: hoare_1167836817_state > $o,X_62: hoare_1167836817_state] :
% 3.28/1.75 ( ( semila1172322802tate_o @ F_33 @ G_8 @ X_62 )
% 3.28/1.75 <=> ( semila10642723_sup_o @ ( F_33 @ X_62 ) @ ( G_8 @ X_62 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_411_single__stateE,axiom,
% 3.28/1.75 ( hoare_1201148605gleton
% 3.28/1.75 => ! [T_1: state] :
% 3.28/1.75 ~ ! [S_3: state] : ( S_3 = T_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_412_state__not__singleton__def,axiom,
% 3.28/1.75 ( hoare_1201148605gleton
% 3.28/1.75 <=> ? [S_3: state,T_1: state] : ( S_3 != T_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_413_sup__assoc,axiom,
% 3.28/1.75 ! [X_61: hoare_1167836817_state > $o,Y_39: hoare_1167836817_state > $o,Z_17: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_61 @ Y_39 ) @ Z_17 )
% 3.28/1.75 = ( semila1172322802tate_o @ X_61 @ ( semila1172322802tate_o @ Y_39 @ Z_17 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_414_inf__sup__aci_I6_J,axiom,
% 3.28/1.75 ! [X_60: hoare_1167836817_state > $o,Y_38: hoare_1167836817_state > $o,Z_16: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_60 @ Y_38 ) @ Z_16 )
% 3.28/1.75 = ( semila1172322802tate_o @ X_60 @ ( semila1172322802tate_o @ Y_38 @ Z_16 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_415_sup_Oassoc,axiom,
% 3.28/1.75 ! [A_74: hoare_1167836817_state > $o,B_55: hoare_1167836817_state > $o,C_26: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_74 @ B_55 ) @ C_26 )
% 3.28/1.75 = ( semila1172322802tate_o @ A_74 @ ( semila1172322802tate_o @ B_55 @ C_26 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_416_sup__left__commute,axiom,
% 3.28/1.75 ! [X_59: hoare_1167836817_state > $o,Y_37: hoare_1167836817_state > $o,Z_15: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_59 @ ( semila1172322802tate_o @ Y_37 @ Z_15 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ Y_37 @ ( semila1172322802tate_o @ X_59 @ Z_15 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_417_inf__sup__aci_I7_J,axiom,
% 3.28/1.75 ! [X_58: hoare_1167836817_state > $o,Y_36: hoare_1167836817_state > $o,Z_14: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_58 @ ( semila1172322802tate_o @ Y_36 @ Z_14 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ Y_36 @ ( semila1172322802tate_o @ X_58 @ Z_14 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_418_sup_Oleft__commute,axiom,
% 3.28/1.75 ! [B_54: hoare_1167836817_state > $o,A_73: hoare_1167836817_state > $o,C_25: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ B_54 @ ( semila1172322802tate_o @ A_73 @ C_25 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ A_73 @ ( semila1172322802tate_o @ B_54 @ C_25 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_419_sup__left__idem,axiom,
% 3.28/1.75 ! [X_57: hoare_1167836817_state > $o,Y_35: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_57 @ ( semila1172322802tate_o @ X_57 @ Y_35 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ X_57 @ Y_35 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_420_inf__sup__aci_I8_J,axiom,
% 3.28/1.75 ! [X_56: hoare_1167836817_state > $o,Y_34: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_56 @ ( semila1172322802tate_o @ X_56 @ Y_34 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ X_56 @ Y_34 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_421_sup_Oleft__idem,axiom,
% 3.28/1.75 ! [A_72: hoare_1167836817_state > $o,B_53: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_72 @ ( semila1172322802tate_o @ A_72 @ B_53 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ A_72 @ B_53 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_422_sup__commute,axiom,
% 3.28/1.75 ! [X_55: hoare_1167836817_state > $o,Y_33: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_55 @ Y_33 )
% 3.28/1.75 = ( semila1172322802tate_o @ Y_33 @ X_55 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_423_inf__sup__aci_I5_J,axiom,
% 3.28/1.75 ! [X_54: hoare_1167836817_state > $o,Y_32: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_54 @ Y_32 )
% 3.28/1.75 = ( semila1172322802tate_o @ Y_32 @ X_54 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_424_sup_Ocommute,axiom,
% 3.28/1.75 ! [A_71: hoare_1167836817_state > $o,B_52: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_71 @ B_52 )
% 3.28/1.75 = ( semila1172322802tate_o @ B_52 @ A_71 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_425_sup__idem,axiom,
% 3.28/1.75 ! [X_53: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_53 @ X_53 )
% 3.28/1.75 = X_53 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_426_sup_Oidem,axiom,
% 3.28/1.75 ! [A_70: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_70 @ A_70 )
% 3.28/1.75 = A_70 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_427_le__supE,axiom,
% 3.28/1.75 ! [A_69: pname > $o,B_51: pname > $o,X_52: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_69 @ B_51 ) @ X_52 )
% 3.28/1.75 => ~ ( ( ord_less_eq_pname_o @ A_69 @ X_52 )
% 3.28/1.75 => ~ ( ord_less_eq_pname_o @ B_51 @ X_52 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_428_le__supE,axiom,
% 3.28/1.75 ! [A_69: hoare_1167836817_state > $o,B_51: hoare_1167836817_state > $o,X_52: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_69 @ B_51 ) @ X_52 )
% 3.28/1.75 => ~ ( ( ord_le827224136tate_o @ A_69 @ X_52 )
% 3.28/1.75 => ~ ( ord_le827224136tate_o @ B_51 @ X_52 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_429_sup__mono,axiom,
% 3.28/1.75 ! [B_50: pname > $o,D_3: pname > $o,A_68: pname > $o,C_24: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_68 @ C_24 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_50 @ D_3 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_68 @ B_50 ) @ ( semila1780557381name_o @ C_24 @ D_3 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_430_sup__mono,axiom,
% 3.28/1.75 ! [B_50: hoare_1167836817_state > $o,D_3: hoare_1167836817_state > $o,A_68: hoare_1167836817_state > $o,C_24: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_68 @ C_24 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_50 @ D_3 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_68 @ B_50 ) @ ( semila1172322802tate_o @ C_24 @ D_3 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_431_sup__least,axiom,
% 3.28/1.75 ! [Z_13: pname > $o,Y_31: pname > $o,X_51: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_31 @ X_51 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ Z_13 @ X_51 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ Y_31 @ Z_13 ) @ X_51 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_432_sup__least,axiom,
% 3.28/1.75 ! [Z_13: hoare_1167836817_state > $o,Y_31: hoare_1167836817_state > $o,X_51: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_31 @ X_51 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ Z_13 @ X_51 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ Y_31 @ Z_13 ) @ X_51 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_433_le__supI,axiom,
% 3.28/1.75 ! [B_49: pname > $o,A_67: pname > $o,X_50: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_67 @ X_50 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_49 @ X_50 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_67 @ B_49 ) @ X_50 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_434_le__supI,axiom,
% 3.28/1.75 ! [B_49: hoare_1167836817_state > $o,A_67: hoare_1167836817_state > $o,X_50: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_67 @ X_50 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_49 @ X_50 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_67 @ B_49 ) @ X_50 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_435_sup__absorb1,axiom,
% 3.28/1.75 ! [Y_30: pname > $o,X_49: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_30 @ X_49 )
% 3.28/1.75 => ( ( semila1780557381name_o @ X_49 @ Y_30 )
% 3.28/1.75 = X_49 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_436_sup__absorb1,axiom,
% 3.28/1.75 ! [Y_30: hoare_1167836817_state > $o,X_49: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_30 @ X_49 )
% 3.28/1.75 => ( ( semila1172322802tate_o @ X_49 @ Y_30 )
% 3.28/1.75 = X_49 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_437_sup__absorb2,axiom,
% 3.28/1.75 ! [X_48: pname > $o,Y_29: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_48 @ Y_29 )
% 3.28/1.75 => ( ( semila1780557381name_o @ X_48 @ Y_29 )
% 3.28/1.75 = Y_29 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_438_sup__absorb2,axiom,
% 3.28/1.75 ! [X_48: hoare_1167836817_state > $o,Y_29: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_48 @ Y_29 )
% 3.28/1.75 => ( ( semila1172322802tate_o @ X_48 @ Y_29 )
% 3.28/1.75 = Y_29 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_439_le__supI2,axiom,
% 3.28/1.75 ! [A_66: pname > $o,X_47: pname > $o,B_48: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_47 @ B_48 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ X_47 @ ( semila1780557381name_o @ A_66 @ B_48 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_440_le__supI2,axiom,
% 3.28/1.75 ! [A_66: hoare_1167836817_state > $o,X_47: hoare_1167836817_state > $o,B_48: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_47 @ B_48 )
% 3.28/1.75 => ( ord_le827224136tate_o @ X_47 @ ( semila1172322802tate_o @ A_66 @ B_48 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_441_le__supI1,axiom,
% 3.28/1.75 ! [B_47: pname > $o,X_46: pname > $o,A_65: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_46 @ A_65 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ X_46 @ ( semila1780557381name_o @ A_65 @ B_47 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_442_le__supI1,axiom,
% 3.28/1.75 ! [B_47: hoare_1167836817_state > $o,X_46: hoare_1167836817_state > $o,A_65: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_46 @ A_65 )
% 3.28/1.75 => ( ord_le827224136tate_o @ X_46 @ ( semila1172322802tate_o @ A_65 @ B_47 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_443_le__sup__iff,axiom,
% 3.28/1.75 ! [X_45: pname > $o,Y_28: pname > $o,Z_12: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_45 @ Y_28 ) @ Z_12 )
% 3.28/1.75 <=> ( ( ord_less_eq_pname_o @ X_45 @ Z_12 )
% 3.28/1.75 & ( ord_less_eq_pname_o @ Y_28 @ Z_12 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_444_le__sup__iff,axiom,
% 3.28/1.75 ! [X_45: hoare_1167836817_state > $o,Y_28: hoare_1167836817_state > $o,Z_12: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ X_45 @ Y_28 ) @ Z_12 )
% 3.28/1.75 <=> ( ( ord_le827224136tate_o @ X_45 @ Z_12 )
% 3.28/1.75 & ( ord_le827224136tate_o @ Y_28 @ Z_12 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_445_le__iff__sup,axiom,
% 3.28/1.75 ! [X_44: pname > $o,Y_27: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_44 @ Y_27 )
% 3.28/1.75 <=> ( ( semila1780557381name_o @ X_44 @ Y_27 )
% 3.28/1.75 = Y_27 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_446_le__iff__sup,axiom,
% 3.28/1.75 ! [X_44: hoare_1167836817_state > $o,Y_27: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_44 @ Y_27 )
% 3.28/1.75 <=> ( ( semila1172322802tate_o @ X_44 @ Y_27 )
% 3.28/1.75 = Y_27 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_447_sup__ge2,axiom,
% 3.28/1.75 ! [Y_26: pname > $o,X_43: pname > $o] : ( ord_less_eq_pname_o @ Y_26 @ ( semila1780557381name_o @ X_43 @ Y_26 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_448_sup__ge2,axiom,
% 3.28/1.75 ! [Y_26: hoare_1167836817_state > $o,X_43: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ Y_26 @ ( semila1172322802tate_o @ X_43 @ Y_26 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_449_inf__sup__ord_I4_J,axiom,
% 3.28/1.75 ! [Y_25: pname > $o,X_42: pname > $o] : ( ord_less_eq_pname_o @ Y_25 @ ( semila1780557381name_o @ X_42 @ Y_25 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_450_inf__sup__ord_I4_J,axiom,
% 3.28/1.75 ! [Y_25: hoare_1167836817_state > $o,X_42: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ Y_25 @ ( semila1172322802tate_o @ X_42 @ Y_25 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_451_sup__ge1,axiom,
% 3.28/1.75 ! [X_41: pname > $o,Y_24: pname > $o] : ( ord_less_eq_pname_o @ X_41 @ ( semila1780557381name_o @ X_41 @ Y_24 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_452_sup__ge1,axiom,
% 3.28/1.75 ! [X_41: hoare_1167836817_state > $o,Y_24: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_41 @ ( semila1172322802tate_o @ X_41 @ Y_24 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_453_inf__sup__ord_I3_J,axiom,
% 3.28/1.75 ! [X_40: pname > $o,Y_23: pname > $o] : ( ord_less_eq_pname_o @ X_40 @ ( semila1780557381name_o @ X_40 @ Y_23 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_454_inf__sup__ord_I3_J,axiom,
% 3.28/1.75 ! [X_40: hoare_1167836817_state > $o,Y_23: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_40 @ ( semila1172322802tate_o @ X_40 @ Y_23 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_455_sup__eq__bot__iff,axiom,
% 3.28/1.75 ! [X_39: pname > $o,Y_22: pname > $o] :
% 3.28/1.75 ( ( ( semila1780557381name_o @ X_39 @ Y_22 )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 <=> ( ( X_39 = bot_bot_pname_o )
% 3.28/1.75 & ( Y_22 = bot_bot_pname_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_456_sup__eq__bot__iff,axiom,
% 3.28/1.75 ! [X_39: hoare_1167836817_state > $o,Y_22: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( semila1172322802tate_o @ X_39 @ Y_22 )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 <=> ( ( X_39 = bot_bo70021908tate_o )
% 3.28/1.75 & ( Y_22 = bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_457_sup__bot__right,axiom,
% 3.28/1.75 ! [X_38: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ X_38 @ bot_bot_pname_o )
% 3.28/1.75 = X_38 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_458_sup__bot__right,axiom,
% 3.28/1.75 ! [X_38: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_38 @ bot_bo70021908tate_o )
% 3.28/1.75 = X_38 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_459_sup__bot__left,axiom,
% 3.28/1.75 ! [X_37: pname > $o] :
% 3.28/1.75 ( ( semila1780557381name_o @ bot_bot_pname_o @ X_37 )
% 3.28/1.75 = X_37 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_460_sup__bot__left,axiom,
% 3.28/1.75 ! [X_37: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ X_37 )
% 3.28/1.75 = X_37 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_461_folding__one__idem_Ounion__idem,axiom,
% 3.28/1.75 ! [B_46: ( pname > $o ) > $o,A_64: ( pname > $o ) > $o,F_32: ( pname > $o ) > ( pname > $o ) > pname > $o,F_31: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite697516351name_o @ F_32 @ F_31 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_64 )
% 3.28/1.75 => ( ( A_64 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( finite297249702name_o @ B_46 )
% 3.28/1.75 => ( ( B_46 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_31 @ ( semila181081674me_o_o @ A_64 @ B_46 ) )
% 3.28/1.75 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_462_folding__one__idem_Ounion__idem,axiom,
% 3.28/1.75 ! [B_46: ( hoare_1167836817_state > $o ) > $o,A_64: ( hoare_1167836817_state > $o ) > $o,F_32: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_31: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite671847800tate_o @ F_32 @ F_31 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_64 )
% 3.28/1.75 => ( ( A_64 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( finite1380128977tate_o @ B_46 )
% 3.28/1.75 => ( ( B_46 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_31 @ ( semila866907787te_o_o @ A_64 @ B_46 ) )
% 3.28/1.75 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_463_folding__one__idem_Ounion__idem,axiom,
% 3.28/1.75 ! [B_46: pname > $o,A_64: pname > $o,F_32: pname > pname > pname,F_31: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite89670078_pname @ F_32 @ F_31 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_64 )
% 3.28/1.75 => ( ( A_64 != bot_bot_pname_o )
% 3.28/1.75 => ( ( finite_finite_pname @ B_46 )
% 3.28/1.75 => ( ( B_46 != bot_bot_pname_o )
% 3.28/1.75 => ( ( F_31 @ ( semila1780557381name_o @ A_64 @ B_46 ) )
% 3.28/1.75 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_464_folding__one__idem_Ounion__idem,axiom,
% 3.28/1.75 ! [B_46: hoare_1167836817_state > $o,A_64: hoare_1167836817_state > $o,F_32: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_31: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite806517911_state @ F_32 @ F_31 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_64 )
% 3.28/1.75 => ( ( A_64 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( finite1084549118_state @ B_46 )
% 3.28/1.75 => ( ( B_46 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_31 @ ( semila1172322802tate_o @ A_64 @ B_46 ) )
% 3.28/1.75 = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_465_folding__one__idem_Osubset__idem,axiom,
% 3.28/1.75 ! [B_45: ( pname > $o ) > $o,A_63: ( pname > $o ) > $o,F_30: ( pname > $o ) > ( pname > $o ) > pname > $o,F_29: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite697516351name_o @ F_30 @ F_29 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_63 )
% 3.28/1.75 => ( ( B_45 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( ord_le1205211808me_o_o @ B_45 @ A_63 )
% 3.28/1.75 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 3.28/1.75 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_466_folding__one__idem_Osubset__idem,axiom,
% 3.28/1.75 ! [B_45: ( hoare_1167836817_state > $o ) > $o,A_63: ( hoare_1167836817_state > $o ) > $o,F_30: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_29: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite671847800tate_o @ F_30 @ F_29 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_63 )
% 3.28/1.75 => ( ( B_45 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( ord_le741939125te_o_o @ B_45 @ A_63 )
% 3.28/1.75 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 3.28/1.75 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_467_folding__one__idem_Osubset__idem,axiom,
% 3.28/1.75 ! [B_45: pname > $o,A_63: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite89670078_pname @ F_30 @ F_29 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_63 )
% 3.28/1.75 => ( ( B_45 != bot_bot_pname_o )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_45 @ A_63 )
% 3.28/1.75 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 3.28/1.75 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_468_folding__one__idem_Osubset__idem,axiom,
% 3.28/1.75 ! [B_45: hoare_1167836817_state > $o,A_63: hoare_1167836817_state > $o,F_30: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_29: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite806517911_state @ F_30 @ F_29 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_63 )
% 3.28/1.75 => ( ( B_45 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_45 @ A_63 )
% 3.28/1.75 => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
% 3.28/1.75 = ( F_29 @ A_63 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_469_hoare__derivs_OSkip,axiom,
% 3.28/1.75 ! [G_7: hoare_1167836817_state > $o,P_11: state > state > $o] : ( hoare_123228589_state @ G_7 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_11 @ skip @ P_11 ) @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_470_folding__one__idem_Oinsert__idem,axiom,
% 3.28/1.75 ! [X_36: pname,A_62: pname > $o,F_28: pname > pname > pname,F_27: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite89670078_pname @ F_28 @ F_27 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_62 )
% 3.28/1.75 => ( ( A_62 != bot_bot_pname_o )
% 3.28/1.75 => ( ( F_27 @ ( insert_pname @ X_36 @ A_62 ) )
% 3.28/1.75 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_471_folding__one__idem_Oinsert__idem,axiom,
% 3.28/1.75 ! [X_36: hoare_1167836817_state,A_62: hoare_1167836817_state > $o,F_28: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_27: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite806517911_state @ F_28 @ F_27 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_62 )
% 3.28/1.75 => ( ( A_62 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_27 @ ( insert2134838167_state @ X_36 @ A_62 ) )
% 3.28/1.75 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_472_folding__one__idem_Oinsert__idem,axiom,
% 3.28/1.75 ! [X_36: pname > $o,A_62: ( pname > $o ) > $o,F_28: ( pname > $o ) > ( pname > $o ) > pname > $o,F_27: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite697516351name_o @ F_28 @ F_27 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_62 )
% 3.28/1.75 => ( ( A_62 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_27 @ ( insert_pname_o @ X_36 @ A_62 ) )
% 3.28/1.75 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_473_folding__one__idem_Oinsert__idem,axiom,
% 3.28/1.75 ! [X_36: hoare_1167836817_state > $o,A_62: ( hoare_1167836817_state > $o ) > $o,F_28: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_27: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite671847800tate_o @ F_28 @ F_27 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_62 )
% 3.28/1.75 => ( ( A_62 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_27 @ ( insert999278200tate_o @ X_36 @ A_62 ) )
% 3.28/1.75 = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_474_finite__ne__induct,axiom,
% 3.28/1.75 ! [P_10: ( pname > $o ) > $o,F_25: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_25 )
% 3.28/1.75 => ( ( F_25 != bot_bot_pname_o )
% 3.28/1.75 => ( ! [X_5: pname] : ( P_10 @ ( insert_pname @ X_5 @ bot_bot_pname_o ) )
% 3.28/1.75 => ( ! [X_5: pname,F_26: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ F_26 )
% 3.28/1.75 => ( ( F_26 != bot_bot_pname_o )
% 3.28/1.75 => ( ~ ( member_pname @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_10 @ F_26 )
% 3.28/1.75 => ( P_10 @ ( insert_pname @ X_5 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_10 @ F_25 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_475_finite__ne__induct,axiom,
% 3.28/1.75 ! [P_10: ( hoare_1167836817_state > $o ) > $o,F_25: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_25 )
% 3.28/1.75 => ( ( F_25 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state] : ( P_10 @ ( insert2134838167_state @ X_5 @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ F_26 )
% 3.28/1.75 => ( ( F_26 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ~ ( member2058392318_state @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_10 @ F_26 )
% 3.28/1.75 => ( P_10 @ ( insert2134838167_state @ X_5 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_10 @ F_25 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_476_finite__ne__induct,axiom,
% 3.28/1.75 ! [P_10: ( ( pname > $o ) > $o ) > $o,F_25: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_25 )
% 3.28/1.75 => ( ( F_25 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ! [X_5: pname > $o] : ( P_10 @ ( insert_pname_o @ X_5 @ bot_bot_pname_o_o ) )
% 3.28/1.75 => ( ! [X_5: pname > $o,F_26: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ F_26 )
% 3.28/1.75 => ( ( F_26 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ~ ( member_pname_o @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_10 @ F_26 )
% 3.28/1.75 => ( P_10 @ ( insert_pname_o @ X_5 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_10 @ F_25 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_477_finite__ne__induct,axiom,
% 3.28/1.75 ! [P_10: ( ( hoare_1167836817_state > $o ) > $o ) > $o,F_25: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_25 )
% 3.28/1.75 => ( ( F_25 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o] : ( P_10 @ ( insert999278200tate_o @ X_5 @ bot_bo691907561te_o_o ) )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ F_26 )
% 3.28/1.75 => ( ( F_26 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ~ ( member864234961tate_o @ X_5 @ F_26 )
% 3.28/1.75 => ( ( P_10 @ F_26 )
% 3.28/1.75 => ( P_10 @ ( insert999278200tate_o @ X_5 @ F_26 ) ) ) ) ) )
% 3.28/1.75 => ( P_10 @ F_25 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_478_com_Osimps_I19_J,axiom,
% 3.28/1.75 ! [Pname: pname] :
% 3.28/1.75 ( ( body_1 @ Pname )
% 3.28/1.75 != skip ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_479_com_Osimps_I18_J,axiom,
% 3.28/1.75 ! [Pname: pname] :
% 3.28/1.75 ( skip
% 3.28/1.75 != ( body_1 @ Pname ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_480_WT_OSkip,axiom,
% 3.28/1.75 wt @ skip ).
% 3.28/1.75
% 3.28/1.75 thf(fact_481_folding__one__idem_Oin__idem,axiom,
% 3.28/1.75 ! [X_35: pname,A_61: pname > $o,F_24: pname > pname > pname,F_23: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite89670078_pname @ F_24 @ F_23 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_61 )
% 3.28/1.75 => ( ( member_pname @ X_35 @ A_61 )
% 3.28/1.75 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 3.28/1.75 = ( F_23 @ A_61 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_482_folding__one__idem_Oin__idem,axiom,
% 3.28/1.75 ! [X_35: hoare_1167836817_state,A_61: hoare_1167836817_state > $o,F_24: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_23: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite806517911_state @ F_24 @ F_23 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_61 )
% 3.28/1.75 => ( ( member2058392318_state @ X_35 @ A_61 )
% 3.28/1.75 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 3.28/1.75 = ( F_23 @ A_61 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_483_folding__one__idem_Oin__idem,axiom,
% 3.28/1.75 ! [X_35: pname > $o,A_61: ( pname > $o ) > $o,F_24: ( pname > $o ) > ( pname > $o ) > pname > $o,F_23: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite697516351name_o @ F_24 @ F_23 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_61 )
% 3.28/1.75 => ( ( member_pname_o @ X_35 @ A_61 )
% 3.28/1.75 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 3.28/1.75 = ( F_23 @ A_61 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_484_folding__one__idem_Oin__idem,axiom,
% 3.28/1.75 ! [X_35: hoare_1167836817_state > $o,A_61: ( hoare_1167836817_state > $o ) > $o,F_24: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_23: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite671847800tate_o @ F_24 @ F_23 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_61 )
% 3.28/1.75 => ( ( member864234961tate_o @ X_35 @ A_61 )
% 3.28/1.75 => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
% 3.28/1.75 = ( F_23 @ A_61 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_485_folding__one__idem_Ohom__commute,axiom,
% 3.28/1.75 ! [N_1: ( pname > $o ) > $o,H: ( pname > $o ) > pname > $o,F_22: ( pname > $o ) > ( pname > $o ) > pname > $o,F_21: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite697516351name_o @ F_22 @ F_21 )
% 3.28/1.75 => ( ! [X_5: pname > $o,Y_2: pname > $o] :
% 3.28/1.75 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 3.28/1.75 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 3.28/1.75 => ( ( finite297249702name_o @ N_1 )
% 3.28/1.75 => ( ( N_1 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( H @ ( F_21 @ N_1 ) )
% 3.28/1.75 = ( F_21 @ ( image_1085733413name_o @ H @ N_1 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_486_folding__one__idem_Ohom__commute,axiom,
% 3.28/1.75 ! [N_1: ( hoare_1167836817_state > $o ) > $o,H: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_22: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_21: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite671847800tate_o @ F_22 @ F_21 )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 3.28/1.75 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 3.28/1.75 => ( ( finite1380128977tate_o @ N_1 )
% 3.28/1.75 => ( ( N_1 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( H @ ( F_21 @ N_1 ) )
% 3.28/1.75 = ( F_21 @ ( image_1488525317tate_o @ H @ N_1 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_487_folding__one__idem_Ohom__commute,axiom,
% 3.28/1.75 ! [N_1: pname > $o,H: pname > pname,F_22: pname > pname > pname,F_21: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite89670078_pname @ F_22 @ F_21 )
% 3.28/1.75 => ( ! [X_5: pname,Y_2: pname] :
% 3.28/1.75 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 3.28/1.75 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 3.28/1.75 => ( ( finite_finite_pname @ N_1 )
% 3.28/1.75 => ( ( N_1 != bot_bot_pname_o )
% 3.28/1.75 => ( ( H @ ( F_21 @ N_1 ) )
% 3.28/1.75 = ( F_21 @ ( image_pname_pname @ H @ N_1 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_488_folding__one__idem_Ohom__commute,axiom,
% 3.28/1.75 ! [N_1: hoare_1167836817_state > $o,H: hoare_1167836817_state > hoare_1167836817_state,F_22: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_21: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite806517911_state @ F_22 @ F_21 )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state,Y_2: hoare_1167836817_state] :
% 3.28/1.75 ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
% 3.28/1.75 = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
% 3.28/1.75 => ( ( finite1084549118_state @ N_1 )
% 3.28/1.75 => ( ( N_1 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( H @ ( F_21 @ N_1 ) )
% 3.28/1.75 = ( F_21 @ ( image_31595733_state @ H @ N_1 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_489_LoopF,axiom,
% 3.28/1.75 ! [G_6: hoare_1167836817_state > $o,P_9: state > state > $o,B_44: state > $o,C_23: com] :
% 3.28/1.75 ( hoare_123228589_state @ G_6
% 3.28/1.75 @ ( insert2134838167_state
% 3.28/1.75 @ ( hoare_908217195_state
% 3.28/1.75 @ ^ [Z_11: state,S_3: state] : ( (&) @ ( P_9 @ Z_11 @ S_3 ) @ ( (~) @ ( B_44 @ S_3 ) ) )
% 3.28/1.75 @ ( while @ B_44 @ C_23 )
% 3.28/1.75 @ P_9 )
% 3.28/1.75 @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_490_Comp,axiom,
% 3.28/1.75 ! [D_2: com,R_1: state > state > $o,G_5: hoare_1167836817_state > $o,P_8: state > state > $o,C_22: com,Q_4: state > state > $o] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_8 @ C_22 @ Q_4 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ Q_4 @ D_2 @ R_1 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_8 @ ( semi @ C_22 @ D_2 ) @ R_1 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_491_the__elem__def,axiom,
% 3.28/1.75 ! [X_34: pname > $o] :
% 3.28/1.75 ( ( the_elem_pname @ X_34 )
% 3.28/1.75 = ( the_pname
% 3.28/1.75 @ ^ [X_5: pname] :
% 3.28/1.75 ( X_34
% 3.28/1.75 = ( insert_pname @ X_5 @ bot_bot_pname_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_492_the__elem__def,axiom,
% 3.28/1.75 ! [X_34: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( the_el323660082_state @ X_34 )
% 3.28/1.75 = ( the_Ho310147232_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( X_34
% 3.28/1.75 = ( insert2134838167_state @ X_5 @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_493_WTs__elim__cases_I6_J,axiom,
% 3.28/1.75 ! [B_42: state > $o,C_21: com] :
% 3.28/1.75 ( ( wt @ ( while @ B_42 @ C_21 ) )
% 3.28/1.75 => ( wt @ C_21 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_494_WTs__elim__cases_I4_J,axiom,
% 3.28/1.75 ! [C1: com,C2: com] :
% 3.28/1.75 ( ( wt @ ( semi @ C1 @ C2 ) )
% 3.28/1.75 => ~ ( ( wt @ C1 )
% 3.28/1.75 => ~ ( wt @ C2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_495_com_Osimps_I46_J,axiom,
% 3.28/1.75 ! [Com1_1: com,Com2_1: com,Fun: state > $o,Com_1: com] :
% 3.28/1.75 ( ( semi @ Com1_1 @ Com2_1 )
% 3.28/1.75 != ( while @ Fun @ Com_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_496_com_Osimps_I47_J,axiom,
% 3.28/1.75 ! [Fun: state > $o,Com_1: com,Com1_1: com,Com2_1: com] :
% 3.28/1.75 ( ( while @ Fun @ Com_1 )
% 3.28/1.75 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_497_com_Osimps_I3_J,axiom,
% 3.28/1.75 ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
% 3.28/1.75 ( ( ( semi @ Com1_1 @ Com2_1 )
% 3.28/1.75 = ( semi @ Com1 @ Com2 ) )
% 3.28/1.75 <=> ( ( Com1_1 = Com1 )
% 3.28/1.75 & ( Com2_1 = Com2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_498_com_Osimps_I5_J,axiom,
% 3.28/1.75 ! [Fun_1: state > $o,Com_2: com,Fun: state > $o,Com_1: com] :
% 3.28/1.75 ( ( ( while @ Fun_1 @ Com_2 )
% 3.28/1.75 = ( while @ Fun @ Com_1 ) )
% 3.28/1.75 <=> ( ( Fun_1 = Fun )
% 3.28/1.75 & ( Com_2 = Com_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_499_com_Osimps_I59_J,axiom,
% 3.28/1.75 ! [Pname: pname,Fun_1: state > $o,Com_2: com] :
% 3.28/1.75 ( ( body_1 @ Pname )
% 3.28/1.75 != ( while @ Fun_1 @ Com_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_500_com_Osimps_I58_J,axiom,
% 3.28/1.75 ! [Fun_1: state > $o,Com_2: com,Pname: pname] :
% 3.28/1.75 ( ( while @ Fun_1 @ Com_2 )
% 3.28/1.75 != ( body_1 @ Pname ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_501_While,axiom,
% 3.28/1.75 ! [B_42: state > $o,C_21: com] :
% 3.28/1.75 ( ( wt @ C_21 )
% 3.28/1.75 => ( wt @ ( while @ B_42 @ C_21 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_502_com_Osimps_I16_J,axiom,
% 3.28/1.75 ! [Fun: state > $o,Com_1: com] :
% 3.28/1.75 ( skip
% 3.28/1.75 != ( while @ Fun @ Com_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_503_com_Osimps_I17_J,axiom,
% 3.28/1.75 ! [Fun: state > $o,Com_1: com] :
% 3.28/1.75 ( ( while @ Fun @ Com_1 )
% 3.28/1.75 != skip ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_504_com_Osimps_I49_J,axiom,
% 3.28/1.75 ! [Pname: pname,Com1_1: com,Com2_1: com] :
% 3.28/1.75 ( ( body_1 @ Pname )
% 3.28/1.75 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_505_com_Osimps_I48_J,axiom,
% 3.28/1.75 ! [Com1_1: com,Com2_1: com,Pname: pname] :
% 3.28/1.75 ( ( semi @ Com1_1 @ Com2_1 )
% 3.28/1.75 != ( body_1 @ Pname ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_506_WT_OSemi,axiom,
% 3.28/1.75 ! [C1: com,C0: com] :
% 3.28/1.75 ( ( wt @ C0 )
% 3.28/1.75 => ( ( wt @ C1 )
% 3.28/1.75 => ( wt @ ( semi @ C0 @ C1 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_507_com_Osimps_I12_J,axiom,
% 3.28/1.75 ! [Com1: com,Com2: com] :
% 3.28/1.75 ( skip
% 3.28/1.75 != ( semi @ Com1 @ Com2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_508_com_Osimps_I13_J,axiom,
% 3.28/1.75 ! [Com1: com,Com2: com] :
% 3.28/1.75 ( ( semi @ Com1 @ Com2 )
% 3.28/1.75 != skip ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_509_folding__one_Oinsert,axiom,
% 3.28/1.75 ! [X_33: pname,A_60: pname > $o,F_20: pname > pname > pname,F_19: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_20 @ F_19 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_60 )
% 3.28/1.75 => ( ~ ( member_pname @ X_33 @ A_60 )
% 3.28/1.75 => ( ( A_60 != bot_bot_pname_o )
% 3.28/1.75 => ( ( F_19 @ ( insert_pname @ X_33 @ A_60 ) )
% 3.28/1.75 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_510_folding__one_Oinsert,axiom,
% 3.28/1.75 ! [X_33: hoare_1167836817_state,A_60: hoare_1167836817_state > $o,F_20: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_19: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_20 @ F_19 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_60 )
% 3.28/1.75 => ( ~ ( member2058392318_state @ X_33 @ A_60 )
% 3.28/1.75 => ( ( A_60 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_19 @ ( insert2134838167_state @ X_33 @ A_60 ) )
% 3.28/1.75 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_511_folding__one_Oinsert,axiom,
% 3.28/1.75 ! [X_33: pname > $o,A_60: ( pname > $o ) > $o,F_20: ( pname > $o ) > ( pname > $o ) > pname > $o,F_19: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite349908348name_o @ F_20 @ F_19 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_60 )
% 3.28/1.75 => ( ~ ( member_pname_o @ X_33 @ A_60 )
% 3.28/1.75 => ( ( A_60 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_19 @ ( insert_pname_o @ X_33 @ A_60 ) )
% 3.28/1.75 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_512_folding__one_Oinsert,axiom,
% 3.28/1.75 ! [X_33: hoare_1167836817_state > $o,A_60: ( hoare_1167836817_state > $o ) > $o,F_20: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_19: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite979047547tate_o @ F_20 @ F_19 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_60 )
% 3.28/1.75 => ( ~ ( member864234961tate_o @ X_33 @ A_60 )
% 3.28/1.75 => ( ( A_60 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_19 @ ( insert999278200tate_o @ X_33 @ A_60 ) )
% 3.28/1.75 = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_513_folding__one_Osingleton,axiom,
% 3.28/1.75 ! [X_32: pname,F_18: pname > pname > pname,F_17: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_18 @ F_17 )
% 3.28/1.75 => ( ( F_17 @ ( insert_pname @ X_32 @ bot_bot_pname_o ) )
% 3.28/1.75 = X_32 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_514_folding__one_Osingleton,axiom,
% 3.28/1.75 ! [X_32: hoare_1167836817_state,F_18: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_17: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_18 @ F_17 )
% 3.28/1.75 => ( ( F_17 @ ( insert2134838167_state @ X_32 @ bot_bo70021908tate_o ) )
% 3.28/1.75 = X_32 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_515_folding__one_Oclosed,axiom,
% 3.28/1.75 ! [A_59: pname > $o,F_16: pname > pname > pname,F_15: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_16 @ F_15 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_59 )
% 3.28/1.75 => ( ( A_59 != bot_bot_pname_o )
% 3.28/1.75 => ( ! [X_5: pname,Y_2: pname] : ( member_pname @ ( F_16 @ X_5 @ Y_2 ) @ ( insert_pname @ X_5 @ ( insert_pname @ Y_2 @ bot_bot_pname_o ) ) )
% 3.28/1.75 => ( member_pname @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_516_folding__one_Oclosed,axiom,
% 3.28/1.75 ! [A_59: hoare_1167836817_state > $o,F_16: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_15: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_16 @ F_15 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_59 )
% 3.28/1.75 => ( ( A_59 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state,Y_2: hoare_1167836817_state] : ( member2058392318_state @ ( F_16 @ X_5 @ Y_2 ) @ ( insert2134838167_state @ X_5 @ ( insert2134838167_state @ Y_2 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 => ( member2058392318_state @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_517_folding__one_Oclosed,axiom,
% 3.28/1.75 ! [A_59: ( pname > $o ) > $o,F_16: ( pname > $o ) > ( pname > $o ) > pname > $o,F_15: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite349908348name_o @ F_16 @ F_15 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_59 )
% 3.28/1.75 => ( ( A_59 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ! [X_5: pname > $o,Y_2: pname > $o] : ( member_pname_o @ ( F_16 @ X_5 @ Y_2 ) @ ( insert_pname_o @ X_5 @ ( insert_pname_o @ Y_2 @ bot_bot_pname_o_o ) ) )
% 3.28/1.75 => ( member_pname_o @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_518_folding__one_Oclosed,axiom,
% 3.28/1.75 ! [A_59: ( hoare_1167836817_state > $o ) > $o,F_16: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_15: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite979047547tate_o @ F_16 @ F_15 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_59 )
% 3.28/1.75 => ( ( A_59 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] : ( member864234961tate_o @ ( F_16 @ X_5 @ Y_2 ) @ ( insert999278200tate_o @ X_5 @ ( insert999278200tate_o @ Y_2 @ bot_bo691907561te_o_o ) ) )
% 3.28/1.75 => ( member864234961tate_o @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_519_triple_Oexhaust,axiom,
% 3.28/1.75 ! [Y_21: hoare_1167836817_state] :
% 3.28/1.75 ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
% 3.28/1.75 ( Y_21
% 3.28/1.75 != ( hoare_908217195_state @ Fun1 @ Com @ Fun2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_520_image__cong,axiom,
% 3.28/1.75 ! [F_14: pname > hoare_1167836817_state,G_4: pname > hoare_1167836817_state,M: pname > $o,N: pname > $o] :
% 3.28/1.75 ( ( M = N )
% 3.28/1.75 => ( ! [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ N )
% 3.28/1.75 => ( ( F_14 @ X_5 )
% 3.28/1.75 = ( G_4 @ X_5 ) ) )
% 3.28/1.75 => ( ( image_575578384_state @ F_14 @ M )
% 3.28/1.75 = ( image_575578384_state @ G_4 @ N ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_521_Collect__mono,axiom,
% 3.28/1.75 ! [Q_3: hoare_1167836817_state > $o,P_7: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( P_7 @ X_5 )
% 3.28/1.75 => ( Q_3 @ X_5 ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( collec1027672124_state @ P_7 ) @ ( collec1027672124_state @ Q_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_522_Collect__mono,axiom,
% 3.28/1.75 ! [Q_3: pname > $o,P_7: pname > $o] :
% 3.28/1.75 ( ! [X_5: pname] :
% 3.28/1.75 ( ( P_7 @ X_5 )
% 3.28/1.75 => ( Q_3 @ X_5 ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( collect_pname @ P_7 ) @ ( collect_pname @ Q_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_523_Collect__mono,axiom,
% 3.28/1.75 ! [Q_3: ( pname > $o ) > $o,P_7: ( pname > $o ) > $o] :
% 3.28/1.75 ( ! [X_5: pname > $o] :
% 3.28/1.75 ( ( P_7 @ X_5 )
% 3.28/1.75 => ( Q_3 @ X_5 ) )
% 3.28/1.75 => ( ord_le1205211808me_o_o @ ( collect_pname_o @ P_7 ) @ ( collect_pname_o @ Q_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_524_Collect__mono,axiom,
% 3.28/1.75 ! [Q_3: ( hoare_1167836817_state > $o ) > $o,P_7: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( P_7 @ X_5 )
% 3.28/1.75 => ( Q_3 @ X_5 ) )
% 3.28/1.75 => ( ord_le741939125te_o_o @ ( collec269976083tate_o @ P_7 ) @ ( collec269976083tate_o @ Q_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_525_predicate1I,axiom,
% 3.28/1.75 ! [Q_2: pname > $o,P_6: pname > $o] :
% 3.28/1.75 ( ! [X_5: pname] :
% 3.28/1.75 ( ( P_6 @ X_5 )
% 3.28/1.75 => ( Q_2 @ X_5 ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ P_6 @ Q_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_526_predicate1I,axiom,
% 3.28/1.75 ! [Q_2: hoare_1167836817_state > $o,P_6: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( P_6 @ X_5 )
% 3.28/1.75 => ( Q_2 @ X_5 ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ P_6 @ Q_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_527_mk__disjoint__insert,axiom,
% 3.28/1.75 ! [A_58: pname,A_57: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_58 @ A_57 )
% 3.28/1.75 => ? [B_43: pname > $o] :
% 3.28/1.75 ( ( A_57
% 3.28/1.75 = ( insert_pname @ A_58 @ B_43 ) )
% 3.28/1.75 & ~ ( member_pname @ A_58 @ B_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_528_mk__disjoint__insert,axiom,
% 3.28/1.75 ! [A_58: hoare_1167836817_state,A_57: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_58 @ A_57 )
% 3.28/1.75 => ? [B_43: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_57
% 3.28/1.75 = ( insert2134838167_state @ A_58 @ B_43 ) )
% 3.28/1.75 & ~ ( member2058392318_state @ A_58 @ B_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_529_Set_Oset__insert,axiom,
% 3.28/1.75 ! [X_31: pname,A_56: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_31 @ A_56 )
% 3.28/1.75 => ~ ! [B_43: pname > $o] :
% 3.28/1.75 ( ( A_56
% 3.28/1.75 = ( insert_pname @ X_31 @ B_43 ) )
% 3.28/1.75 => ( member_pname @ X_31 @ B_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_530_Set_Oset__insert,axiom,
% 3.28/1.75 ! [X_31: hoare_1167836817_state,A_56: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_31 @ A_56 )
% 3.28/1.75 => ~ ! [B_43: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_56
% 3.28/1.75 = ( insert2134838167_state @ X_31 @ B_43 ) )
% 3.28/1.75 => ( member2058392318_state @ X_31 @ B_43 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_531_equals0I,axiom,
% 3.28/1.75 ! [A_55: pname > $o] :
% 3.28/1.75 ( ! [Y_2: pname] :
% 3.28/1.75 ~ ( member_pname @ Y_2 @ A_55 )
% 3.28/1.75 => ( A_55 = bot_bot_pname_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_532_equals0I,axiom,
% 3.28/1.75 ! [A_55: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [Y_2: hoare_1167836817_state] :
% 3.28/1.75 ~ ( member2058392318_state @ Y_2 @ A_55 )
% 3.28/1.75 => ( A_55 = bot_bo70021908tate_o ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_533_MGT__alternD,axiom,
% 3.28/1.75 ! [G_3: hoare_1167836817_state > $o,C_21: com] :
% 3.28/1.75 ( hoare_1201148605gleton
% 3.28/1.75 => ( ( hoare_123228589_state @ G_3
% 3.28/1.75 @ ( insert2134838167_state
% 3.28/1.75 @ ( hoare_908217195_state
% 3.28/1.75 @ ^ [Z_11: state,S0_1: state] :
% 3.28/1.75 ! [S1: state] : ( (=>) @ ( evalc @ C_21 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 3.28/1.75 @ C_21
% 3.28/1.75 @ fequal_state )
% 3.28/1.75 @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_534_MGT__alternI,axiom,
% 3.28/1.75 ! [G_3: hoare_1167836817_state > $o,C_21: com] :
% 3.28/1.75 ( ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) )
% 3.28/1.75 => ( hoare_123228589_state @ G_3
% 3.28/1.75 @ ( insert2134838167_state
% 3.28/1.75 @ ( hoare_908217195_state
% 3.28/1.75 @ ^ [Z_11: state,S0_1: state] :
% 3.28/1.75 ! [S1: state] : ( (=>) @ ( evalc @ C_21 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 3.28/1.75 @ C_21
% 3.28/1.75 @ fequal_state )
% 3.28/1.75 @ bot_bo70021908tate_o ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_535_MGT__def,axiom,
% 3.28/1.75 ! [C_21: com] :
% 3.28/1.75 ( ( hoare_Mirabelle_MGT @ C_21 )
% 3.28/1.75 = ( hoare_908217195_state @ fequal_state @ C_21 @ ( evalc @ C_21 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_536_evalc_OBody,axiom,
% 3.28/1.75 ! [Pn_1: pname,S0: state,S1_1: state] :
% 3.28/1.75 ( ( evalc @ ( the_com @ ( body @ Pn_1 ) ) @ S0 @ S1_1 )
% 3.28/1.75 => ( evalc @ ( body_1 @ Pn_1 ) @ S0 @ S1_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_537_evalc__elim__cases_I6_J,axiom,
% 3.28/1.75 ! [P: pname,S_2: state,S1_1: state] :
% 3.28/1.75 ( ( evalc @ ( body_1 @ P ) @ S_2 @ S1_1 )
% 3.28/1.75 => ( evalc @ ( the_com @ ( body @ P ) ) @ S_2 @ S1_1 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_538_evalc__elim__cases_I1_J,axiom,
% 3.28/1.75 ! [S_2: state,T: state] :
% 3.28/1.75 ( ( evalc @ skip @ S_2 @ T )
% 3.28/1.75 => ( T = S_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_539_evalc_OWhileFalse,axiom,
% 3.28/1.75 ! [C_21: com,B_42: state > $o,S_2: state] :
% 3.28/1.75 ( ~ ( B_42 @ S_2 )
% 3.28/1.75 => ( evalc @ ( while @ B_42 @ C_21 ) @ S_2 @ S_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_540_evalc_OWhileTrue,axiom,
% 3.28/1.75 ! [S2: state,C_21: com,S1_1: state,B_42: state > $o,S0: state] :
% 3.28/1.75 ( ( B_42 @ S0 )
% 3.28/1.75 => ( ( evalc @ C_21 @ S0 @ S1_1 )
% 3.28/1.75 => ( ( evalc @ ( while @ B_42 @ C_21 ) @ S1_1 @ S2 )
% 3.28/1.75 => ( evalc @ ( while @ B_42 @ C_21 ) @ S0 @ S2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_541_evalc_OSemi,axiom,
% 3.28/1.75 ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
% 3.28/1.75 ( ( evalc @ C0 @ S0 @ S1_1 )
% 3.28/1.75 => ( ( evalc @ C1 @ S1_1 @ S2 )
% 3.28/1.75 => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_542_evalc_OSkip,axiom,
% 3.28/1.75 ! [S_2: state] : ( evalc @ skip @ S_2 @ S_2 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_543_com__det,axiom,
% 3.28/1.75 ! [U: state,C_21: com,S_2: state,T: state] :
% 3.28/1.75 ( ( evalc @ C_21 @ S_2 @ T )
% 3.28/1.75 => ( ( evalc @ C_21 @ S_2 @ U )
% 3.28/1.75 => ( U = T ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_544_evalc__elim__cases_I4_J,axiom,
% 3.28/1.75 ! [C1: com,C2: com,S_2: state,T: state] :
% 3.28/1.75 ( ( evalc @ ( semi @ C1 @ C2 ) @ S_2 @ T )
% 3.28/1.75 => ~ ! [S1: state] :
% 3.28/1.75 ( ( evalc @ C1 @ S_2 @ S1 )
% 3.28/1.75 => ~ ( evalc @ C2 @ S1 @ T ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_545_evalc__WHILE__case,axiom,
% 3.28/1.75 ! [B_42: state > $o,C_21: com,S_2: state,T: state] :
% 3.28/1.75 ( ( evalc @ ( while @ B_42 @ C_21 ) @ S_2 @ T )
% 3.28/1.75 => ( ( ( T = S_2 )
% 3.28/1.75 => ( B_42 @ S_2 ) )
% 3.28/1.75 => ~ ( ( B_42 @ S_2 )
% 3.28/1.75 => ! [S1: state] :
% 3.28/1.75 ( ( evalc @ C_21 @ S_2 @ S1 )
% 3.28/1.75 => ~ ( evalc @ ( while @ B_42 @ C_21 ) @ S1 @ T ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_546_xt1_I15_J,axiom,
% 3.28/1.75 ! [C_20: pname > $o,A_54: pname > $o,F_13: ( pname > $o ) > pname > $o,B_41: pname > $o] :
% 3.28/1.75 ( ( A_54
% 3.28/1.75 = ( F_13 @ B_41 ) )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ C_20 @ B_41 )
% 3.28/1.75 => ( ! [X_5: pname > $o,Y_2: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_2 @ X_5 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( F_13 @ Y_2 ) @ ( F_13 @ X_5 ) ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( F_13 @ C_20 ) @ A_54 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_547_xt1_I15_J,axiom,
% 3.28/1.75 ! [C_20: hoare_1167836817_state > $o,A_54: hoare_1167836817_state > $o,F_13: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B_41: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( A_54
% 3.28/1.75 = ( F_13 @ B_41 ) )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ C_20 @ B_41 )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_2 @ X_5 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( F_13 @ Y_2 ) @ ( F_13 @ X_5 ) ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( F_13 @ C_20 ) @ A_54 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_548_xt1_I16_J,axiom,
% 3.28/1.75 ! [F_12: ( pname > $o ) > pname > $o,C_19: pname > $o,B_40: pname > $o,A_53: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ B_40 @ A_53 )
% 3.28/1.75 => ( ( ( F_12 @ B_40 )
% 3.28/1.75 = C_19 )
% 3.28/1.75 => ( ! [X_5: pname > $o,Y_2: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_2 @ X_5 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( F_12 @ Y_2 ) @ ( F_12 @ X_5 ) ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ C_19 @ ( F_12 @ A_53 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_549_xt1_I16_J,axiom,
% 3.28/1.75 ! [F_12: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,C_19: hoare_1167836817_state > $o,B_40: hoare_1167836817_state > $o,A_53: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ B_40 @ A_53 )
% 3.28/1.75 => ( ( ( F_12 @ B_40 )
% 3.28/1.75 = C_19 )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_2 @ X_5 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( F_12 @ Y_2 ) @ ( F_12 @ X_5 ) ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ C_19 @ ( F_12 @ A_53 ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_550_folding__one_Ounion__inter,axiom,
% 3.28/1.75 ! [B_39: ( pname > $o ) > $o,A_52: ( pname > $o ) > $o,F_11: ( pname > $o ) > ( pname > $o ) > pname > $o,F_10: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite349908348name_o @ F_11 @ F_10 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_52 )
% 3.28/1.75 => ( ( finite297249702name_o @ B_39 )
% 3.28/1.75 => ( ( ( semila2013987940me_o_o @ A_52 @ B_39 )
% 3.28/1.75 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_11 @ ( F_10 @ ( semila181081674me_o_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila2013987940me_o_o @ A_52 @ B_39 ) ) )
% 3.28/1.75 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_551_folding__one_Ounion__inter,axiom,
% 3.28/1.75 ! [B_39: ( hoare_1167836817_state > $o ) > $o,A_52: ( hoare_1167836817_state > $o ) > $o,F_11: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_10: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite979047547tate_o @ F_11 @ F_10 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_52 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ B_39 )
% 3.28/1.75 => ( ( ( semila1758709489te_o_o @ A_52 @ B_39 )
% 3.28/1.75 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_11 @ ( F_10 @ ( semila866907787te_o_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila1758709489te_o_o @ A_52 @ B_39 ) ) )
% 3.28/1.75 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_552_folding__one_Ounion__inter,axiom,
% 3.28/1.75 ! [B_39: pname > $o,A_52: pname > $o,F_11: pname > pname > pname,F_10: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_11 @ F_10 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_52 )
% 3.28/1.75 => ( ( finite_finite_pname @ B_39 )
% 3.28/1.75 => ( ( ( semila1673364395name_o @ A_52 @ B_39 )
% 3.28/1.75 != bot_bot_pname_o )
% 3.28/1.75 => ( ( F_11 @ ( F_10 @ ( semila1780557381name_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila1673364395name_o @ A_52 @ B_39 ) ) )
% 3.28/1.75 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_553_folding__one_Ounion__inter,axiom,
% 3.28/1.75 ! [B_39: hoare_1167836817_state > $o,A_52: hoare_1167836817_state > $o,F_11: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_10: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_11 @ F_10 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_52 )
% 3.28/1.75 => ( ( finite1084549118_state @ B_39 )
% 3.28/1.75 => ( ( ( semila179895820tate_o @ A_52 @ B_39 )
% 3.28/1.75 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_11 @ ( F_10 @ ( semila1172322802tate_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila179895820tate_o @ A_52 @ B_39 ) ) )
% 3.28/1.75 = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_554_folding__one_Ounion__disjoint,axiom,
% 3.28/1.75 ! [B_38: ( pname > $o ) > $o,A_51: ( pname > $o ) > $o,F_9: ( pname > $o ) > ( pname > $o ) > pname > $o,F_8: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite349908348name_o @ F_9 @ F_8 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_51 )
% 3.28/1.75 => ( ( A_51 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( finite297249702name_o @ B_38 )
% 3.28/1.75 => ( ( B_38 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( ( semila2013987940me_o_o @ A_51 @ B_38 )
% 3.28/1.75 = bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_8 @ ( semila181081674me_o_o @ A_51 @ B_38 ) )
% 3.28/1.75 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_555_folding__one_Ounion__disjoint,axiom,
% 3.28/1.75 ! [B_38: ( hoare_1167836817_state > $o ) > $o,A_51: ( hoare_1167836817_state > $o ) > $o,F_9: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_8: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite979047547tate_o @ F_9 @ F_8 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_51 )
% 3.28/1.75 => ( ( A_51 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( finite1380128977tate_o @ B_38 )
% 3.28/1.75 => ( ( B_38 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( ( semila1758709489te_o_o @ A_51 @ B_38 )
% 3.28/1.75 = bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_8 @ ( semila866907787te_o_o @ A_51 @ B_38 ) )
% 3.28/1.75 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_556_folding__one_Ounion__disjoint,axiom,
% 3.28/1.75 ! [B_38: pname > $o,A_51: pname > $o,F_9: pname > pname > pname,F_8: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_9 @ F_8 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_51 )
% 3.28/1.75 => ( ( A_51 != bot_bot_pname_o )
% 3.28/1.75 => ( ( finite_finite_pname @ B_38 )
% 3.28/1.75 => ( ( B_38 != bot_bot_pname_o )
% 3.28/1.75 => ( ( ( semila1673364395name_o @ A_51 @ B_38 )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 => ( ( F_8 @ ( semila1780557381name_o @ A_51 @ B_38 ) )
% 3.28/1.75 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_557_folding__one_Ounion__disjoint,axiom,
% 3.28/1.75 ! [B_38: hoare_1167836817_state > $o,A_51: hoare_1167836817_state > $o,F_9: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_8: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_9 @ F_8 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_51 )
% 3.28/1.75 => ( ( A_51 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( finite1084549118_state @ B_38 )
% 3.28/1.75 => ( ( B_38 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( ( semila179895820tate_o @ A_51 @ B_38 )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_8 @ ( semila1172322802tate_o @ A_51 @ B_38 ) )
% 3.28/1.75 = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_558_IntI,axiom,
% 3.28/1.75 ! [B_37: pname > $o,C_18: pname,A_50: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_18 @ A_50 )
% 3.28/1.75 => ( ( member_pname @ C_18 @ B_37 )
% 3.28/1.75 => ( member_pname @ C_18 @ ( semila1673364395name_o @ A_50 @ B_37 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_559_IntI,axiom,
% 3.28/1.75 ! [B_37: hoare_1167836817_state > $o,C_18: hoare_1167836817_state,A_50: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_18 @ A_50 )
% 3.28/1.75 => ( ( member2058392318_state @ C_18 @ B_37 )
% 3.28/1.75 => ( member2058392318_state @ C_18 @ ( semila179895820tate_o @ A_50 @ B_37 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_560_IntE,axiom,
% 3.28/1.75 ! [C_17: pname,A_49: pname > $o,B_36: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_17 @ ( semila1673364395name_o @ A_49 @ B_36 ) )
% 3.28/1.75 => ~ ( ( member_pname @ C_17 @ A_49 )
% 3.28/1.75 => ~ ( member_pname @ C_17 @ B_36 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_561_IntE,axiom,
% 3.28/1.75 ! [C_17: hoare_1167836817_state,A_49: hoare_1167836817_state > $o,B_36: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_17 @ ( semila179895820tate_o @ A_49 @ B_36 ) )
% 3.28/1.75 => ~ ( ( member2058392318_state @ C_17 @ A_49 )
% 3.28/1.75 => ~ ( member2058392318_state @ C_17 @ B_36 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_562_finite__Int,axiom,
% 3.28/1.75 ! [G_2: ( pname > $o ) > $o,F_7: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ( finite297249702name_o @ F_7 )
% 3.28/1.75 | ( finite297249702name_o @ G_2 ) )
% 3.28/1.75 => ( finite297249702name_o @ ( semila2013987940me_o_o @ F_7 @ G_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_563_finite__Int,axiom,
% 3.28/1.75 ! [G_2: ( hoare_1167836817_state > $o ) > $o,F_7: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ( finite1380128977tate_o @ F_7 )
% 3.28/1.75 | ( finite1380128977tate_o @ G_2 ) )
% 3.28/1.75 => ( finite1380128977tate_o @ ( semila1758709489te_o_o @ F_7 @ G_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_564_finite__Int,axiom,
% 3.28/1.75 ! [G_2: pname > $o,F_7: pname > $o] :
% 3.28/1.75 ( ( ( finite_finite_pname @ F_7 )
% 3.28/1.75 | ( finite_finite_pname @ G_2 ) )
% 3.28/1.75 => ( finite_finite_pname @ ( semila1673364395name_o @ F_7 @ G_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_565_finite__Int,axiom,
% 3.28/1.75 ! [G_2: hoare_1167836817_state > $o,F_7: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( finite1084549118_state @ F_7 )
% 3.28/1.75 | ( finite1084549118_state @ G_2 ) )
% 3.28/1.75 => ( finite1084549118_state @ ( semila179895820tate_o @ F_7 @ G_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_566_disjoint__iff__not__equal,axiom,
% 3.28/1.75 ! [A_48: pname > $o,B_35: pname > $o] :
% 3.28/1.75 ( ( ( semila1673364395name_o @ A_48 @ B_35 )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 <=> ! [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_48 )
% 3.28/1.75 => ! [Xa: pname] :
% 3.28/1.75 ( ( member_pname @ Xa @ B_35 )
% 3.28/1.75 => ( X_5 != Xa ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_567_disjoint__iff__not__equal,axiom,
% 3.28/1.75 ! [A_48: hoare_1167836817_state > $o,B_35: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( semila179895820tate_o @ A_48 @ B_35 )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 <=> ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_48 )
% 3.28/1.75 => ! [Xa: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ Xa @ B_35 )
% 3.28/1.75 => ( X_5 != Xa ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_568_Int__empty__right,axiom,
% 3.28/1.75 ! [A_47: pname > $o] :
% 3.28/1.75 ( ( semila1673364395name_o @ A_47 @ bot_bot_pname_o )
% 3.28/1.75 = bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_569_Int__empty__right,axiom,
% 3.28/1.75 ! [A_47: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ A_47 @ bot_bo70021908tate_o )
% 3.28/1.75 = bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_570_Int__empty__left,axiom,
% 3.28/1.75 ! [B_34: pname > $o] :
% 3.28/1.75 ( ( semila1673364395name_o @ bot_bot_pname_o @ B_34 )
% 3.28/1.75 = bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_571_Int__empty__left,axiom,
% 3.28/1.75 ! [B_34: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ bot_bo70021908tate_o @ B_34 )
% 3.28/1.75 = bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_572_Int__def,axiom,
% 3.28/1.75 ! [A_46: pname > $o,B_33: pname > $o] :
% 3.28/1.75 ( ( semila1673364395name_o @ A_46 @ B_33 )
% 3.28/1.75 = ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( member_pname @ X_5 @ A_46 ) @ ( member_pname @ X_5 @ B_33 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_573_Int__def,axiom,
% 3.28/1.75 ! [A_46: hoare_1167836817_state > $o,B_33: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ A_46 @ B_33 )
% 3.28/1.75 = ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( member2058392318_state @ X_5 @ A_46 ) @ ( member2058392318_state @ X_5 @ B_33 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_574_Int__def,axiom,
% 3.28/1.75 ! [A_46: ( pname > $o ) > $o,B_33: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( semila2013987940me_o_o @ A_46 @ B_33 )
% 3.28/1.75 = ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( member_pname_o @ X_5 @ A_46 ) @ ( member_pname_o @ X_5 @ B_33 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_575_Int__def,axiom,
% 3.28/1.75 ! [A_46: ( hoare_1167836817_state > $o ) > $o,B_33: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( semila1758709489te_o_o @ A_46 @ B_33 )
% 3.28/1.75 = ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( member864234961tate_o @ X_5 @ A_46 ) @ ( member864234961tate_o @ X_5 @ B_33 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_576_Int__iff,axiom,
% 3.28/1.75 ! [C_16: pname,A_45: pname > $o,B_32: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_16 @ ( semila1673364395name_o @ A_45 @ B_32 ) )
% 3.28/1.75 <=> ( ( member_pname @ C_16 @ A_45 )
% 3.28/1.75 & ( member_pname @ C_16 @ B_32 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_577_Int__iff,axiom,
% 3.28/1.75 ! [C_16: hoare_1167836817_state,A_45: hoare_1167836817_state > $o,B_32: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_16 @ ( semila179895820tate_o @ A_45 @ B_32 ) )
% 3.28/1.75 <=> ( ( member2058392318_state @ C_16 @ A_45 )
% 3.28/1.75 & ( member2058392318_state @ C_16 @ B_32 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_578_IntD1,axiom,
% 3.28/1.75 ! [C_15: pname,A_44: pname > $o,B_31: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_15 @ ( semila1673364395name_o @ A_44 @ B_31 ) )
% 3.28/1.75 => ( member_pname @ C_15 @ A_44 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_579_IntD1,axiom,
% 3.28/1.75 ! [C_15: hoare_1167836817_state,A_44: hoare_1167836817_state > $o,B_31: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_15 @ ( semila179895820tate_o @ A_44 @ B_31 ) )
% 3.28/1.75 => ( member2058392318_state @ C_15 @ A_44 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_580_IntD2,axiom,
% 3.28/1.75 ! [C_14: pname,A_43: pname > $o,B_30: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_14 @ ( semila1673364395name_o @ A_43 @ B_30 ) )
% 3.28/1.75 => ( member_pname @ C_14 @ B_30 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_581_IntD2,axiom,
% 3.28/1.75 ! [C_14: hoare_1167836817_state,A_43: hoare_1167836817_state > $o,B_30: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_14 @ ( semila179895820tate_o @ A_43 @ B_30 ) )
% 3.28/1.75 => ( member2058392318_state @ C_14 @ B_30 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_582_Collect__conj__eq,axiom,
% 3.28/1.75 ! [P_5: hoare_1167836817_state > $o,Q_1: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( collec1027672124_state
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 3.28/1.75 = ( semila179895820tate_o @ ( collec1027672124_state @ P_5 ) @ ( collec1027672124_state @ Q_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_583_Collect__conj__eq,axiom,
% 3.28/1.75 ! [P_5: pname > $o,Q_1: pname > $o] :
% 3.28/1.75 ( ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 3.28/1.75 = ( semila1673364395name_o @ ( collect_pname @ P_5 ) @ ( collect_pname @ Q_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_584_Collect__conj__eq,axiom,
% 3.28/1.75 ! [P_5: ( pname > $o ) > $o,Q_1: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( collect_pname_o
% 3.28/1.75 @ ^ [X_5: pname > $o] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 3.28/1.75 = ( semila2013987940me_o_o @ ( collect_pname_o @ P_5 ) @ ( collect_pname_o @ Q_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_585_Collect__conj__eq,axiom,
% 3.28/1.75 ! [P_5: ( hoare_1167836817_state > $o ) > $o,Q_1: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( collec269976083tate_o
% 3.28/1.75 @ ^ [X_5: hoare_1167836817_state > $o] : ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
% 3.28/1.75 = ( semila1758709489te_o_o @ ( collec269976083tate_o @ P_5 ) @ ( collec269976083tate_o @ Q_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_586_Int__Collect,axiom,
% 3.28/1.75 ! [X_30: pname,A_42: pname > $o,P_4: pname > $o] :
% 3.28/1.75 ( ( member_pname @ X_30 @ ( semila1673364395name_o @ A_42 @ ( collect_pname @ P_4 ) ) )
% 3.28/1.75 <=> ( ( member_pname @ X_30 @ A_42 )
% 3.28/1.75 & ( P_4 @ X_30 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_587_Int__Collect,axiom,
% 3.28/1.75 ! [X_30: hoare_1167836817_state,A_42: hoare_1167836817_state > $o,P_4: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ X_30 @ ( semila179895820tate_o @ A_42 @ ( collec1027672124_state @ P_4 ) ) )
% 3.28/1.75 <=> ( ( member2058392318_state @ X_30 @ A_42 )
% 3.28/1.75 & ( P_4 @ X_30 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_588_Int__Collect,axiom,
% 3.28/1.75 ! [X_30: pname > $o,A_42: ( pname > $o ) > $o,P_4: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( member_pname_o @ X_30 @ ( semila2013987940me_o_o @ A_42 @ ( collect_pname_o @ P_4 ) ) )
% 3.28/1.75 <=> ( ( member_pname_o @ X_30 @ A_42 )
% 3.28/1.75 & ( P_4 @ X_30 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_589_Int__Collect,axiom,
% 3.28/1.75 ! [X_30: hoare_1167836817_state > $o,A_42: ( hoare_1167836817_state > $o ) > $o,P_4: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( member864234961tate_o @ X_30 @ ( semila1758709489te_o_o @ A_42 @ ( collec269976083tate_o @ P_4 ) ) )
% 3.28/1.75 <=> ( ( member864234961tate_o @ X_30 @ A_42 )
% 3.28/1.75 & ( P_4 @ X_30 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_590_inf__Int__eq,axiom,
% 3.28/1.75 ! [R: pname > $o,S_1: pname > $o,X_5: pname] :
% 3.28/1.75 ( ( semila1673364395name_o
% 3.28/1.75 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ R )
% 3.28/1.75 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ S_1 )
% 3.28/1.75 @ X_5 )
% 3.28/1.75 <=> ( member_pname @ X_5 @ ( semila1673364395name_o @ R @ S_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_591_inf__Int__eq,axiom,
% 3.28/1.75 ! [R: hoare_1167836817_state > $o,S_1: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( semila179895820tate_o
% 3.28/1.75 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ R )
% 3.28/1.75 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ S_1 )
% 3.28/1.75 @ X_5 )
% 3.28/1.75 <=> ( member2058392318_state @ X_5 @ ( semila179895820tate_o @ R @ S_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_592_Un__Int__crazy,axiom,
% 3.28/1.75 ! [A_41: hoare_1167836817_state > $o,B_29: hoare_1167836817_state > $o,C_13: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A_41 @ B_29 ) @ ( semila179895820tate_o @ B_29 @ C_13 ) ) @ ( semila179895820tate_o @ C_13 @ A_41 ) )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A_41 @ B_29 ) @ ( semila1172322802tate_o @ B_29 @ C_13 ) ) @ ( semila1172322802tate_o @ C_13 @ A_41 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_593_Un__Int__distrib2,axiom,
% 3.28/1.75 ! [B_28: hoare_1167836817_state > $o,C_12: hoare_1167836817_state > $o,A_40: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila179895820tate_o @ B_28 @ C_12 ) @ A_40 )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila1172322802tate_o @ B_28 @ A_40 ) @ ( semila1172322802tate_o @ C_12 @ A_40 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_594_Int__Un__distrib2,axiom,
% 3.28/1.75 ! [B_27: hoare_1167836817_state > $o,C_11: hoare_1167836817_state > $o,A_39: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ ( semila1172322802tate_o @ B_27 @ C_11 ) @ A_39 )
% 3.28/1.75 = ( semila1172322802tate_o @ ( semila179895820tate_o @ B_27 @ A_39 ) @ ( semila179895820tate_o @ C_11 @ A_39 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_595_Un__Int__distrib,axiom,
% 3.28/1.75 ! [A_38: hoare_1167836817_state > $o,B_26: hoare_1167836817_state > $o,C_10: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ A_38 @ ( semila179895820tate_o @ B_26 @ C_10 ) )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila1172322802tate_o @ A_38 @ B_26 ) @ ( semila1172322802tate_o @ A_38 @ C_10 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_596_Int__Un__distrib,axiom,
% 3.28/1.75 ! [A_37: hoare_1167836817_state > $o,B_25: hoare_1167836817_state > $o,C_9: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ A_37 @ ( semila1172322802tate_o @ B_25 @ C_9 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ ( semila179895820tate_o @ A_37 @ B_25 ) @ ( semila179895820tate_o @ A_37 @ C_9 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_597_Int__mono,axiom,
% 3.28/1.75 ! [B_24: pname > $o,D_1: pname > $o,A_36: pname > $o,C_8: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_36 @ C_8 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_24 @ D_1 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_36 @ B_24 ) @ ( semila1673364395name_o @ C_8 @ D_1 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_598_Int__mono,axiom,
% 3.28/1.75 ! [B_24: hoare_1167836817_state > $o,D_1: hoare_1167836817_state > $o,A_36: hoare_1167836817_state > $o,C_8: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_36 @ C_8 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_24 @ D_1 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_36 @ B_24 ) @ ( semila179895820tate_o @ C_8 @ D_1 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_599_Int__greatest,axiom,
% 3.28/1.75 ! [B_23: pname > $o,C_7: pname > $o,A_35: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ C_7 @ A_35 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ C_7 @ B_23 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ C_7 @ ( semila1673364395name_o @ A_35 @ B_23 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_600_Int__greatest,axiom,
% 3.28/1.75 ! [B_23: hoare_1167836817_state > $o,C_7: hoare_1167836817_state > $o,A_35: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ C_7 @ A_35 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ C_7 @ B_23 )
% 3.28/1.75 => ( ord_le827224136tate_o @ C_7 @ ( semila179895820tate_o @ A_35 @ B_23 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_601_Int__absorb1,axiom,
% 3.28/1.75 ! [B_22: pname > $o,A_34: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ B_22 @ A_34 )
% 3.28/1.75 => ( ( semila1673364395name_o @ A_34 @ B_22 )
% 3.28/1.75 = B_22 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_602_Int__absorb1,axiom,
% 3.28/1.75 ! [B_22: hoare_1167836817_state > $o,A_34: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ B_22 @ A_34 )
% 3.28/1.75 => ( ( semila179895820tate_o @ A_34 @ B_22 )
% 3.28/1.75 = B_22 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_603_Int__absorb2,axiom,
% 3.28/1.75 ! [A_33: pname > $o,B_21: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_33 @ B_21 )
% 3.28/1.75 => ( ( semila1673364395name_o @ A_33 @ B_21 )
% 3.28/1.75 = A_33 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_604_Int__absorb2,axiom,
% 3.28/1.75 ! [A_33: hoare_1167836817_state > $o,B_21: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_33 @ B_21 )
% 3.28/1.75 => ( ( semila179895820tate_o @ A_33 @ B_21 )
% 3.28/1.75 = A_33 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_605_Int__lower2,axiom,
% 3.28/1.75 ! [A_32: pname > $o,B_20: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_32 @ B_20 ) @ B_20 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_606_Int__lower2,axiom,
% 3.28/1.75 ! [A_32: hoare_1167836817_state > $o,B_20: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_32 @ B_20 ) @ B_20 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_607_Int__lower1,axiom,
% 3.28/1.75 ! [A_31: pname > $o,B_19: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_31 @ B_19 ) @ A_31 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_608_Int__lower1,axiom,
% 3.28/1.75 ! [A_31: hoare_1167836817_state > $o,B_19: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_31 @ B_19 ) @ A_31 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_609_Int__insert__left__if1,axiom,
% 3.28/1.75 ! [B_18: pname > $o,A_30: pname,C_6: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_30 @ C_6 )
% 3.28/1.75 => ( ( semila1673364395name_o @ ( insert_pname @ A_30 @ B_18 ) @ C_6 )
% 3.28/1.75 = ( insert_pname @ A_30 @ ( semila1673364395name_o @ B_18 @ C_6 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_610_Int__insert__left__if1,axiom,
% 3.28/1.75 ! [B_18: hoare_1167836817_state > $o,A_30: hoare_1167836817_state,C_6: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_30 @ C_6 )
% 3.28/1.75 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_30 @ B_18 ) @ C_6 )
% 3.28/1.75 = ( insert2134838167_state @ A_30 @ ( semila179895820tate_o @ B_18 @ C_6 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_611_Int__insert__right__if1,axiom,
% 3.28/1.75 ! [B_17: pname > $o,A_29: pname,A_28: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_29 @ A_28 )
% 3.28/1.75 => ( ( semila1673364395name_o @ A_28 @ ( insert_pname @ A_29 @ B_17 ) )
% 3.28/1.75 = ( insert_pname @ A_29 @ ( semila1673364395name_o @ A_28 @ B_17 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_612_Int__insert__right__if1,axiom,
% 3.28/1.75 ! [B_17: hoare_1167836817_state > $o,A_29: hoare_1167836817_state,A_28: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_29 @ A_28 )
% 3.28/1.75 => ( ( semila179895820tate_o @ A_28 @ ( insert2134838167_state @ A_29 @ B_17 ) )
% 3.28/1.75 = ( insert2134838167_state @ A_29 @ ( semila179895820tate_o @ A_28 @ B_17 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_613_Int__insert__left__if0,axiom,
% 3.28/1.75 ! [B_16: pname > $o,A_27: pname,C_5: pname > $o] :
% 3.28/1.75 ( ~ ( member_pname @ A_27 @ C_5 )
% 3.28/1.75 => ( ( semila1673364395name_o @ ( insert_pname @ A_27 @ B_16 ) @ C_5 )
% 3.28/1.75 = ( semila1673364395name_o @ B_16 @ C_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_614_Int__insert__left__if0,axiom,
% 3.28/1.75 ! [B_16: hoare_1167836817_state > $o,A_27: hoare_1167836817_state,C_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( member2058392318_state @ A_27 @ C_5 )
% 3.28/1.75 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_27 @ B_16 ) @ C_5 )
% 3.28/1.75 = ( semila179895820tate_o @ B_16 @ C_5 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_615_Int__insert__right__if0,axiom,
% 3.28/1.75 ! [B_15: pname > $o,A_26: pname,A_25: pname > $o] :
% 3.28/1.75 ( ~ ( member_pname @ A_26 @ A_25 )
% 3.28/1.75 => ( ( semila1673364395name_o @ A_25 @ ( insert_pname @ A_26 @ B_15 ) )
% 3.28/1.75 = ( semila1673364395name_o @ A_25 @ B_15 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_616_Int__insert__right__if0,axiom,
% 3.28/1.75 ! [B_15: hoare_1167836817_state > $o,A_26: hoare_1167836817_state,A_25: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( member2058392318_state @ A_26 @ A_25 )
% 3.28/1.75 => ( ( semila179895820tate_o @ A_25 @ ( insert2134838167_state @ A_26 @ B_15 ) )
% 3.28/1.75 = ( semila179895820tate_o @ A_25 @ B_15 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_617_insert__inter__insert,axiom,
% 3.28/1.75 ! [A_24: pname,A_23: pname > $o,B_14: pname > $o] :
% 3.28/1.75 ( ( semila1673364395name_o @ ( insert_pname @ A_24 @ A_23 ) @ ( insert_pname @ A_24 @ B_14 ) )
% 3.28/1.75 = ( insert_pname @ A_24 @ ( semila1673364395name_o @ A_23 @ B_14 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_618_insert__inter__insert,axiom,
% 3.28/1.75 ! [A_24: hoare_1167836817_state,A_23: hoare_1167836817_state > $o,B_14: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ ( insert2134838167_state @ A_24 @ A_23 ) @ ( insert2134838167_state @ A_24 @ B_14 ) )
% 3.28/1.75 = ( insert2134838167_state @ A_24 @ ( semila179895820tate_o @ A_23 @ B_14 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_619_Int__insert__left,axiom,
% 3.28/1.75 ! [B_13: pname > $o,A_22: pname,C_4: pname > $o] :
% 3.28/1.75 ( ( ( member_pname @ A_22 @ C_4 )
% 3.28/1.75 => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_13 ) @ C_4 )
% 3.28/1.75 = ( insert_pname @ A_22 @ ( semila1673364395name_o @ B_13 @ C_4 ) ) ) )
% 3.28/1.75 & ( ~ ( member_pname @ A_22 @ C_4 )
% 3.28/1.75 => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_13 ) @ C_4 )
% 3.28/1.75 = ( semila1673364395name_o @ B_13 @ C_4 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_620_Int__insert__left,axiom,
% 3.28/1.75 ! [B_13: hoare_1167836817_state > $o,A_22: hoare_1167836817_state,C_4: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( member2058392318_state @ A_22 @ C_4 )
% 3.28/1.75 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_13 ) @ C_4 )
% 3.28/1.75 = ( insert2134838167_state @ A_22 @ ( semila179895820tate_o @ B_13 @ C_4 ) ) ) )
% 3.28/1.75 & ( ~ ( member2058392318_state @ A_22 @ C_4 )
% 3.28/1.75 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_13 ) @ C_4 )
% 3.28/1.75 = ( semila179895820tate_o @ B_13 @ C_4 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_621_Int__insert__right,axiom,
% 3.28/1.75 ! [B_12: pname > $o,A_21: pname,A_20: pname > $o] :
% 3.28/1.75 ( ( ( member_pname @ A_21 @ A_20 )
% 3.28/1.75 => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_12 ) )
% 3.28/1.75 = ( insert_pname @ A_21 @ ( semila1673364395name_o @ A_20 @ B_12 ) ) ) )
% 3.28/1.75 & ( ~ ( member_pname @ A_21 @ A_20 )
% 3.28/1.75 => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_12 ) )
% 3.28/1.75 = ( semila1673364395name_o @ A_20 @ B_12 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_622_Int__insert__right,axiom,
% 3.28/1.75 ! [B_12: hoare_1167836817_state > $o,A_21: hoare_1167836817_state,A_20: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( member2058392318_state @ A_21 @ A_20 )
% 3.28/1.75 => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_12 ) )
% 3.28/1.75 = ( insert2134838167_state @ A_21 @ ( semila179895820tate_o @ A_20 @ B_12 ) ) ) )
% 3.28/1.75 & ( ~ ( member2058392318_state @ A_21 @ A_20 )
% 3.28/1.75 => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_12 ) )
% 3.28/1.75 = ( semila179895820tate_o @ A_20 @ B_12 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_623_inf__sup__ord_I1_J,axiom,
% 3.28/1.75 ! [X_29: pname > $o,Y_20: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_29 @ Y_20 ) @ X_29 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_624_inf__sup__ord_I1_J,axiom,
% 3.28/1.75 ! [X_29: hoare_1167836817_state > $o,Y_20: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_29 @ Y_20 ) @ X_29 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_625_inf__le1,axiom,
% 3.28/1.75 ! [X_28: pname > $o,Y_19: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_28 @ Y_19 ) @ X_28 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_626_inf__le1,axiom,
% 3.28/1.75 ! [X_28: hoare_1167836817_state > $o,Y_19: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_28 @ Y_19 ) @ X_28 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_627_inf__sup__ord_I2_J,axiom,
% 3.28/1.75 ! [X_27: pname > $o,Y_18: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_27 @ Y_18 ) @ Y_18 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_628_inf__sup__ord_I2_J,axiom,
% 3.28/1.75 ! [X_27: hoare_1167836817_state > $o,Y_18: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_27 @ Y_18 ) @ Y_18 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_629_inf__le2,axiom,
% 3.28/1.75 ! [X_26: pname > $o,Y_17: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_26 @ Y_17 ) @ Y_17 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_630_inf__le2,axiom,
% 3.28/1.75 ! [X_26: hoare_1167836817_state > $o,Y_17: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_26 @ Y_17 ) @ Y_17 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_631_le__iff__inf,axiom,
% 3.28/1.75 ! [X_25: pname > $o,Y_16: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_25 @ Y_16 )
% 3.28/1.75 <=> ( ( semila1673364395name_o @ X_25 @ Y_16 )
% 3.28/1.75 = X_25 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_632_le__iff__inf,axiom,
% 3.28/1.75 ! [X_25: hoare_1167836817_state > $o,Y_16: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_25 @ Y_16 )
% 3.28/1.75 <=> ( ( semila179895820tate_o @ X_25 @ Y_16 )
% 3.28/1.75 = X_25 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_633_le__inf__iff,axiom,
% 3.28/1.75 ! [X_24: pname > $o,Y_15: pname > $o,Z_10: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_24 @ ( semila1673364395name_o @ Y_15 @ Z_10 ) )
% 3.28/1.75 <=> ( ( ord_less_eq_pname_o @ X_24 @ Y_15 )
% 3.28/1.75 & ( ord_less_eq_pname_o @ X_24 @ Z_10 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_634_le__inf__iff,axiom,
% 3.28/1.75 ! [X_24: hoare_1167836817_state > $o,Y_15: hoare_1167836817_state > $o,Z_10: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_24 @ ( semila179895820tate_o @ Y_15 @ Z_10 ) )
% 3.28/1.75 <=> ( ( ord_le827224136tate_o @ X_24 @ Y_15 )
% 3.28/1.75 & ( ord_le827224136tate_o @ X_24 @ Z_10 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_635_le__infI1,axiom,
% 3.28/1.75 ! [B_11: pname > $o,A_19: pname > $o,X_23: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_19 @ X_23 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_19 @ B_11 ) @ X_23 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_636_le__infI1,axiom,
% 3.28/1.75 ! [B_11: hoare_1167836817_state > $o,A_19: hoare_1167836817_state > $o,X_23: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_19 @ X_23 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_19 @ B_11 ) @ X_23 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_637_le__infI2,axiom,
% 3.28/1.75 ! [A_18: pname > $o,B_10: pname > $o,X_22: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ B_10 @ X_22 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_18 @ B_10 ) @ X_22 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_638_le__infI2,axiom,
% 3.28/1.75 ! [A_18: hoare_1167836817_state > $o,B_10: hoare_1167836817_state > $o,X_22: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ B_10 @ X_22 )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_18 @ B_10 ) @ X_22 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_639_inf__absorb1,axiom,
% 3.28/1.75 ! [X_21: pname > $o,Y_14: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_21 @ Y_14 )
% 3.28/1.75 => ( ( semila1673364395name_o @ X_21 @ Y_14 )
% 3.28/1.75 = X_21 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_640_inf__absorb1,axiom,
% 3.28/1.75 ! [X_21: hoare_1167836817_state > $o,Y_14: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_21 @ Y_14 )
% 3.28/1.75 => ( ( semila179895820tate_o @ X_21 @ Y_14 )
% 3.28/1.75 = X_21 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_641_inf__absorb2,axiom,
% 3.28/1.75 ! [Y_13: pname > $o,X_20: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ Y_13 @ X_20 )
% 3.28/1.75 => ( ( semila1673364395name_o @ X_20 @ Y_13 )
% 3.28/1.75 = Y_13 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_642_inf__absorb2,axiom,
% 3.28/1.75 ! [Y_13: hoare_1167836817_state > $o,X_20: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ Y_13 @ X_20 )
% 3.28/1.75 => ( ( semila179895820tate_o @ X_20 @ Y_13 )
% 3.28/1.75 = Y_13 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_643_le__infI,axiom,
% 3.28/1.75 ! [B_9: pname > $o,X_19: pname > $o,A_17: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_19 @ A_17 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ X_19 @ B_9 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ X_19 @ ( semila1673364395name_o @ A_17 @ B_9 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_644_le__infI,axiom,
% 3.28/1.75 ! [B_9: hoare_1167836817_state > $o,X_19: hoare_1167836817_state > $o,A_17: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_19 @ A_17 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ X_19 @ B_9 )
% 3.28/1.75 => ( ord_le827224136tate_o @ X_19 @ ( semila179895820tate_o @ A_17 @ B_9 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_645_inf__greatest,axiom,
% 3.28/1.75 ! [Z_9: pname > $o,X_18: pname > $o,Y_12: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_18 @ Y_12 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ X_18 @ Z_9 )
% 3.28/1.75 => ( ord_less_eq_pname_o @ X_18 @ ( semila1673364395name_o @ Y_12 @ Z_9 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_646_inf__greatest,axiom,
% 3.28/1.75 ! [Z_9: hoare_1167836817_state > $o,X_18: hoare_1167836817_state > $o,Y_12: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_18 @ Y_12 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ X_18 @ Z_9 )
% 3.28/1.75 => ( ord_le827224136tate_o @ X_18 @ ( semila179895820tate_o @ Y_12 @ Z_9 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_647_inf__mono,axiom,
% 3.28/1.75 ! [B_8: pname > $o,D: pname > $o,A_16: pname > $o,C_3: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_16 @ C_3 )
% 3.28/1.75 => ( ( ord_less_eq_pname_o @ B_8 @ D )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_16 @ B_8 ) @ ( semila1673364395name_o @ C_3 @ D ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_648_inf__mono,axiom,
% 3.28/1.75 ! [B_8: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o,A_16: hoare_1167836817_state > $o,C_3: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_16 @ C_3 )
% 3.28/1.75 => ( ( ord_le827224136tate_o @ B_8 @ D )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_16 @ B_8 ) @ ( semila179895820tate_o @ C_3 @ D ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_649_le__infE,axiom,
% 3.28/1.75 ! [X_17: pname > $o,A_15: pname > $o,B_7: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ X_17 @ ( semila1673364395name_o @ A_15 @ B_7 ) )
% 3.28/1.75 => ~ ( ( ord_less_eq_pname_o @ X_17 @ A_15 )
% 3.28/1.75 => ~ ( ord_less_eq_pname_o @ X_17 @ B_7 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_650_le__infE,axiom,
% 3.28/1.75 ! [X_17: hoare_1167836817_state > $o,A_15: hoare_1167836817_state > $o,B_7: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ X_17 @ ( semila179895820tate_o @ A_15 @ B_7 ) )
% 3.28/1.75 => ~ ( ( ord_le827224136tate_o @ X_17 @ A_15 )
% 3.28/1.75 => ~ ( ord_le827224136tate_o @ X_17 @ B_7 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_651_inf__sup__absorb,axiom,
% 3.28/1.75 ! [X_16: hoare_1167836817_state > $o,Y_11: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ X_16 @ ( semila1172322802tate_o @ X_16 @ Y_11 ) )
% 3.28/1.75 = X_16 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_652_sup__inf__absorb,axiom,
% 3.28/1.75 ! [X_15: hoare_1167836817_state > $o,Y_10: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_15 @ ( semila179895820tate_o @ X_15 @ Y_10 ) )
% 3.28/1.75 = X_15 ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_653_inf__sup__distrib1,axiom,
% 3.28/1.75 ! [X_14: hoare_1167836817_state > $o,Y_9: hoare_1167836817_state > $o,Z_8: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ X_14 @ ( semila1172322802tate_o @ Y_9 @ Z_8 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_14 @ Y_9 ) @ ( semila179895820tate_o @ X_14 @ Z_8 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_654_sup__inf__distrib1,axiom,
% 3.28/1.75 ! [X_13: hoare_1167836817_state > $o,Y_8: hoare_1167836817_state > $o,Z_7: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_13 @ ( semila179895820tate_o @ Y_8 @ Z_7 ) )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_13 @ Y_8 ) @ ( semila1172322802tate_o @ X_13 @ Z_7 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_655_inf__sup__distrib2,axiom,
% 3.28/1.75 ! [Y_7: hoare_1167836817_state > $o,Z_6: hoare_1167836817_state > $o,X_12: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_7 @ Z_6 ) @ X_12 )
% 3.28/1.75 = ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_7 @ X_12 ) @ ( semila179895820tate_o @ Z_6 @ X_12 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_656_sup__inf__distrib2,axiom,
% 3.28/1.75 ! [Y_6: hoare_1167836817_state > $o,Z_5: hoare_1167836817_state > $o,X_11: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_6 @ Z_5 ) @ X_11 )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_6 @ X_11 ) @ ( semila1172322802tate_o @ Z_5 @ X_11 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_657_inf__bot__right,axiom,
% 3.28/1.75 ! [X_10: pname > $o] :
% 3.28/1.75 ( ( semila1673364395name_o @ X_10 @ bot_bot_pname_o )
% 3.28/1.75 = bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_658_inf__bot__right,axiom,
% 3.28/1.75 ! [X_10: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ X_10 @ bot_bo70021908tate_o )
% 3.28/1.75 = bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_659_inf__bot__left,axiom,
% 3.28/1.75 ! [X_9: pname > $o] :
% 3.28/1.75 ( ( semila1673364395name_o @ bot_bot_pname_o @ X_9 )
% 3.28/1.75 = bot_bot_pname_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_660_inf__bot__left,axiom,
% 3.28/1.75 ! [X_9: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ bot_bo70021908tate_o @ X_9 )
% 3.28/1.75 = bot_bo70021908tate_o ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_661_distrib__sup__le,axiom,
% 3.28/1.75 ! [X_8: pname > $o,Y_5: pname > $o,Z_4: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_8 @ ( semila1673364395name_o @ Y_5 @ Z_4 ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ X_8 @ Y_5 ) @ ( semila1780557381name_o @ X_8 @ Z_4 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_662_distrib__sup__le,axiom,
% 3.28/1.75 ! [X_8: hoare_1167836817_state > $o,Y_5: hoare_1167836817_state > $o,Z_4: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ X_8 @ ( semila179895820tate_o @ Y_5 @ Z_4 ) ) @ ( semila179895820tate_o @ ( semila1172322802tate_o @ X_8 @ Y_5 ) @ ( semila1172322802tate_o @ X_8 @ Z_4 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_663_distrib__inf__le,axiom,
% 3.28/1.75 ! [X_7: pname > $o,Y_4: pname > $o,Z_3: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ X_7 @ Y_4 ) @ ( semila1673364395name_o @ X_7 @ Z_3 ) ) @ ( semila1673364395name_o @ X_7 @ ( semila1780557381name_o @ Y_4 @ Z_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_664_distrib__inf__le,axiom,
% 3.28/1.75 ! [X_7: hoare_1167836817_state > $o,Y_4: hoare_1167836817_state > $o,Z_3: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ X_7 @ Y_4 ) @ ( semila179895820tate_o @ X_7 @ Z_3 ) ) @ ( semila179895820tate_o @ X_7 @ ( semila1172322802tate_o @ Y_4 @ Z_3 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_665_image__Int__subset,axiom,
% 3.28/1.75 ! [F_6: pname > hoare_1167836817_state,A_14: pname > $o,B_6: pname > $o] : ( ord_le827224136tate_o @ ( image_575578384_state @ F_6 @ ( semila1673364395name_o @ A_14 @ B_6 ) ) @ ( semila179895820tate_o @ ( image_575578384_state @ F_6 @ A_14 ) @ ( image_575578384_state @ F_6 @ B_6 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_666_Un__Int__assoc__eq,axiom,
% 3.28/1.75 ! [A_13: pname > $o,B_5: pname > $o,C_2: pname > $o] :
% 3.28/1.75 ( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A_13 @ B_5 ) @ C_2 )
% 3.28/1.75 = ( semila1673364395name_o @ A_13 @ ( semila1780557381name_o @ B_5 @ C_2 ) ) )
% 3.28/1.75 <=> ( ord_less_eq_pname_o @ C_2 @ A_13 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_667_Un__Int__assoc__eq,axiom,
% 3.28/1.75 ! [A_13: hoare_1167836817_state > $o,B_5: hoare_1167836817_state > $o,C_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ( semila1172322802tate_o @ ( semila179895820tate_o @ A_13 @ B_5 ) @ C_2 )
% 3.28/1.75 = ( semila179895820tate_o @ A_13 @ ( semila1172322802tate_o @ B_5 @ C_2 ) ) )
% 3.28/1.75 <=> ( ord_le827224136tate_o @ C_2 @ A_13 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_668_if__image__distrib,axiom,
% 3.28/1.75 ! [P_3: pname > $o,F_5: pname > hoare_1167836817_state,G_1: pname > hoare_1167836817_state,S: pname > $o] :
% 3.28/1.75 ( ( image_575578384_state
% 3.28/1.75 @ ^ [X_5: pname] : ( if_Hoa833675553_state @ ( P_3 @ X_5 ) @ ( F_5 @ X_5 ) @ ( G_1 @ X_5 ) )
% 3.28/1.75 @ S )
% 3.28/1.75 = ( semila1172322802tate_o @ ( image_575578384_state @ F_5 @ ( semila1673364395name_o @ S @ ( collect_pname @ P_3 ) ) )
% 3.28/1.75 @ ( image_575578384_state @ G_1
% 3.28/1.75 @ ( semila1673364395name_o @ S
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (~) @ ( P_3 @ X_5 ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_669_dom__if,axiom,
% 3.28/1.75 ! [P_2: pname > $o,F_4: pname > option_com,G: pname > option_com] :
% 3.28/1.75 ( ( dom_pname_com
% 3.28/1.75 @ ^ [X_5: pname] : ( if_option_com @ ( P_2 @ X_5 ) @ ( F_4 @ X_5 ) @ ( G @ X_5 ) ) )
% 3.28/1.75 = ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ F_4 ) @ ( collect_pname @ P_2 ) )
% 3.28/1.75 @ ( semila1673364395name_o @ ( dom_pname_com @ G )
% 3.28/1.75 @ ( collect_pname
% 3.28/1.75 @ ^ [X_5: pname] : ( (~) @ ( P_2 @ X_5 ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_670_Int__Collect__mono,axiom,
% 3.28/1.75 ! [Q: pname > $o,P_1: pname > $o,A_12: pname > $o,B_4: pname > $o] :
% 3.28/1.75 ( ( ord_less_eq_pname_o @ A_12 @ B_4 )
% 3.28/1.75 => ( ! [X_5: pname] :
% 3.28/1.75 ( ( member_pname @ X_5 @ A_12 )
% 3.28/1.75 => ( ( P_1 @ X_5 )
% 3.28/1.75 => ( Q @ X_5 ) ) )
% 3.28/1.75 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_12 @ ( collect_pname @ P_1 ) ) @ ( semila1673364395name_o @ B_4 @ ( collect_pname @ Q ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_671_Int__Collect__mono,axiom,
% 3.28/1.75 ! [Q: hoare_1167836817_state > $o,P_1: hoare_1167836817_state > $o,A_12: hoare_1167836817_state > $o,B_4: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( ord_le827224136tate_o @ A_12 @ B_4 )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state] :
% 3.28/1.75 ( ( member2058392318_state @ X_5 @ A_12 )
% 3.28/1.75 => ( ( P_1 @ X_5 )
% 3.28/1.75 => ( Q @ X_5 ) ) )
% 3.28/1.75 => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_12 @ ( collec1027672124_state @ P_1 ) ) @ ( semila179895820tate_o @ B_4 @ ( collec1027672124_state @ Q ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_672_Int__Collect__mono,axiom,
% 3.28/1.75 ! [Q: ( pname > $o ) > $o,P_1: ( pname > $o ) > $o,A_12: ( pname > $o ) > $o,B_4: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( ord_le1205211808me_o_o @ A_12 @ B_4 )
% 3.28/1.75 => ( ! [X_5: pname > $o] :
% 3.28/1.75 ( ( member_pname_o @ X_5 @ A_12 )
% 3.28/1.75 => ( ( P_1 @ X_5 )
% 3.28/1.75 => ( Q @ X_5 ) ) )
% 3.28/1.75 => ( ord_le1205211808me_o_o @ ( semila2013987940me_o_o @ A_12 @ ( collect_pname_o @ P_1 ) ) @ ( semila2013987940me_o_o @ B_4 @ ( collect_pname_o @ Q ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_673_Int__Collect__mono,axiom,
% 3.28/1.75 ! [Q: ( hoare_1167836817_state > $o ) > $o,P_1: ( hoare_1167836817_state > $o ) > $o,A_12: ( hoare_1167836817_state > $o ) > $o,B_4: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( ord_le741939125te_o_o @ A_12 @ B_4 )
% 3.28/1.75 => ( ! [X_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member864234961tate_o @ X_5 @ A_12 )
% 3.28/1.75 => ( ( P_1 @ X_5 )
% 3.28/1.75 => ( Q @ X_5 ) ) )
% 3.28/1.75 => ( ord_le741939125te_o_o @ ( semila1758709489te_o_o @ A_12 @ ( collec269976083tate_o @ P_1 ) ) @ ( semila1758709489te_o_o @ B_4 @ ( collec269976083tate_o @ Q ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_674_distrib__imp1,axiom,
% 3.28/1.75 ! [X_6: hoare_1167836817_state > $o,Y_3: hoare_1167836817_state > $o,Z_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila179895820tate_o @ X_5 @ ( semila1172322802tate_o @ Y_2 @ Z_1 ) )
% 3.28/1.75 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_5 @ Y_2 ) @ ( semila179895820tate_o @ X_5 @ Z_1 ) ) )
% 3.28/1.75 => ( ( semila1172322802tate_o @ X_6 @ ( semila179895820tate_o @ Y_3 @ Z_2 ) )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_6 @ Y_3 ) @ ( semila1172322802tate_o @ X_6 @ Z_2 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_675_distrib__imp2,axiom,
% 3.28/1.75 ! [X_4: hoare_1167836817_state > $o,Y_1: hoare_1167836817_state > $o,Z: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( semila1172322802tate_o @ X_5 @ ( semila179895820tate_o @ Y_2 @ Z_1 ) )
% 3.28/1.75 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_5 @ Y_2 ) @ ( semila1172322802tate_o @ X_5 @ Z_1 ) ) )
% 3.28/1.75 => ( ( semila179895820tate_o @ X_4 @ ( semila1172322802tate_o @ Y_1 @ Z ) )
% 3.28/1.75 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_4 @ Y_1 ) @ ( semila179895820tate_o @ X_4 @ Z ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_676_folding__one_Oremove,axiom,
% 3.28/1.75 ! [X_3: pname,A_11: pname > $o,F_3: pname > pname > pname,F_2: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_3 @ F_2 )
% 3.28/1.75 => ( ( finite_finite_pname @ A_11 )
% 3.28/1.75 => ( ( member_pname @ X_3 @ A_11 )
% 3.28/1.75 => ( ( ( ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = X_3 ) )
% 3.28/1.75 & ( ( ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 3.28/1.75 != bot_bot_pname_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = ( F_3 @ X_3 @ ( F_2 @ ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_677_folding__one_Oremove,axiom,
% 3.28/1.75 ! [X_3: hoare_1167836817_state,A_11: hoare_1167836817_state > $o,F_3: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_2: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_3 @ F_2 )
% 3.28/1.75 => ( ( finite1084549118_state @ A_11 )
% 3.28/1.75 => ( ( member2058392318_state @ X_3 @ A_11 )
% 3.28/1.75 => ( ( ( ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = X_3 ) )
% 3.28/1.75 & ( ( ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) )
% 3.28/1.75 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = ( F_3 @ X_3 @ ( F_2 @ ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_678_folding__one_Oremove,axiom,
% 3.28/1.75 ! [X_3: pname > $o,A_11: ( pname > $o ) > $o,F_3: ( pname > $o ) > ( pname > $o ) > pname > $o,F_2: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite349908348name_o @ F_3 @ F_2 )
% 3.28/1.75 => ( ( finite297249702name_o @ A_11 )
% 3.28/1.75 => ( ( member_pname_o @ X_3 @ A_11 )
% 3.28/1.75 => ( ( ( ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 3.28/1.75 = bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = X_3 ) )
% 3.28/1.75 & ( ( ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 3.28/1.75 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = ( F_3 @ X_3 @ ( F_2 @ ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_679_folding__one_Oremove,axiom,
% 3.28/1.75 ! [X_3: hoare_1167836817_state > $o,A_11: ( hoare_1167836817_state > $o ) > $o,F_3: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_2: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite979047547tate_o @ F_3 @ F_2 )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_11 )
% 3.28/1.75 => ( ( member864234961tate_o @ X_3 @ A_11 )
% 3.28/1.75 => ( ( ( ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) )
% 3.28/1.75 = bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = X_3 ) )
% 3.28/1.75 & ( ( ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) )
% 3.28/1.75 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F_2 @ A_11 )
% 3.28/1.75 = ( F_3 @ X_3 @ ( F_2 @ ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_680_folding__one_Oinsert__remove,axiom,
% 3.28/1.75 ! [X_2: pname,A_10: pname > $o,F_1: pname > pname > pname,F: ( pname > $o ) > pname] :
% 3.28/1.75 ( ( finite1282449217_pname @ F_1 @ F )
% 3.28/1.75 => ( ( finite_finite_pname @ A_10 )
% 3.28/1.75 => ( ( ( ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) )
% 3.28/1.75 = bot_bot_pname_o )
% 3.28/1.75 => ( ( F @ ( insert_pname @ X_2 @ A_10 ) )
% 3.28/1.75 = X_2 ) )
% 3.28/1.75 & ( ( ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) )
% 3.28/1.75 != bot_bot_pname_o )
% 3.28/1.75 => ( ( F @ ( insert_pname @ X_2 @ A_10 ) )
% 3.28/1.75 = ( F_1 @ X_2 @ ( F @ ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_681_folding__one_Oinsert__remove,axiom,
% 3.28/1.75 ! [X_2: hoare_1167836817_state,A_10: hoare_1167836817_state > $o,F_1: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 3.28/1.75 ( ( finite1074406356_state @ F_1 @ F )
% 3.28/1.75 => ( ( finite1084549118_state @ A_10 )
% 3.28/1.75 => ( ( ( ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) )
% 3.28/1.75 = bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F @ ( insert2134838167_state @ X_2 @ A_10 ) )
% 3.28/1.75 = X_2 ) )
% 3.28/1.75 & ( ( ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) )
% 3.28/1.75 != bot_bo70021908tate_o )
% 3.28/1.75 => ( ( F @ ( insert2134838167_state @ X_2 @ A_10 ) )
% 3.28/1.75 = ( F_1 @ X_2 @ ( F @ ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_682_folding__one_Oinsert__remove,axiom,
% 3.28/1.75 ! [X_2: pname > $o,A_10: ( pname > $o ) > $o,F_1: ( pname > $o ) > ( pname > $o ) > pname > $o,F: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.28/1.75 ( ( finite349908348name_o @ F_1 @ F )
% 3.28/1.75 => ( ( finite297249702name_o @ A_10 )
% 3.28/1.75 => ( ( ( ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) )
% 3.28/1.75 = bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F @ ( insert_pname_o @ X_2 @ A_10 ) )
% 3.28/1.75 = X_2 ) )
% 3.28/1.75 & ( ( ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) )
% 3.28/1.75 != bot_bot_pname_o_o )
% 3.28/1.75 => ( ( F @ ( insert_pname_o @ X_2 @ A_10 ) )
% 3.28/1.75 = ( F_1 @ X_2 @ ( F @ ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_683_folding__one_Oinsert__remove,axiom,
% 3.28/1.75 ! [X_2: hoare_1167836817_state > $o,A_10: ( hoare_1167836817_state > $o ) > $o,F_1: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite979047547tate_o @ F_1 @ F )
% 3.28/1.75 => ( ( finite1380128977tate_o @ A_10 )
% 3.28/1.75 => ( ( ( ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) )
% 3.28/1.75 = bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F @ ( insert999278200tate_o @ X_2 @ A_10 ) )
% 3.28/1.75 = X_2 ) )
% 3.28/1.75 & ( ( ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) )
% 3.28/1.75 != bot_bo691907561te_o_o )
% 3.28/1.75 => ( ( F @ ( insert999278200tate_o @ X_2 @ A_10 ) )
% 3.28/1.75 = ( F_1 @ X_2 @ ( F @ ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) ) ) ) ) ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_684_DiffI,axiom,
% 3.28/1.75 ! [B_3: pname > $o,C_1: pname,A_9: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C_1 @ A_9 )
% 3.28/1.75 => ( ~ ( member_pname @ C_1 @ B_3 )
% 3.28/1.75 => ( member_pname @ C_1 @ ( minus_minus_pname_o @ A_9 @ B_3 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_685_DiffI,axiom,
% 3.28/1.75 ! [B_3: hoare_1167836817_state > $o,C_1: hoare_1167836817_state,A_9: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C_1 @ A_9 )
% 3.28/1.75 => ( ~ ( member2058392318_state @ C_1 @ B_3 )
% 3.28/1.75 => ( member2058392318_state @ C_1 @ ( minus_2107060239tate_o @ A_9 @ B_3 ) ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_686_DiffE,axiom,
% 3.28/1.75 ! [C: pname,A_8: pname > $o,B_2: pname > $o] :
% 3.28/1.75 ( ( member_pname @ C @ ( minus_minus_pname_o @ A_8 @ B_2 ) )
% 3.28/1.75 => ~ ( ( member_pname @ C @ A_8 )
% 3.28/1.75 => ( member_pname @ C @ B_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_687_DiffE,axiom,
% 3.28/1.75 ! [C: hoare_1167836817_state,A_8: hoare_1167836817_state > $o,B_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ C @ ( minus_2107060239tate_o @ A_8 @ B_2 ) )
% 3.28/1.75 => ~ ( ( member2058392318_state @ C @ A_8 )
% 3.28/1.75 => ( member2058392318_state @ C @ B_2 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_688_finite__Diff,axiom,
% 3.28/1.75 ! [B_1: ( pname > $o ) > $o,A_7: ( pname > $o ) > $o] :
% 3.28/1.75 ( ( finite297249702name_o @ A_7 )
% 3.28/1.75 => ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_7 @ B_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_689_finite__Diff,axiom,
% 3.28/1.75 ! [B_1: ( hoare_1167836817_state > $o ) > $o,A_7: ( hoare_1167836817_state > $o ) > $o] :
% 3.28/1.75 ( ( finite1380128977tate_o @ A_7 )
% 3.28/1.75 => ( finite1380128977tate_o @ ( minus_1708687022te_o_o @ A_7 @ B_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_690_finite__Diff,axiom,
% 3.28/1.75 ! [B_1: pname > $o,A_7: pname > $o] :
% 3.28/1.75 ( ( finite_finite_pname @ A_7 )
% 3.28/1.75 => ( finite_finite_pname @ ( minus_minus_pname_o @ A_7 @ B_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_691_finite__Diff,axiom,
% 3.28/1.75 ! [B_1: hoare_1167836817_state > $o,A_7: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( finite1084549118_state @ A_7 )
% 3.28/1.75 => ( finite1084549118_state @ ( minus_2107060239tate_o @ A_7 @ B_1 ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_692_insert__Diff,axiom,
% 3.28/1.75 ! [A_6: pname,A_5: pname > $o] :
% 3.28/1.75 ( ( member_pname @ A_6 @ A_5 )
% 3.28/1.75 => ( ( insert_pname @ A_6 @ ( minus_minus_pname_o @ A_5 @ ( insert_pname @ A_6 @ bot_bot_pname_o ) ) )
% 3.28/1.75 = A_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_693_insert__Diff,axiom,
% 3.28/1.75 ! [A_6: hoare_1167836817_state,A_5: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( member2058392318_state @ A_6 @ A_5 )
% 3.28/1.75 => ( ( insert2134838167_state @ A_6 @ ( minus_2107060239tate_o @ A_5 @ ( insert2134838167_state @ A_6 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 = A_5 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_694_Diff__insert__absorb,axiom,
% 3.28/1.75 ! [X_1: pname,A_4: pname > $o] :
% 3.28/1.75 ( ~ ( member_pname @ X_1 @ A_4 )
% 3.28/1.75 => ( ( minus_minus_pname_o @ ( insert_pname @ X_1 @ A_4 ) @ ( insert_pname @ X_1 @ bot_bot_pname_o ) )
% 3.28/1.75 = A_4 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_695_Diff__insert__absorb,axiom,
% 3.28/1.75 ! [X_1: hoare_1167836817_state,A_4: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( member2058392318_state @ X_1 @ A_4 )
% 3.28/1.75 => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_1 @ A_4 ) @ ( insert2134838167_state @ X_1 @ bot_bo70021908tate_o ) )
% 3.28/1.75 = A_4 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_696_insert__Diff__single,axiom,
% 3.28/1.75 ! [A_3: pname,A_2: pname > $o] :
% 3.28/1.75 ( ( insert_pname @ A_3 @ ( minus_minus_pname_o @ A_2 @ ( insert_pname @ A_3 @ bot_bot_pname_o ) ) )
% 3.28/1.75 = ( insert_pname @ A_3 @ A_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_697_insert__Diff__single,axiom,
% 3.28/1.75 ! [A_3: hoare_1167836817_state,A_2: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( insert2134838167_state @ A_3 @ ( minus_2107060239tate_o @ A_2 @ ( insert2134838167_state @ A_3 @ bot_bo70021908tate_o ) ) )
% 3.28/1.75 = ( insert2134838167_state @ A_3 @ A_2 ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(fact_698_Diff__insert2,axiom,
% 3.28/1.75 ! [A_1: hoare_1167836817_state > $o,A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( minus_2107060239tate_o @ A_1 @ ( insert2134838167_state @ A @ B ) )
% 3.28/1.75 = ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A_1 @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) @ B ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 3.28/1.75 ! [X: pname,Y: pname] :
% 3.28/1.75 ( ~ ( fequal_pname @ X @ Y )
% 3.28/1.75 | ( X = Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 3.28/1.75 ! [X: pname,Y: pname] :
% 3.28/1.75 ( ( X != Y )
% 3.28/1.75 | ( fequal_pname @ X @ Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
% 3.28/1.75 ! [X: state,Y: state] :
% 3.28/1.75 ( ~ ( fequal_state @ X @ Y )
% 3.28/1.75 | ( X = Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
% 3.28/1.75 ! [X: state,Y: state] :
% 3.28/1.75 ( ( X != Y )
% 3.28/1.75 | ( fequal_state @ X @ Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 3.28/1.75 ! [X: pname > $o,Y: pname > $o] :
% 3.28/1.75 ( ~ ( fequal_pname_o @ X @ Y )
% 3.28/1.75 | ( X = Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 3.28/1.75 ! [X: pname > $o,Y: pname > $o] :
% 3.28/1.75 ( ( X != Y )
% 3.28/1.75 | ( fequal_pname_o @ X @ Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 3.28/1.75 ! [X: option_com,Y: option_com] :
% 3.28/1.75 ( ( if_option_com @ $true @ X @ Y )
% 3.28/1.75 = X ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 3.28/1.75 ! [X: option_com,Y: option_com] :
% 3.28/1.75 ( ( if_option_com @ $false @ X @ Y )
% 3.28/1.75 = Y ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 3.28/1.75 ! [P: $o] :
% 3.28/1.75 ( ( P = $true )
% 3.28/1.75 | ( P = $false ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 3.28/1.75 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 3.28/1.75 ( ( if_Hoa833675553_state @ $true @ X @ Y )
% 3.28/1.75 = X ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 3.28/1.75 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 3.28/1.75 ( ( if_Hoa833675553_state @ $false @ X @ Y )
% 3.28/1.75 = Y ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 3.28/1.75 ! [P: $o] :
% 3.28/1.75 ( ( P = $true )
% 3.28/1.75 | ( P = $false ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,
% 3.28/1.75 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 3.28/1.75 ( ~ ( fequal1831255762_state @ X @ Y )
% 3.28/1.75 | ( X = Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,
% 3.28/1.75 ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 3.28/1.75 ( ( X != Y )
% 3.28/1.75 | ( fequal1831255762_state @ X @ Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It,axiom,
% 3.28/1.75 ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ~ ( fequal1486222077tate_o @ X @ Y )
% 3.28/1.75 | ( X = Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It,axiom,
% 3.28/1.75 ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 3.28/1.75 ( ( X != Y )
% 3.28/1.75 | ( fequal1486222077tate_o @ X @ Y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(conj_0,hypothesis,
% 3.28/1.75 hoare_1201148605gleton ).
% 3.28/1.75
% 3.28/1.75 thf(conj_1,hypothesis,
% 3.28/1.75 wT_bodies ).
% 3.28/1.75
% 3.28/1.75 thf(conj_2,hypothesis,
% 3.28/1.75 finite1084549118_state @ fa ).
% 3.28/1.75
% 3.28/1.75 thf(conj_3,hypothesis,
% 3.28/1.75 ~ ( member2058392318_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 3.28/1.75
% 3.28/1.75 thf(conj_4,hypothesis,
% 3.28/1.75 ( ord_le827224136tate_o @ fa
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 3.28/1.75 @ ( dom_pname_com @ body ) ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(conj_5,hypothesis,
% 3.28/1.75 ( ( body @ pn )
% 3.28/1.75 = ( some_com @ y ) ) ).
% 3.28/1.75
% 3.28/1.75 thf(conj_6,hypothesis,
% 3.28/1.75 ( hoare_123228589_state
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.28/1.75 @ ( dom_pname_com @ body ) )
% 3.28/1.75 @ fa ) ).
% 3.28/1.75
% 3.28/1.75 thf(conj_7,conjecture,
% 3.28/1.75 ( hoare_123228589_state
% 3.28/1.75 @ ( image_575578384_state
% 3.28/1.75 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.28/1.75 @ ( dom_pname_com @ body ) )
% 3.28/1.75 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ).
% 3.28/1.75 ------------------------
% 3.28/1.79 % (3573)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_3263 for (2999ds/27Mi)
% 3.40/1.80 % (3571)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/183Mi)
% 3.40/1.80 % (3572)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_3263 for (2999ds/4Mi)
% 3.40/1.80 % (3574)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/2Mi)
% 3.40/1.80 % (3575)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_3263 for (2999ds/2Mi)
% 3.40/1.80 % (3576)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_3263 for (2999ds/275Mi)
% 3.40/1.80 % (3577)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/18Mi)
% 3.40/1.80 % (3574)Instruction limit reached!
% 3.40/1.80 % (3574)------------------------------
% 3.40/1.80 % (3574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.80 % (3574)Termination reason: Unknown
% 3.40/1.80 % (3574)Termination phase: shuffling
% 3.40/1.80
% 3.40/1.80 % (3574)Memory used [KB]: 2302
% 3.40/1.80 % (3574)Time elapsed: 0.004 s
% 3.40/1.80 % (3574)Instructions burned: 2 (million)
% 3.40/1.80 % (3574)------------------------------
% 3.40/1.80 % (3574)------------------------------
% 3.40/1.80 % (3575)Instruction limit reached!
% 3.40/1.80 % (3575)------------------------------
% 3.40/1.80 % (3575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.80 % (3575)Termination reason: Unknown
% 3.40/1.80 % (3575)Termination phase: shuffling
% 3.40/1.80
% 3.40/1.80 % (3575)Memory used [KB]: 2302
% 3.40/1.80 % (3575)Time elapsed: 0.004 s
% 3.40/1.80 % (3575)Instructions burned: 2 (million)
% 3.40/1.80 % (3575)------------------------------
% 3.40/1.80 % (3575)------------------------------
% 3.40/1.80 % (3573)Instruction limit reached!
% 3.40/1.80 % (3573)------------------------------
% 3.40/1.80 % (3573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.80 % (3573)Termination reason: Unknown
% 3.40/1.80 % (3573)Termination phase: shuffling
% 3.40/1.80
% 3.40/1.80 % (3573)Memory used [KB]: 3837
% 3.40/1.80 % (3573)Time elapsed: 0.012 s
% 3.40/1.80 % (3573)Instructions burned: 29 (million)
% 3.40/1.80 % (3573)------------------------------
% 3.40/1.80 % (3573)------------------------------
% 3.40/1.80 % (3572)Instruction limit reached!
% 3.40/1.80 % (3572)------------------------------
% 3.40/1.80 % (3572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.80 % (3572)Termination reason: Unknown
% 3.40/1.80 % (3572)Termination phase: shuffling
% 3.40/1.80
% 3.40/1.80 % (3572)Memory used [KB]: 2558
% 3.40/1.80 % (3572)Time elapsed: 0.006 s
% 3.40/1.80 % (3572)Instructions burned: 5 (million)
% 3.40/1.80 % (3572)------------------------------
% 3.40/1.80 % (3572)------------------------------
% 3.40/1.81 % (3580)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_3263 for (2999ds/15Mi)
% 3.40/1.81 % (3577)Instruction limit reached!
% 3.40/1.81 % (3577)------------------------------
% 3.40/1.81 % (3577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.81 % (3577)Termination reason: Unknown
% 3.40/1.81 % (3577)Termination phase: shuffling
% 3.40/1.81
% 3.40/1.81 % (3577)Memory used [KB]: 3198
% 3.40/1.81 % (3577)Time elapsed: 0.015 s
% 3.40/1.81 % (3577)Instructions burned: 19 (million)
% 3.40/1.81 % (3577)------------------------------
% 3.40/1.81 % (3577)------------------------------
% 3.40/1.82 % (3580)Instruction limit reached!
% 3.40/1.82 % (3580)------------------------------
% 3.40/1.82 % (3580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.82 % (3580)Termination reason: Unknown
% 3.40/1.82 % (3580)Termination phase: shuffling
% 3.40/1.82
% 3.40/1.82 % (3580)Memory used [KB]: 3198
% 3.40/1.82 % (3580)Time elapsed: 0.007 s
% 3.40/1.82 % (3580)Instructions burned: 16 (million)
% 3.40/1.82 % (3580)------------------------------
% 3.40/1.82 % (3580)------------------------------
% 3.40/1.82 % (3578)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/3Mi)
% 3.40/1.82 % (3579)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_3263 for (2999ds/37Mi)
% 3.40/1.82 % (3581)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_3263 for (2999ds/3Mi)
% 3.40/1.82 % (3578)Instruction limit reached!
% 3.40/1.82 % (3578)------------------------------
% 3.40/1.82 % (3578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.82 % (3578)Termination reason: Unknown
% 3.40/1.82 % (3578)Termination phase: shuffling
% 3.40/1.82
% 3.40/1.82 % (3578)Memory used [KB]: 2430
% 3.40/1.82 % (3578)Time elapsed: 0.005 s
% 3.40/1.82 % (3578)Instructions burned: 3 (million)
% 3.40/1.82 % (3578)------------------------------
% 3.40/1.82 % (3578)------------------------------
% 3.40/1.82 % (3581)Instruction limit reached!
% 3.40/1.82 % (3581)------------------------------
% 3.40/1.82 % (3581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.82 % (3581)Termination reason: Unknown
% 3.40/1.82 % (3581)Termination phase: shuffling
% 3.40/1.82
% 3.40/1.82 % (3581)Memory used [KB]: 2430
% 3.40/1.82 % (3581)Time elapsed: 0.005 s
% 3.40/1.82 % (3581)Instructions burned: 3 (million)
% 3.40/1.82 % (3581)------------------------------
% 3.40/1.82 % (3581)------------------------------
% 3.40/1.83 % (3583)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/7Mi)
% 3.40/1.83 % (3583)Instruction limit reached!
% 3.40/1.83 % (3583)------------------------------
% 3.40/1.83 % (3583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.83 % (3583)Termination reason: Unknown
% 3.40/1.83 % (3583)Termination phase: shuffling
% 3.40/1.83
% 3.40/1.83 % (3583)Memory used [KB]: 2686
% 3.40/1.83 % (3583)Time elapsed: 0.004 s
% 3.40/1.83 % (3583)Instructions burned: 7 (million)
% 3.40/1.83 % (3583)------------------------------
% 3.40/1.83 % (3583)------------------------------
% 3.40/1.83 % (3582)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_3263 for (2999ds/1041Mi)
% 3.40/1.84 % (3586)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_3263 for (2999ds/3Mi)
% 3.40/1.84 % (3584)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/16Mi)
% 3.40/1.84 % (3579)Instruction limit reached!
% 3.40/1.84 % (3579)------------------------------
% 3.40/1.84 % (3579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.84 % (3579)Termination reason: Unknown
% 3.40/1.84 % (3579)Termination phase: shuffling
% 3.40/1.84
% 3.40/1.84 % (3579)Memory used [KB]: 4221
% 3.40/1.84 % (3579)Time elapsed: 0.023 s
% 3.40/1.84 % (3579)Instructions burned: 38 (million)
% 3.40/1.84 % (3579)------------------------------
% 3.40/1.84 % (3579)------------------------------
% 3.40/1.84 % (3586)Instruction limit reached!
% 3.40/1.84 % (3586)------------------------------
% 3.40/1.84 % (3586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.84 % (3586)Termination reason: Unknown
% 3.40/1.84 % (3586)Termination phase: shuffling
% 3.40/1.84
% 3.40/1.84 % (3586)Memory used [KB]: 2558
% 3.40/1.84 % (3586)Time elapsed: 0.003 s
% 3.40/1.84 % (3586)Instructions burned: 5 (million)
% 3.40/1.84 % (3586)------------------------------
% 3.40/1.84 % (3586)------------------------------
% 3.40/1.84 % (3585)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_3263 for (2999ds/3Mi)
% 3.40/1.84 % (3585)Instruction limit reached!
% 3.40/1.84 % (3585)------------------------------
% 3.40/1.84 % (3585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.84 % (3585)Termination reason: Unknown
% 3.40/1.84 % (3585)Termination phase: shuffling
% 3.40/1.84
% 3.40/1.84 % (3585)Memory used [KB]: 2430
% 3.40/1.84 % (3585)Time elapsed: 0.005 s
% 3.40/1.84 % (3585)Instructions burned: 3 (million)
% 3.40/1.84 % (3585)------------------------------
% 3.40/1.84 % (3585)------------------------------
% 3.40/1.85 % (3584)Instruction limit reached!
% 3.40/1.85 % (3584)------------------------------
% 3.40/1.85 % (3584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.85 % (3584)Termination reason: Unknown
% 3.40/1.85 % (3584)Termination phase: shuffling
% 3.40/1.85
% 3.40/1.85 % (3584)Memory used [KB]: 3198
% 3.40/1.85 % (3584)Time elapsed: 0.013 s
% 3.40/1.85 % (3584)Instructions burned: 16 (million)
% 3.40/1.85 % (3584)------------------------------
% 3.40/1.85 % (3584)------------------------------
% 3.40/1.85 % (3588)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/3Mi)
% 3.40/1.85 % (3588)Instruction limit reached!
% 3.40/1.85 % (3588)------------------------------
% 3.40/1.85 % (3588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.85 % (3588)Termination reason: Unknown
% 3.40/1.85 % (3588)Termination phase: shuffling
% 3.40/1.85
% 3.40/1.85 % (3588)Memory used [KB]: 2558
% 3.40/1.85 % (3588)Time elapsed: 0.003 s
% 3.40/1.85 % (3588)Instructions burned: 5 (million)
% 3.40/1.85 % (3588)------------------------------
% 3.40/1.85 % (3588)------------------------------
% 3.40/1.86 % (3587)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/7Mi)
% 3.40/1.86 % (3589)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/4Mi)
% 3.40/1.86 % (3591)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/710Mi)
% 3.40/1.86 % (3587)Instruction limit reached!
% 3.40/1.86 % (3587)------------------------------
% 3.40/1.86 % (3587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.86 % (3587)Termination reason: Unknown
% 3.40/1.86 % (3587)Termination phase: shuffling
% 3.40/1.86
% 3.40/1.86 % (3587)Memory used [KB]: 2686
% 3.40/1.86 % (3587)Time elapsed: 0.007 s
% 3.40/1.86 % (3587)Instructions burned: 8 (million)
% 3.40/1.86 % (3587)------------------------------
% 3.40/1.86 % (3587)------------------------------
% 3.40/1.86 % (3589)Instruction limit reached!
% 3.40/1.86 % (3589)------------------------------
% 3.40/1.86 % (3589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.86 % (3589)Termination reason: Unknown
% 3.40/1.86 % (3589)Termination phase: shuffling
% 3.40/1.86
% 3.40/1.86 % (3589)Memory used [KB]: 2430
% 3.40/1.86 % (3589)Time elapsed: 0.005 s
% 3.40/1.86 % (3589)Instructions burned: 5 (million)
% 3.40/1.86 % (3589)------------------------------
% 3.40/1.86 % (3589)------------------------------
% 3.40/1.87 % (3590)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/18Mi)
% 3.40/1.88 % (3592)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3263 for (2999ds/6Mi)
% 3.40/1.88 % (3593)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_3263 for (2999ds/902Mi)
% 3.40/1.88 % (3571)Instruction limit reached!
% 3.40/1.88 % (3571)------------------------------
% 3.40/1.88 % (3571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.88 % (3571)Termination reason: Unknown
% 3.40/1.88 % (3571)Termination phase: Function definition elimination
% 3.40/1.88
% 3.40/1.88 % (3571)Memory used [KB]: 7164
% 3.40/1.88 % (3571)Time elapsed: 0.083 s
% 3.40/1.88 % (3571)Instructions burned: 185 (million)
% 3.40/1.88 % (3571)------------------------------
% 3.40/1.88 % (3571)------------------------------
% 3.40/1.88 % (3590)Instruction limit reached!
% 3.40/1.88 % (3590)------------------------------
% 3.40/1.88 % (3590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.88 % (3590)Termination reason: Unknown
% 3.40/1.88 % (3590)Termination phase: shuffling
% 3.40/1.88
% 3.40/1.88 % (3590)Memory used [KB]: 3198
% 3.40/1.88 % (3590)Time elapsed: 0.014 s
% 3.40/1.88 % (3590)Instructions burned: 18 (million)
% 3.40/1.88 % (3590)------------------------------
% 3.40/1.88 % (3590)------------------------------
% 3.40/1.88 % (3592)Instruction limit reached!
% 3.40/1.88 % (3592)------------------------------
% 3.40/1.88 % (3592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.88 % (3592)Termination reason: Unknown
% 3.40/1.88 % (3592)Termination phase: shuffling
% 3.40/1.88
% 3.40/1.88 % (3592)Memory used [KB]: 2558
% 3.40/1.88 % (3592)Time elapsed: 0.005 s
% 3.40/1.88 % (3592)Instructions burned: 7 (million)
% 3.40/1.88 % (3592)------------------------------
% 3.40/1.88 % (3592)------------------------------
% 3.40/1.89 % (3596)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_3263 for (2998ds/6Mi)
% 3.40/1.89 % (3594)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_3263 for (2998ds/21Mi)
% 3.40/1.89 % (3596)Instruction limit reached!
% 3.40/1.89 % (3596)------------------------------
% 3.40/1.89 % (3596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.89 % (3596)Termination reason: Unknown
% 3.40/1.89 % (3596)Termination phase: shuffling
% 3.40/1.89
% 3.40/1.89 % (3596)Memory used [KB]: 2558
% 3.40/1.89 % (3596)Time elapsed: 0.004 s
% 3.40/1.89 % (3596)Instructions burned: 6 (million)
% 3.40/1.89 % (3596)------------------------------
% 3.40/1.89 % (3596)------------------------------
% 3.40/1.90 % (3595)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3263 for (2998ds/5Mi)
% 3.40/1.90 % (3594)Instruction limit reached!
% 3.40/1.90 % (3594)------------------------------
% 3.40/1.90 % (3594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.90 % (3594)Termination reason: Unknown
% 3.40/1.90 % (3594)Termination phase: shuffling
% 3.40/1.90
% 3.40/1.90 % (3594)Memory used [KB]: 3326
% 3.40/1.90 % (3594)Time elapsed: 0.009 s
% 3.40/1.90 % (3594)Instructions burned: 21 (million)
% 3.40/1.90 % (3594)------------------------------
% 3.40/1.90 % (3594)------------------------------
% 3.40/1.90 % (3595)Instruction limit reached!
% 3.40/1.90 % (3595)------------------------------
% 3.40/1.90 % (3595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.90 % (3595)Termination reason: Unknown
% 3.40/1.90 % (3595)Termination phase: shuffling
% 3.40/1.90
% 3.40/1.90 % (3595)Memory used [KB]: 2558
% 3.40/1.90 % (3595)Time elapsed: 0.006 s
% 3.40/1.90 % (3595)Instructions burned: 6 (million)
% 3.40/1.90 % (3595)------------------------------
% 3.40/1.90 % (3595)------------------------------
% 3.40/1.90 % (3597)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3263 for (2998ds/377Mi)
% 3.40/1.91 % (3598)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_3263 for (2998ds/779Mi)
% 3.40/1.92 % (3599)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_3263 for (2998ds/19Mi)
% 3.40/1.93 % (3599)Instruction limit reached!
% 3.40/1.93 % (3599)------------------------------
% 3.40/1.93 % (3599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.93 % (3599)Termination reason: Unknown
% 3.40/1.93 % (3599)Termination phase: shuffling
% 3.40/1.93
% 3.40/1.93 % (3599)Memory used [KB]: 3326
% 3.40/1.93 % (3599)Time elapsed: 0.013 s
% 3.40/1.93 % (3599)Instructions burned: 19 (million)
% 3.40/1.93 % (3599)------------------------------
% 3.40/1.93 % (3599)------------------------------
% 3.40/1.93 % (3576)Instruction limit reached!
% 3.40/1.93 % (3576)------------------------------
% 3.40/1.93 % (3576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.93 % (3576)Termination reason: Unknown
% 3.40/1.93 % (3576)Termination phase: Saturation
% 3.40/1.93
% 3.40/1.93 % (3576)Memory used [KB]: 11769
% 3.40/1.93 % (3576)Time elapsed: 0.136 s
% 3.40/1.93 % (3576)Instructions burned: 275 (million)
% 3.40/1.93 % (3576)------------------------------
% 3.40/1.93 % (3576)------------------------------
% 3.40/1.94 % (3601)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3263 for (2998ds/17Mi)
% 3.40/1.94 % (3600)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3263 for (2998ds/879Mi)
% 3.40/1.95 % (3601)Instruction limit reached!
% 3.40/1.95 % (3601)------------------------------
% 3.40/1.95 % (3601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.95 % (3601)Termination reason: Unknown
% 3.40/1.95 % (3601)Termination phase: shuffling
% 3.40/1.95
% 3.40/1.95 % (3601)Memory used [KB]: 3454
% 3.40/1.95 % (3601)Time elapsed: 0.008 s
% 3.40/1.95 % (3601)Instructions burned: 19 (million)
% 3.40/1.95 % (3601)------------------------------
% 3.40/1.95 % (3601)------------------------------
% 3.40/1.96 % (3602)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3263 for (2998ds/3Mi)
% 3.40/1.96 % (3602)Instruction limit reached!
% 3.40/1.96 % (3602)------------------------------
% 3.40/1.96 % (3602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.96 % (3602)Termination reason: Unknown
% 3.40/1.96 % (3602)Termination phase: shuffling
% 3.40/1.96
% 3.40/1.96 % (3602)Memory used [KB]: 2558
% 3.40/1.96 % (3602)Time elapsed: 0.003 s
% 3.40/1.96 % (3602)Instructions burned: 5 (million)
% 3.40/1.96 % (3602)------------------------------
% 3.40/1.96 % (3602)------------------------------
% 3.40/1.97 % (3603)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3263 for (2998ds/30Mi)
% 3.40/1.98 % (3603)Instruction limit reached!
% 3.40/1.98 % (3603)------------------------------
% 3.40/1.98 % (3603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.98 % (3603)Termination reason: Unknown
% 3.40/1.98 % (3603)Termination phase: shuffling
% 3.40/1.98
% 3.40/1.98 % (3603)Memory used [KB]: 3965
% 3.40/1.98 % (3603)Time elapsed: 0.012 s
% 3.40/1.98 % (3603)Instructions burned: 31 (million)
% 3.40/1.98 % (3603)------------------------------
% 3.40/1.98 % (3603)------------------------------
% 3.40/1.99 % (3604)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3263 for (2997ds/127Mi)
% 3.40/2.01 % (3597)Instruction limit reached!
% 3.40/2.01 % (3597)------------------------------
% 3.40/2.01 % (3597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/2.01 % (3597)Termination reason: Unknown
% 3.40/2.01 % (3597)Termination phase: Saturation
% 3.40/2.01
% 3.40/2.01 % (3597)Memory used [KB]: 12409
% 3.40/2.01 % (3597)Time elapsed: 0.113 s
% 3.40/2.01 % (3597)Instructions burned: 378 (million)
% 3.40/2.01 % (3597)------------------------------
% 3.40/2.01 % (3597)------------------------------
% 3.40/2.02 % (3605)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3263 for (2997ds/100Mi)
% 5.01/2.03 % (3604)Instruction limit reached!
% 5.01/2.03 % (3604)------------------------------
% 5.01/2.03 % (3604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.03 % (3604)Termination reason: Unknown
% 5.01/2.03 % (3604)Termination phase: Preprocessing 1
% 5.01/2.03
% 5.01/2.03 % (3604)Memory used [KB]: 5884
% 5.01/2.03 % (3604)Time elapsed: 0.040 s
% 5.01/2.03 % (3604)Instructions burned: 129 (million)
% 5.01/2.03 % (3604)------------------------------
% 5.01/2.03 % (3604)------------------------------
% 5.01/2.04 % (3606)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_3263 for (2997ds/3Mi)
% 5.01/2.04 % (3606)Instruction limit reached!
% 5.01/2.04 % (3606)------------------------------
% 5.01/2.04 % (3606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.04 % (3606)Termination reason: Unknown
% 5.01/2.04 % (3606)Termination phase: shuffling
% 5.01/2.04
% 5.01/2.04 % (3606)Memory used [KB]: 2558
% 5.01/2.04 % (3606)Time elapsed: 0.003 s
% 5.01/2.04 % (3606)Instructions burned: 5 (million)
% 5.01/2.04 % (3606)------------------------------
% 5.01/2.04 % (3606)------------------------------
% 5.01/2.05 % (3607)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_3263 for (2997ds/20Mi)
% 5.01/2.05 % (3605)Instruction limit reached!
% 5.01/2.05 % (3605)------------------------------
% 5.01/2.05 % (3605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.05 % (3605)Termination reason: Unknown
% 5.01/2.05 % (3605)Termination phase: shuffling
% 5.01/2.05
% 5.01/2.05 % (3605)Memory used [KB]: 6524
% 5.01/2.05 % (3605)Time elapsed: 0.029 s
% 5.01/2.05 % (3605)Instructions burned: 100 (million)
% 5.01/2.05 % (3605)------------------------------
% 5.01/2.05 % (3605)------------------------------
% 5.01/2.06 % (3607)Instruction limit reached!
% 5.01/2.06 % (3607)------------------------------
% 5.01/2.06 % (3607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.06 % (3607)Termination reason: Unknown
% 5.01/2.06 % (3607)Termination phase: shuffling
% 5.01/2.06
% 5.01/2.06 % (3607)Memory used [KB]: 3454
% 5.01/2.06 % (3607)Time elapsed: 0.009 s
% 5.01/2.06 % (3607)Instructions burned: 22 (million)
% 5.01/2.06 % (3607)------------------------------
% 5.01/2.06 % (3607)------------------------------
% 5.01/2.06 % (3608)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_3263 for (2997ds/86Mi)
% 5.01/2.07 % (3609)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_3263 for (2996ds/107Mi)
% 5.01/2.08 % (3591)Instruction limit reached!
% 5.01/2.08 % (3591)------------------------------
% 5.01/2.08 % (3591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.08 % (3591)Termination reason: Unknown
% 5.01/2.08 % (3591)Termination phase: Saturation
% 5.01/2.08
% 5.01/2.08 % (3591)Memory used [KB]: 12537
% 5.01/2.08 % (3591)Time elapsed: 0.218 s
% 5.01/2.08 % (3591)Instructions burned: 711 (million)
% 5.01/2.08 % (3591)------------------------------
% 5.01/2.08 % (3591)------------------------------
% 5.01/2.09 % (3610)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_3263 for (2996ds/39Mi)
% 5.01/2.09 % (3608)Instruction limit reached!
% 5.01/2.09 % (3608)------------------------------
% 5.01/2.09 % (3608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.09 % (3608)Termination reason: Unknown
% 5.01/2.09 % (3608)Termination phase: Property scanning
% 5.01/2.09
% 5.01/2.09 % (3608)Memory used [KB]: 5756
% 5.01/2.09 % (3608)Time elapsed: 0.029 s
% 5.01/2.09 % (3608)Instructions burned: 87 (million)
% 5.01/2.09 % (3608)------------------------------
% 5.01/2.09 % (3608)------------------------------
% 5.01/2.10 % (3611)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_3263 for (2996ds/448Mi)
% 5.01/2.10 % (3610)Instruction limit reached!
% 5.01/2.10 % (3610)------------------------------
% 5.01/2.10 % (3610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.10 % (3610)Termination reason: Unknown
% 5.01/2.10 % (3610)Termination phase: shuffling
% 5.01/2.10
% 5.01/2.10 % (3610)Memory used [KB]: 4093
% 5.01/2.10 % (3610)Time elapsed: 0.013 s
% 5.01/2.10 % (3610)Instructions burned: 40 (million)
% 5.01/2.10 % (3610)------------------------------
% 5.01/2.10 % (3610)------------------------------
% 5.01/2.10 % (3609)Instruction limit reached!
% 5.01/2.10 % (3609)------------------------------
% 5.01/2.10 % (3609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.01/2.10 % (3609)Termination reason: Unknown
% 5.01/2.10 % (3609)Termination phase: Property scanning
% 5.01/2.10
% 5.01/2.10 % (3609)Memory used [KB]: 5628
% 5.01/2.10 % (3609)Time elapsed: 0.035 s
% 5.01/2.10 % (3609)Instructions burned: 107 (million)
% 5.01/2.10 % (3609)------------------------------
% 5.01/2.10 % (3609)------------------------------
% 5.01/2.11 % (3612)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_3263 for (2996ds/46Mi)
% 5.01/2.11 % (3613)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_3263 for (2996ds/98Mi)
% 5.70/2.13 % (3612)Instruction limit reached!
% 5.70/2.13 % (3612)------------------------------
% 5.70/2.13 % (3612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.13 % (3612)Termination reason: Unknown
% 5.70/2.13 % (3612)Termination phase: shuffling
% 5.70/2.13
% 5.70/2.13 % (3612)Memory used [KB]: 4477
% 5.70/2.13 % (3612)Time elapsed: 0.017 s
% 5.70/2.13 % (3612)Instructions burned: 47 (million)
% 5.70/2.13 % (3612)------------------------------
% 5.70/2.13 % (3612)------------------------------
% 5.70/2.13 % (3614)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_3263 for (2996ds/507Mi)
% 5.70/2.14 % (3613)Instruction limit reached!
% 5.70/2.14 % (3613)------------------------------
% 5.70/2.14 % (3613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.14 % (3613)Termination reason: Unknown
% 5.70/2.14 % (3613)Termination phase: shuffling
% 5.70/2.14
% 5.70/2.14 % (3613)Memory used [KB]: 6268
% 5.70/2.14 % (3613)Time elapsed: 0.029 s
% 5.70/2.14 % (3613)Instructions burned: 100 (million)
% 5.70/2.14 % (3613)------------------------------
% 5.70/2.14 % (3613)------------------------------
% 5.70/2.14 % (3598)Instruction limit reached!
% 5.70/2.14 % (3598)------------------------------
% 5.70/2.14 % (3598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.14 % (3598)Termination reason: Unknown
% 5.70/2.14 % (3598)Termination phase: Saturation
% 5.70/2.14
% 5.70/2.14 % (3598)Memory used [KB]: 14072
% 5.70/2.14 % (3598)Time elapsed: 0.237 s
% 5.70/2.14 % (3598)Instructions burned: 779 (million)
% 5.70/2.14 % (3598)------------------------------
% 5.70/2.14 % (3598)------------------------------
% 5.70/2.15 % (3615)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_3263 for (2996ds/149Mi)
% 5.70/2.15 % (3616)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3263 for (2996ds/39Mi)
% 5.70/2.16 % (3582)Instruction limit reached!
% 5.70/2.16 % (3582)------------------------------
% 5.70/2.16 % (3582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.16 % (3582)Termination reason: Unknown
% 5.70/2.16 % (3582)Termination phase: Saturation
% 5.70/2.16
% 5.70/2.16 % (3582)Memory used [KB]: 14456
% 5.70/2.16 % (3582)Time elapsed: 0.330 s
% 5.70/2.16 % (3582)Instructions burned: 1043 (million)
% 5.70/2.16 % (3582)------------------------------
% 5.70/2.16 % (3582)------------------------------
% 5.70/2.17 % (3617)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_3263 for (2996ds/6Mi)
% 5.70/2.17 % (3593)Instruction limit reached!
% 5.70/2.17 % (3593)------------------------------
% 5.70/2.17 % (3593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.17 % (3593)Termination reason: Unknown
% 5.70/2.17 % (3593)Termination phase: Saturation
% 5.70/2.17
% 5.70/2.17 % (3593)Memory used [KB]: 12665
% 5.70/2.17 % (3593)Time elapsed: 0.292 s
% 5.70/2.17 % (3593)Instructions burned: 904 (million)
% 5.70/2.17 % (3593)------------------------------
% 5.70/2.17 % (3593)------------------------------
% 5.70/2.17 % (3616)Instruction limit reached!
% 5.70/2.17 % (3616)------------------------------
% 5.70/2.17 % (3616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.17 % (3616)Termination reason: Unknown
% 5.70/2.17 % (3616)Termination phase: shuffling
% 5.70/2.17
% 5.70/2.17 % (3616)Memory used [KB]: 4221
% 5.70/2.17 % (3616)Time elapsed: 0.016 s
% 5.70/2.17 % (3616)Instructions burned: 40 (million)
% 5.70/2.17 % (3616)------------------------------
% 5.70/2.17 % (3616)------------------------------
% 5.70/2.17 % (3617)Instruction limit reached!
% 5.70/2.17 % (3617)------------------------------
% 5.70/2.17 % (3617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.17 % (3617)Termination reason: Unknown
% 5.70/2.17 % (3617)Termination phase: shuffling
% 5.70/2.17
% 5.70/2.17 % (3617)Memory used [KB]: 2686
% 5.70/2.17 % (3617)Time elapsed: 0.004 s
% 5.70/2.17 % (3617)Instructions burned: 8 (million)
% 5.70/2.17 % (3617)------------------------------
% 5.70/2.17 % (3617)------------------------------
% 5.70/2.18 % (3620)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_3263 for (2995ds/44Mi)
% 5.70/2.18 % (3618)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_3263 for (2995ds/1087Mi)
% 5.70/2.18 % (3619)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3263 for (2995ds/47Mi)
% 5.70/2.19 % (3620)Instruction limit reached!
% 5.70/2.19 % (3620)------------------------------
% 5.70/2.19 % (3620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.19 % (3620)Termination reason: Unknown
% 5.70/2.19 % (3620)Termination phase: shuffling
% 5.70/2.19
% 5.70/2.19 % (3620)Memory used [KB]: 4349
% 5.70/2.19 % (3620)Time elapsed: 0.014 s
% 5.70/2.19 % (3620)Instructions burned: 45 (million)
% 5.70/2.19 % (3620)------------------------------
% 5.70/2.19 % (3620)------------------------------
% 5.70/2.20 % (3615)Instruction limit reached!
% 5.70/2.20 % (3615)------------------------------
% 5.70/2.20 % (3615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.20 % (3615)Termination reason: Unknown
% 5.70/2.20 % (3615)Termination phase: Property scanning
% 5.70/2.20
% 5.70/2.20 % (3615)Memory used [KB]: 7164
% 5.70/2.20 % (3615)Time elapsed: 0.048 s
% 5.70/2.20 % (3615)Instructions burned: 151 (million)
% 5.70/2.20 % (3615)------------------------------
% 5.70/2.20 % (3615)------------------------------
% 6.03/2.20 % (3619)Instruction limit reached!
% 6.03/2.20 % (3619)------------------------------
% 6.03/2.20 % (3619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.20 % (3619)Termination reason: Unknown
% 6.03/2.20 % (3619)Termination phase: shuffling
% 6.03/2.20
% 6.03/2.20 % (3619)Memory used [KB]: 4605
% 6.03/2.20 % (3619)Time elapsed: 0.019 s
% 6.03/2.20 % (3619)Instructions burned: 49 (million)
% 6.03/2.20 % (3619)------------------------------
% 6.03/2.20 % (3619)------------------------------
% 6.03/2.20 % (3621)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_3263 for (2995ds/432Mi)
% 6.03/2.21 % (3622)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3263 for (2995ds/62Mi)
% 6.03/2.21 % (3623)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_3263 for (2995ds/31Mi)
% 6.03/2.22 % (3611)Instruction limit reached!
% 6.03/2.22 % (3611)------------------------------
% 6.03/2.22 % (3611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.22 % (3611)Termination reason: Unknown
% 6.03/2.22 % (3611)Termination phase: Saturation
% 6.03/2.22
% 6.03/2.22 % (3611)Memory used [KB]: 12537
% 6.03/2.22 % (3611)Time elapsed: 0.118 s
% 6.03/2.22 % (3611)Instructions burned: 450 (million)
% 6.03/2.22 % (3611)------------------------------
% 6.03/2.22 % (3611)------------------------------
% 6.03/2.22 % (3623)Instruction limit reached!
% 6.03/2.22 % (3623)------------------------------
% 6.03/2.22 % (3623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.22 % (3623)Termination reason: Unknown
% 6.03/2.22 % (3623)Termination phase: shuffling
% 6.03/2.22
% 6.03/2.22 % (3623)Memory used [KB]: 3837
% 6.03/2.22 % (3623)Time elapsed: 0.012 s
% 6.03/2.22 % (3623)Instructions burned: 31 (million)
% 6.03/2.22 % (3623)------------------------------
% 6.03/2.22 % (3623)------------------------------
% 6.03/2.22 % (3622)Instruction limit reached!
% 6.03/2.22 % (3622)------------------------------
% 6.03/2.22 % (3622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.22 % (3622)Termination reason: Unknown
% 6.03/2.22 % (3622)Termination phase: shuffling
% 6.03/2.22
% 6.03/2.22 % (3622)Memory used [KB]: 5245
% 6.03/2.22 % (3622)Time elapsed: 0.019 s
% 6.03/2.22 % (3622)Instructions burned: 62 (million)
% 6.03/2.22 % (3622)------------------------------
% 6.03/2.22 % (3622)------------------------------
% 6.03/2.23 % (3624)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3263 for (2995ds/96Mi)
% 6.03/2.23 % (3625)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_3263 for (2995ds/453Mi)
% 6.03/2.23 % (3626)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_3263 for (2995ds/71Mi)
% 6.03/2.25 % (3600)Instruction limit reached!
% 6.03/2.25 % (3600)------------------------------
% 6.03/2.25 % (3600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.25 % (3600)Termination reason: Unknown
% 6.03/2.25 % (3600)Termination phase: Saturation
% 6.03/2.25
% 6.03/2.25 % (3600)Memory used [KB]: 12025
% 6.03/2.25 % (3600)Time elapsed: 0.326 s
% 6.03/2.25 % (3600)Instructions burned: 881 (million)
% 6.03/2.25 % (3600)------------------------------
% 6.03/2.25 % (3600)------------------------------
% 6.03/2.26 % (3627)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3263 for (2995ds/83Mi)
% 6.03/2.26 % (3624)Instruction limit reached!
% 6.03/2.26 % (3624)------------------------------
% 6.03/2.26 % (3624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.26 % (3624)Termination reason: Unknown
% 6.03/2.26 % (3624)Termination phase: Property scanning
% 6.03/2.26
% 6.03/2.26 % (3624)Memory used [KB]: 5628
% 6.03/2.26 % (3624)Time elapsed: 0.033 s
% 6.03/2.26 % (3624)Instructions burned: 99 (million)
% 6.03/2.26 % (3624)------------------------------
% 6.03/2.26 % (3624)------------------------------
% 6.03/2.26 % (3626)Instruction limit reached!
% 6.03/2.26 % (3626)------------------------------
% 6.03/2.26 % (3626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.26 % (3626)Termination reason: Unknown
% 6.03/2.26 % (3626)Termination phase: shuffling
% 6.03/2.26
% 6.03/2.26 % (3626)Memory used [KB]: 5756
% 6.03/2.26 % (3626)Time elapsed: 0.026 s
% 6.03/2.26 % (3626)Instructions burned: 73 (million)
% 6.03/2.26 % (3626)------------------------------
% 6.03/2.26 % (3626)------------------------------
% 6.03/2.27 % (3628)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3263 for (2995ds/11Mi)
% 6.03/2.27 % (3629)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_3263 for (2995ds/41Mi)
% 6.03/2.27 % (3628)Instruction limit reached!
% 6.03/2.27 % (3628)------------------------------
% 6.03/2.27 % (3628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.27 % (3628)Termination reason: Unknown
% 6.03/2.27 % (3628)Termination phase: shuffling
% 6.03/2.27
% 6.03/2.27 % (3628)Memory used [KB]: 2942
% 6.03/2.27 % (3628)Time elapsed: 0.005 s
% 6.03/2.27 % (3628)Instructions burned: 12 (million)
% 6.03/2.27 % (3628)------------------------------
% 6.03/2.27 % (3628)------------------------------
% 6.03/2.28 % (3631)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3263 for (2994ds/6Mi)
% 6.03/2.28 % (3629)Instruction limit reached!
% 6.03/2.28 % (3629)------------------------------
% 6.03/2.28 % (3629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.28 % (3629)Termination reason: Unknown
% 6.03/2.28 % (3629)Termination phase: shuffling
% 6.03/2.28
% 6.03/2.28 % (3629)Memory used [KB]: 4221
% 6.03/2.28 % (3629)Time elapsed: 0.013 s
% 6.03/2.28 % (3629)Instructions burned: 42 (million)
% 6.03/2.28 % (3629)------------------------------
% 6.03/2.28 % (3629)------------------------------
% 6.03/2.28 % (3631)Instruction limit reached!
% 6.03/2.28 % (3631)------------------------------
% 6.03/2.28 % (3631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.28 % (3631)Termination reason: Unknown
% 6.03/2.28 % (3631)Termination phase: shuffling
% 6.03/2.28
% 6.03/2.28 % (3631)Memory used [KB]: 2686
% 6.03/2.28 % (3631)Time elapsed: 0.004 s
% 6.03/2.28 % (3631)Instructions burned: 8 (million)
% 6.03/2.28 % (3631)------------------------------
% 6.03/2.28 % (3631)------------------------------
% 6.03/2.29 % (3627)Instruction limit reached!
% 6.03/2.29 % (3627)------------------------------
% 6.03/2.29 % (3627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.29 % (3627)Termination reason: Unknown
% 6.03/2.29 % (3627)Termination phase: Property scanning
% 6.03/2.29
% 6.03/2.29 % (3627)Memory used [KB]: 5756
% 6.03/2.29 % (3627)Time elapsed: 0.030 s
% 6.03/2.29 % (3627)Instructions burned: 84 (million)
% 6.03/2.29 % (3627)------------------------------
% 6.03/2.29 % (3627)------------------------------
% 6.03/2.29 % (3614)Instruction limit reached!
% 6.03/2.29 % (3614)------------------------------
% 6.03/2.29 % (3614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.29 % (3614)Termination reason: Unknown
% 6.03/2.29 % (3614)Termination phase: Saturation
% 6.03/2.29
% 6.03/2.29 % (3614)Memory used [KB]: 13048
% 6.03/2.29 % (3614)Time elapsed: 0.154 s
% 6.03/2.29 % (3614)Instructions burned: 507 (million)
% 6.03/2.29 % (3614)------------------------------
% 6.03/2.29 % (3614)------------------------------
% 6.03/2.29 % (3632)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3263 for (2994ds/150Mi)
% 6.03/2.29 % (3633)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3263 for (2994ds/343Mi)
% 6.03/2.30 % (3634)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_3263 for (2994ds/109Mi)
% 6.69/2.30 % (3635)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_3263 for (2994ds/253Mi)
% 6.69/2.32 % (3621)Instruction limit reached!
% 6.69/2.32 % (3621)------------------------------
% 6.69/2.32 % (3621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.32 % (3621)Termination reason: Unknown
% 6.69/2.32 % (3621)Termination phase: Saturation
% 6.69/2.32
% 6.69/2.32 % (3621)Memory used [KB]: 8059
% 6.69/2.32 % (3621)Time elapsed: 0.116 s
% 6.69/2.32 % (3621)Instructions burned: 432 (million)
% 6.69/2.32 % (3621)------------------------------
% 6.69/2.32 % (3621)------------------------------
% 6.69/2.33 % (3636)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3263 for (2994ds/140Mi)
% 6.69/2.33 % (3634)Instruction limit reached!
% 6.69/2.33 % (3634)------------------------------
% 6.69/2.33 % (3634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.33 % (3634)Termination reason: Unknown
% 6.69/2.33 % (3634)Termination phase: SInE selection
% 6.69/2.33
% 6.69/2.33 % (3634)Memory used [KB]: 5628
% 6.69/2.33 % (3634)Time elapsed: 0.035 s
% 6.69/2.33 % (3634)Instructions burned: 109 (million)
% 6.69/2.33 % (3634)------------------------------
% 6.69/2.33 % (3634)------------------------------
% 6.69/2.34 % (3632)Instruction limit reached!
% 6.69/2.34 % (3632)------------------------------
% 6.69/2.34 % (3632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.34 % (3632)Termination reason: Unknown
% 6.69/2.34 % (3632)Termination phase: Clausification
% 6.69/2.34
% 6.69/2.34 % (3632)Memory used [KB]: 7164
% 6.69/2.34 % (3632)Time elapsed: 0.048 s
% 6.69/2.34 % (3632)Instructions burned: 150 (million)
% 6.69/2.34 % (3632)------------------------------
% 6.69/2.34 % (3632)------------------------------
% 6.69/2.34 % (3637)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_3263 for (2994ds/614Mi)
% 6.69/2.35 % (3625)Instruction limit reached!
% 6.69/2.35 % (3625)------------------------------
% 6.69/2.35 % (3625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.35 % (3625)Termination reason: Unknown
% 6.69/2.35 % (3625)Termination phase: Saturation
% 6.69/2.35
% 6.69/2.35 % (3625)Memory used [KB]: 12537
% 6.69/2.35 % (3625)Time elapsed: 0.119 s
% 6.69/2.35 % (3625)Instructions burned: 455 (million)
% 6.69/2.35 % (3625)------------------------------
% 6.69/2.35 % (3625)------------------------------
% 6.69/2.35 % (3638)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_3263 for (2994ds/202Mi)
% 6.69/2.36 % (3639)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_3263 for (2994ds/339Mi)
% 6.69/2.37 % (3636)Instruction limit reached!
% 6.69/2.37 % (3636)------------------------------
% 6.69/2.37 % (3636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.37 % (3636)Termination reason: Unknown
% 6.69/2.37 % (3636)Termination phase: Property scanning
% 6.69/2.37
% 6.69/2.37 % (3636)Memory used [KB]: 6396
% 6.69/2.37 % (3636)Time elapsed: 0.045 s
% 6.69/2.37 % (3636)Instructions burned: 140 (million)
% 6.69/2.37 % (3636)------------------------------
% 6.69/2.37 % (3636)------------------------------
% 6.69/2.37 % (3635)Instruction limit reached!
% 6.69/2.37 % (3635)------------------------------
% 6.69/2.37 % (3635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.37 % (3635)Termination reason: Unknown
% 6.69/2.37 % (3635)Termination phase: Saturation
% 6.69/2.37
% 6.69/2.37 % (3635)Memory used [KB]: 7291
% 6.69/2.37 % (3635)Time elapsed: 0.076 s
% 6.69/2.37 % (3635)Instructions burned: 254 (million)
% 6.69/2.37 % (3635)------------------------------
% 6.69/2.37 % (3635)------------------------------
% 6.69/2.38 % (3640)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_3263 for (2993ds/283Mi)
% 6.69/2.38 % (3641)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3263 for (2993ds/134Mi)
% 6.69/2.39 % (3633)Instruction limit reached!
% 6.69/2.39 % (3633)------------------------------
% 6.69/2.39 % (3633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.39 % (3633)Termination reason: Unknown
% 6.69/2.39 % (3633)Termination phase: Saturation
% 6.69/2.39
% 6.69/2.39 % (3633)Memory used [KB]: 11769
% 6.69/2.39 % (3633)Time elapsed: 0.102 s
% 6.69/2.39 % (3633)Instructions burned: 344 (million)
% 6.69/2.39 % (3633)------------------------------
% 6.69/2.39 % (3633)------------------------------
% 7.28/2.40 % (3642)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3263 for (2993ds/298Mi)
% 7.28/2.41 % (3638)Instruction limit reached!
% 7.28/2.41 % (3638)------------------------------
% 7.28/2.41 % (3638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.41 % (3638)Termination reason: Unknown
% 7.28/2.41 % (3638)Termination phase: Saturation
% 7.28/2.41
% 7.28/2.41 % (3638)Memory used [KB]: 6652
% 7.28/2.41 % (3638)Time elapsed: 0.061 s
% 7.28/2.41 % (3638)Instructions burned: 202 (million)
% 7.28/2.41 % (3638)------------------------------
% 7.28/2.41 % (3638)------------------------------
% 7.28/2.42 % (3643)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3263 for (2993ds/192Mi)
% 7.28/2.43 % (3641)Instruction limit reached!
% 7.28/2.43 % (3641)------------------------------
% 7.28/2.43 % (3641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.43 % (3641)Termination reason: Unknown
% 7.28/2.43 % (3641)Termination phase: Preprocessing 3
% 7.28/2.43
% 7.28/2.43 % (3641)Memory used [KB]: 6780
% 7.28/2.43 % (3641)Time elapsed: 0.044 s
% 7.28/2.43 % (3641)Instructions burned: 137 (million)
% 7.28/2.43 % (3641)------------------------------
% 7.28/2.43 % (3641)------------------------------
% 7.28/2.44 % (3644)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_3263 for (2993ds/258Mi)
% 7.28/2.46 % (3640)Instruction limit reached!
% 7.28/2.46 % (3640)------------------------------
% 7.28/2.46 % (3640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.46 % (3640)Termination reason: Unknown
% 7.28/2.46 % (3640)Termination phase: Property scanning
% 7.28/2.46
% 7.28/2.46 % (3640)Memory used [KB]: 7803
% 7.28/2.46 % (3640)Time elapsed: 0.076 s
% 7.28/2.46 % (3640)Instructions burned: 285 (million)
% 7.28/2.46 % (3640)------------------------------
% 7.28/2.46 % (3640)------------------------------
% 7.28/2.46 % (3639)Instruction limit reached!
% 7.28/2.46 % (3639)------------------------------
% 7.28/2.46 % (3639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.46 % (3639)Termination reason: Unknown
% 7.28/2.46 % (3639)Termination phase: Saturation
% 7.28/2.46
% 7.28/2.46 % (3639)Memory used [KB]: 11897
% 7.28/2.46 % (3639)Time elapsed: 0.102 s
% 7.28/2.46 % (3639)Instructions burned: 341 (million)
% 7.28/2.46 % (3639)------------------------------
% 7.28/2.46 % (3639)------------------------------
% 7.28/2.47 % (3645)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_3263 for (2992ds/90Mi)
% 7.28/2.47 % (3646)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_3263 for (2992ds/231Mi)
% 7.28/2.47 % (3643)Instruction limit reached!
% 7.28/2.47 % (3643)------------------------------
% 7.28/2.47 % (3643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.47 % (3643)Termination reason: Unknown
% 7.28/2.47 % (3643)Termination phase: Function definition elimination
% 7.28/2.47
% 7.28/2.47 % (3643)Memory used [KB]: 7164
% 7.28/2.47 % (3643)Time elapsed: 0.058 s
% 7.28/2.47 % (3643)Instructions burned: 192 (million)
% 7.28/2.47 % (3643)------------------------------
% 7.28/2.47 % (3643)------------------------------
% 7.28/2.48 % (3642)Instruction limit reached!
% 7.28/2.48 % (3642)------------------------------
% 7.28/2.48 % (3642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.48 % (3642)Termination reason: Unknown
% 7.28/2.48 % (3642)Termination phase: Property scanning
% 7.28/2.48
% 7.28/2.48 % (3642)Memory used [KB]: 7803
% 7.28/2.48 % (3642)Time elapsed: 0.079 s
% 7.28/2.48 % (3642)Instructions burned: 298 (million)
% 7.28/2.48 % (3642)------------------------------
% 7.28/2.48 % (3642)------------------------------
% 7.28/2.48 % (3647)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_3263 for (2992ds/458Mi)
% 7.28/2.49 % (3648)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_3263 for (2992ds/31Mi)
% 7.28/2.50 % (3645)Instruction limit reached!
% 7.28/2.50 % (3645)------------------------------
% 7.28/2.50 % (3645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.50 % (3645)Termination reason: Unknown
% 7.28/2.50 % (3645)Termination phase: Property scanning
% 7.28/2.50
% 7.28/2.50 % (3645)Memory used [KB]: 5373
% 7.28/2.50 % (3645)Time elapsed: 0.031 s
% 7.28/2.50 % (3645)Instructions burned: 91 (million)
% 7.28/2.50 % (3645)------------------------------
% 7.28/2.50 % (3645)------------------------------
% 7.76/2.50 % (3648)Instruction limit reached!
% 7.76/2.50 % (3648)------------------------------
% 7.76/2.50 % (3648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.50 % (3648)Termination reason: Unknown
% 7.76/2.50 % (3648)Termination phase: shuffling
% 7.76/2.50
% 7.76/2.50 % (3648)Memory used [KB]: 3837
% 7.76/2.50 % (3648)Time elapsed: 0.012 s
% 7.76/2.50 % (3648)Instructions burned: 32 (million)
% 7.76/2.50 % (3648)------------------------------
% 7.76/2.50 % (3648)------------------------------
% 7.76/2.51 % (3649)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_3263 for (2992ds/297Mi)
% 7.76/2.51 % (3644)Instruction limit reached!
% 7.76/2.51 % (3644)------------------------------
% 7.76/2.51 % (3644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.51 % (3644)Termination reason: Unknown
% 7.76/2.51 % (3644)Termination phase: Saturation
% 7.76/2.51
% 7.76/2.51 % (3644)Memory used [KB]: 7419
% 7.76/2.51 % (3644)Time elapsed: 0.077 s
% 7.76/2.51 % (3644)Instructions burned: 258 (million)
% 7.76/2.51 % (3644)------------------------------
% 7.76/2.51 % (3644)------------------------------
% 7.76/2.51 % (3650)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_3263 for (2992ds/987Mi)
% 7.76/2.52 % (3651)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_3263 for (2992ds/182Mi)
% 7.76/2.52 % (3618)Instruction limit reached!
% 7.76/2.52 % (3618)------------------------------
% 7.76/2.52 % (3618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.52 % (3618)Termination reason: Unknown
% 7.76/2.52 % (3618)Termination phase: Saturation
% 7.76/2.52
% 7.76/2.52 % (3618)Memory used [KB]: 12025
% 7.76/2.52 % (3618)Time elapsed: 0.346 s
% 7.76/2.52 % (3618)Instructions burned: 1089 (million)
% 7.76/2.52 % (3618)------------------------------
% 7.76/2.52 % (3618)------------------------------
% 7.76/2.53 % (3637)Instruction limit reached!
% 7.76/2.53 % (3637)------------------------------
% 7.76/2.53 % (3637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.53 % (3637)Termination reason: Unknown
% 7.76/2.53 % (3637)Termination phase: Saturation
% 7.76/2.53
% 7.76/2.53 % (3637)Memory used [KB]: 13048
% 7.76/2.53 % (3637)Time elapsed: 0.190 s
% 7.76/2.53 % (3637)Instructions burned: 615 (million)
% 7.76/2.53 % (3637)------------------------------
% 7.76/2.53 % (3637)------------------------------
% 7.76/2.53 % (3646)Instruction limit reached!
% 7.76/2.53 % (3646)------------------------------
% 7.76/2.53 % (3646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.53 % (3646)Termination reason: Unknown
% 7.76/2.53 % (3646)Termination phase: Property scanning
% 7.76/2.53
% 7.76/2.53 % (3646)Memory used [KB]: 7675
% 7.76/2.53 % (3646)Time elapsed: 0.063 s
% 7.76/2.53 % (3646)Instructions burned: 233 (million)
% 7.76/2.53 % (3646)------------------------------
% 7.76/2.53 % (3646)------------------------------
% 7.76/2.53 % (3652)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_3263 for (2992ds/182Mi)
% 7.76/2.54 % (3653)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_3263 for (2992ds/154Mi)
% 7.76/2.54 % (3654)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_3263 for (2992ds/79Mi)
% 7.76/2.57 % (3654)Instruction limit reached!
% 7.76/2.57 % (3654)------------------------------
% 7.76/2.57 % (3654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.57 % (3654)Termination reason: Unknown
% 7.76/2.57 % (3654)Termination phase: Property scanning
% 7.76/2.57
% 7.76/2.57 % (3654)Memory used [KB]: 5628
% 7.76/2.57 % (3654)Time elapsed: 0.028 s
% 7.76/2.57 % (3654)Instructions burned: 79 (million)
% 7.76/2.57 % (3654)------------------------------
% 7.76/2.57 % (3654)------------------------------
% 7.76/2.58 % (3655)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_3263 for (2991ds/216Mi)
% 7.76/2.58 % (3651)Instruction limit reached!
% 7.76/2.58 % (3651)------------------------------
% 7.76/2.58 % (3651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.58 % (3651)Termination reason: Unknown
% 7.76/2.58 % (3651)Termination phase: Function definition elimination
% 7.76/2.58
% 7.76/2.58 % (3651)Memory used [KB]: 7164
% 7.76/2.58 % (3651)Time elapsed: 0.056 s
% 7.76/2.58 % (3651)Instructions burned: 184 (million)
% 7.76/2.58 % (3651)------------------------------
% 7.76/2.58 % (3651)------------------------------
% 7.76/2.58 % (3653)Instruction limit reached!
% 7.76/2.58 % (3653)------------------------------
% 7.76/2.58 % (3653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.58 % (3653)Termination reason: Unknown
% 7.76/2.58 % (3653)Termination phase: Property scanning
% 7.76/2.58
% 7.76/2.58 % (3653)Memory used [KB]: 7547
% 7.76/2.58 % (3653)Time elapsed: 0.044 s
% 7.76/2.58 % (3653)Instructions burned: 155 (million)
% 7.76/2.58 % (3653)------------------------------
% 7.76/2.58 % (3653)------------------------------
% 7.76/2.58 % (3649)Instruction limit reached!
% 7.76/2.58 % (3649)------------------------------
% 7.76/2.58 % (3649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.58 % (3649)Termination reason: Unknown
% 7.76/2.58 % (3649)Termination phase: Property scanning
% 7.76/2.58
% 7.76/2.58 % (3649)Memory used [KB]: 7291
% 7.76/2.58 % (3649)Time elapsed: 0.079 s
% 7.76/2.58 % (3649)Instructions burned: 298 (million)
% 7.76/2.58 % (3649)------------------------------
% 7.76/2.58 % (3649)------------------------------
% 7.76/2.59 % (3656)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3263 for (2991ds/114Mi)
% 7.76/2.59 % (3652)Instruction limit reached!
% 7.76/2.59 % (3652)------------------------------
% 7.76/2.59 % (3652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.59 % (3652)Termination reason: Unknown
% 7.76/2.59 % (3652)Termination phase: Property scanning
% 7.76/2.59
% 7.76/2.59 % (3652)Memory used [KB]: 7164
% 7.76/2.59 % (3652)Time elapsed: 0.057 s
% 7.76/2.59 % (3652)Instructions burned: 186 (million)
% 7.76/2.59 % (3652)------------------------------
% 7.76/2.59 % (3652)------------------------------
% 7.76/2.59 % (3657)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_3263 for (2991ds/922Mi)
% 7.76/2.59 % (3658)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_3263 for (2991ds/182Mi)
% 8.85/2.60 % (3659)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_3263 for (2991ds/164Mi)
% 8.85/2.62 % (3647)Instruction limit reached!
% 8.85/2.62 % (3647)------------------------------
% 8.85/2.62 % (3647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.62 % (3647)Termination reason: Unknown
% 8.85/2.62 % (3647)Termination phase: Saturation
% 8.85/2.62
% 8.85/2.62 % (3647)Memory used [KB]: 12409
% 8.85/2.62 % (3647)Time elapsed: 0.138 s
% 8.85/2.62 % (3647)Instructions burned: 458 (million)
% 8.85/2.62 % (3647)------------------------------
% 8.85/2.62 % (3647)------------------------------
% 8.85/2.62 % (3656)Instruction limit reached!
% 8.85/2.62 % (3656)------------------------------
% 8.85/2.62 % (3656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.62 % (3656)Termination reason: Unknown
% 8.85/2.62 % (3656)Termination phase: Preprocessing 1
% 8.85/2.62
% 8.85/2.62 % (3656)Memory used [KB]: 6012
% 8.85/2.62 % (3656)Time elapsed: 0.037 s
% 8.85/2.62 % (3656)Instructions burned: 114 (million)
% 8.85/2.62 % (3656)------------------------------
% 8.85/2.62 % (3656)------------------------------
% 8.85/2.63 % (3660)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_3263 for (2991ds/50Mi)
% 8.85/2.63 % (3661)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3263 for (2991ds/368Mi)
% 8.85/2.64 % (3655)Instruction limit reached!
% 8.85/2.64 % (3655)------------------------------
% 8.85/2.64 % (3655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.64 % (3655)Termination reason: Unknown
% 8.85/2.64 % (3655)Termination phase: SInE selection
% 8.85/2.64
% 8.85/2.64 % (3655)Memory used [KB]: 7547
% 8.85/2.64 % (3655)Time elapsed: 0.060 s
% 8.85/2.64 % (3655)Instructions burned: 218 (million)
% 8.85/2.64 % (3655)------------------------------
% 8.85/2.64 % (3655)------------------------------
% 8.85/2.64 % (3658)Instruction limit reached!
% 8.85/2.64 % (3658)------------------------------
% 8.85/2.64 % (3658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.64 % (3658)Termination reason: Unknown
% 8.85/2.64 % (3658)Termination phase: Property scanning
% 8.85/2.64
% 8.85/2.64 % (3658)Memory used [KB]: 7547
% 8.85/2.64 % (3658)Time elapsed: 0.051 s
% 8.85/2.64 % (3658)Instructions burned: 183 (million)
% 8.85/2.64 % (3658)------------------------------
% 8.85/2.64 % (3658)------------------------------
% 8.85/2.65 % (3662)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_3263 for (2991ds/1021Mi)
% 8.85/2.65 % (3659)Instruction limit reached!
% 8.85/2.65 % (3659)------------------------------
% 8.85/2.65 % (3659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.65 % (3659)Termination reason: Unknown
% 8.85/2.65 % (3659)Termination phase: Property scanning
% 8.85/2.65
% 8.85/2.65 % (3659)Memory used [KB]: 7547
% 8.85/2.65 % (3659)Time elapsed: 0.047 s
% 8.85/2.65 % (3659)Instructions burned: 167 (million)
% 8.85/2.65 % (3659)------------------------------
% 8.85/2.65 % (3659)------------------------------
% 8.85/2.65 % (3660)Instruction limit reached!
% 8.85/2.65 % (3660)------------------------------
% 8.85/2.65 % (3660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.65 % (3660)Termination reason: Unknown
% 8.85/2.65 % (3660)Termination phase: shuffling
% 8.85/2.65
% 8.85/2.65 % (3660)Memory used [KB]: 4733
% 8.85/2.65 % (3660)Time elapsed: 0.016 s
% 8.85/2.65 % (3660)Instructions burned: 50 (million)
% 8.85/2.65 % (3660)------------------------------
% 8.85/2.65 % (3660)------------------------------
% 8.85/2.65 % (3663)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_3263 for (2991ds/267Mi)
% 8.85/2.66 % (3664)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_3263 for (2991ds/204Mi)
% 8.85/2.66 % (3665)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_3263 for (2991ds/26Mi)
% 8.85/2.66 % (3665)Instruction limit reached!
% 8.85/2.66 % (3665)------------------------------
% 8.85/2.66 % (3665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.66 % (3665)Termination reason: Unknown
% 8.85/2.66 % (3665)Termination phase: shuffling
% 8.85/2.66
% 8.85/2.66 % (3665)Memory used [KB]: 3709
% 8.85/2.66 % (3665)Time elapsed: 0.009 s
% 8.85/2.66 % (3665)Instructions burned: 26 (million)
% 8.85/2.66 % (3665)------------------------------
% 8.85/2.66 % (3665)------------------------------
% 8.85/2.67 % (3666)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_3263 for (2990ds/53Mi)
% 8.85/2.69 % (3666)Instruction limit reached!
% 8.85/2.69 % (3666)------------------------------
% 8.85/2.69 % (3666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.69 % (3666)Termination reason: Unknown
% 8.85/2.69 % (3666)Termination phase: shuffling
% 8.85/2.69
% 8.85/2.69 % (3666)Memory used [KB]: 4733
% 8.85/2.69 % (3666)Time elapsed: 0.018 s
% 8.85/2.69 % (3666)Instructions burned: 56 (million)
% 8.85/2.69 % (3666)------------------------------
% 8.85/2.69 % (3666)------------------------------
% 9.29/2.70 % (3667)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_3263 for (2990ds/4436Mi)
% 9.29/2.72 % (3664)Instruction limit reached!
% 9.29/2.72 % (3664)------------------------------
% 9.29/2.72 % (3664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.29/2.72 % (3664)Termination reason: Unknown
% 9.29/2.72 % (3664)Termination phase: Property scanning
% 9.29/2.72
% 9.29/2.72 % (3664)Memory used [KB]: 6908
% 9.29/2.72 % (3664)Time elapsed: 0.063 s
% 9.29/2.72 % (3664)Instructions burned: 207 (million)
% 9.29/2.72 % (3664)------------------------------
% 9.29/2.72 % (3664)------------------------------
% 9.29/2.73 % (3663)Instruction limit reached!
% 9.29/2.73 % (3663)------------------------------
% 9.29/2.73 % (3663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.29/2.73 % (3663)Termination reason: Unknown
% 9.29/2.73 % (3663)Termination phase: Function definition elimination
% 9.29/2.73
% 9.29/2.73 % (3663)Memory used [KB]: 7675
% 9.29/2.73 % (3663)Time elapsed: 0.073 s
% 9.29/2.73 % (3663)Instructions burned: 269 (million)
% 9.29/2.73 % (3663)------------------------------
% 9.29/2.73 % (3663)------------------------------
% 9.29/2.73 % (3668)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_3263 for (2990ds/1539Mi)
% 9.29/2.74 % (3669)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_3263 for (2990ds/408Mi)
% 9.29/2.74 % (3661)Instruction limit reached!
% 9.29/2.74 % (3661)------------------------------
% 9.29/2.74 % (3661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.29/2.74 % (3661)Termination reason: Unknown
% 9.29/2.74 % (3661)Termination phase: Saturation
% 9.29/2.74
% 9.29/2.74 % (3661)Memory used [KB]: 12665
% 9.29/2.74 % (3661)Time elapsed: 0.134 s
% 9.29/2.74 % (3661)Instructions burned: 368 (million)
% 9.29/2.74 % (3661)------------------------------
% 9.29/2.74 % (3661)------------------------------
% 9.29/2.76 % (3670)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_3263 for (2990ds/5205Mi)
% 9.57/2.80 % (3650)Instruction limit reached!
% 9.57/2.80 % (3650)------------------------------
% 9.57/2.80 % (3650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.80 % (3650)Termination reason: Unknown
% 9.57/2.80 % (3650)Termination phase: Saturation
% 9.57/2.80
% 9.57/2.80 % (3650)Memory used [KB]: 14072
% 9.57/2.80 % (3650)Time elapsed: 0.287 s
% 9.57/2.80 % (3650)Instructions burned: 989 (million)
% 9.57/2.80 % (3650)------------------------------
% 9.57/2.80 % (3650)------------------------------
% 9.57/2.81 % (3671)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_3263 for (2989ds/1913Mi)
% 9.57/2.86 % (3669)Instruction limit reached!
% 9.57/2.86 % (3669)------------------------------
% 9.57/2.86 % (3669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.86 % (3669)Termination reason: Unknown
% 9.57/2.86 % (3669)Termination phase: Saturation
% 9.57/2.86
% 9.57/2.86 % (3669)Memory used [KB]: 12920
% 9.57/2.86 % (3669)Time elapsed: 0.121 s
% 9.57/2.86 % (3669)Instructions burned: 408 (million)
% 9.57/2.86 % (3669)------------------------------
% 9.57/2.86 % (3669)------------------------------
% 9.57/2.87 % (3672)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_3263 for (2988ds/4350Mi)
% 9.57/2.88 % (3657)Instruction limit reached!
% 9.57/2.88 % (3657)------------------------------
% 9.57/2.88 % (3657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.88 % (3657)Termination reason: Unknown
% 9.57/2.88 % (3657)Termination phase: Saturation
% 9.57/2.88
% 9.57/2.88 % (3657)Memory used [KB]: 12665
% 9.57/2.88 % (3657)Time elapsed: 0.289 s
% 9.57/2.88 % (3657)Instructions burned: 923 (million)
% 9.57/2.88 % (3657)------------------------------
% 9.57/2.88 % (3657)------------------------------
% 9.57/2.89 % (3673)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_3263 for (2988ds/68Mi)
% 10.29/2.91 % (3673)Instruction limit reached!
% 10.29/2.91 % (3673)------------------------------
% 10.29/2.91 % (3673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.91 % (3673)Termination reason: Unknown
% 10.29/2.91 % (3673)Termination phase: shuffling
% 10.29/2.91
% 10.29/2.91 % (3673)Memory used [KB]: 5500
% 10.29/2.91 % (3673)Time elapsed: 0.025 s
% 10.29/2.91 % (3673)Instructions burned: 70 (million)
% 10.29/2.91 % (3673)------------------------------
% 10.29/2.91 % (3673)------------------------------
% 10.29/2.92 % (3674)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_3263 for (2988ds/358Mi)
% 10.29/2.96 % (3662)Instruction limit reached!
% 10.29/2.96 % (3662)------------------------------
% 10.29/2.96 % (3662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.96 % (3662)Termination reason: Unknown
% 10.29/2.96 % (3662)Termination phase: Saturation
% 10.29/2.96
% 10.29/2.96 % (3662)Memory used [KB]: 13560
% 10.29/2.96 % (3662)Time elapsed: 0.335 s
% 10.29/2.96 % (3662)Instructions burned: 1022 (million)
% 10.29/2.96 % (3662)------------------------------
% 10.29/2.96 % (3662)------------------------------
% 10.29/2.97 % (3675)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_3263 for (2987ds/31Mi)
% 10.29/2.98 % (3675)Instruction limit reached!
% 10.29/2.98 % (3675)------------------------------
% 10.29/2.98 % (3675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.98 % (3675)Termination reason: Unknown
% 10.29/2.98 % (3675)Termination phase: shuffling
% 10.29/2.98
% 10.29/2.98 % (3675)Memory used [KB]: 3837
% 10.29/2.98 % (3675)Time elapsed: 0.013 s
% 10.29/2.98 % (3675)Instructions burned: 33 (million)
% 10.29/2.98 % (3675)------------------------------
% 10.29/2.98 % (3675)------------------------------
% 10.29/2.99 % (3676)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3263 for (2987ds/279Mi)
% 12.04/3.03 % (3674)Instruction limit reached!
% 12.04/3.03 % (3674)------------------------------
% 12.04/3.03 % (3674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.04/3.03 % (3674)Termination reason: Unknown
% 12.04/3.03 % (3674)Termination phase: Saturation
% 12.04/3.03
% 12.04/3.03 % (3674)Memory used [KB]: 11769
% 12.04/3.03 % (3674)Time elapsed: 0.107 s
% 12.04/3.03 % (3674)Instructions burned: 358 (million)
% 12.04/3.03 % (3674)------------------------------
% 12.04/3.03 % (3674)------------------------------
% 12.04/3.04 % (3677)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3263 for (2987ds/258Mi)
% 12.04/3.06 % (3676)Instruction limit reached!
% 12.04/3.06 % (3676)------------------------------
% 12.04/3.06 % (3676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.04/3.06 % (3676)Termination reason: Unknown
% 12.04/3.06 % (3676)Termination phase: Property scanning
% 12.04/3.06
% 12.04/3.06 % (3676)Memory used [KB]: 7803
% 12.04/3.06 % (3676)Time elapsed: 0.073 s
% 12.04/3.06 % (3676)Instructions burned: 281 (million)
% 12.04/3.06 % (3676)------------------------------
% 12.04/3.06 % (3676)------------------------------
% 12.04/3.07 % (3678)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_3263 for (2986ds/26Mi)
% 12.04/3.08 % (3678)Instruction limit reached!
% 12.04/3.08 % (3678)------------------------------
% 12.04/3.08 % (3678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.04/3.08 % (3678)Termination reason: Unknown
% 12.04/3.08 % (3678)Termination phase: shuffling
% 12.04/3.08
% 12.04/3.08 % (3678)Memory used [KB]: 3709
% 12.04/3.08 % (3678)Time elapsed: 0.009 s
% 12.04/3.08 % (3678)Instructions burned: 26 (million)
% 12.04/3.08 % (3678)------------------------------
% 12.04/3.08 % (3678)------------------------------
% 12.04/3.09 % (3679)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_3263 for (2986ds/995Mi)
% 12.04/3.11 % (3677)Instruction limit reached!
% 12.04/3.11 % (3677)------------------------------
% 12.04/3.11 % (3677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.04/3.11 % (3677)Termination reason: Unknown
% 12.04/3.11 % (3677)Termination phase: Saturation
% 12.04/3.11
% 12.04/3.11 % (3677)Memory used [KB]: 11513
% 12.04/3.11 % (3677)Time elapsed: 0.075 s
% 12.04/3.11 % (3677)Instructions burned: 258 (million)
% 12.04/3.11 % (3677)------------------------------
% 12.04/3.11 % (3677)------------------------------
% 12.04/3.12 % (3680)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_3263 for (2986ds/373Mi)
% 13.10/3.21 % (3668)Instruction limit reached!
% 13.10/3.21 % (3668)------------------------------
% 13.10/3.21 % (3668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.21 % (3668)Termination reason: Unknown
% 13.10/3.21 % (3668)Termination phase: Saturation
% 13.10/3.21
% 13.10/3.21 % (3668)Memory used [KB]: 14456
% 13.10/3.21 % (3668)Time elapsed: 0.478 s
% 13.10/3.21 % (3668)Instructions burned: 1540 (million)
% 13.10/3.21 % (3668)------------------------------
% 13.10/3.21 % (3668)------------------------------
% 13.10/3.22 % (3681)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_3263 for (2985ds/253Mi)
% 13.10/3.24 % (3680)Instruction limit reached!
% 13.10/3.24 % (3680)------------------------------
% 13.10/3.24 % (3680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.24 % (3680)Termination reason: Unknown
% 13.10/3.24 % (3680)Termination phase: Saturation
% 13.10/3.24
% 13.10/3.24 % (3680)Memory used [KB]: 12537
% 13.10/3.24 % (3680)Time elapsed: 0.113 s
% 13.10/3.24 % (3680)Instructions burned: 375 (million)
% 13.10/3.24 % (3680)------------------------------
% 13.10/3.24 % (3680)------------------------------
% 13.10/3.25 % (3682)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_3263 for (2985ds/832Mi)
% 13.10/3.28 % (3681)Instruction limit reached!
% 13.10/3.28 % (3681)------------------------------
% 13.10/3.28 % (3681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.28 % (3681)Termination reason: Unknown
% 13.10/3.28 % (3681)Termination phase: Property scanning
% 13.10/3.28
% 13.10/3.28 % (3681)Memory used [KB]: 7675
% 13.10/3.28 % (3681)Time elapsed: 0.068 s
% 13.10/3.28 % (3681)Instructions burned: 256 (million)
% 13.10/3.28 % (3681)------------------------------
% 13.10/3.28 % (3681)------------------------------
% 13.10/3.29 % (3683)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_3263 for (2984ds/668Mi)
% 13.72/3.38 % (3679)Instruction limit reached!
% 13.72/3.38 % (3679)------------------------------
% 13.72/3.38 % (3679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.38 % (3679)Termination reason: Unknown
% 13.72/3.38 % (3679)Termination phase: Saturation
% 13.72/3.38
% 13.72/3.38 % (3679)Memory used [KB]: 15735
% 13.72/3.38 % (3679)Time elapsed: 0.287 s
% 13.72/3.38 % (3679)Instructions burned: 996 (million)
% 13.72/3.38 % (3679)------------------------------
% 13.72/3.38 % (3679)------------------------------
% 13.72/3.38 % (3671)Instruction limit reached!
% 13.72/3.38 % (3671)------------------------------
% 13.72/3.38 % (3671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.38 % (3671)Termination reason: Unknown
% 13.72/3.38 % (3671)Termination phase: Saturation
% 13.72/3.38
% 13.72/3.38 % (3671)Memory used [KB]: 9338
% 13.72/3.38 % (3671)Time elapsed: 0.573 s
% 13.72/3.38 % (3671)Instructions burned: 1914 (million)
% 13.72/3.38 % (3671)------------------------------
% 13.72/3.38 % (3671)------------------------------
% 13.72/3.39 % (3684)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_3263 for (2983ds/40Mi)
% 13.72/3.39 % (3685)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_3263 for (2983ds/294Mi)
% 14.42/3.40 % (3684)Instruction limit reached!
% 14.42/3.40 % (3684)------------------------------
% 14.42/3.40 % (3684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.40 % (3684)Termination reason: Unknown
% 14.42/3.40 % (3684)Termination phase: shuffling
% 14.42/3.40
% 14.42/3.40 % (3684)Memory used [KB]: 4221
% 14.42/3.40 % (3684)Time elapsed: 0.013 s
% 14.42/3.40 % (3684)Instructions burned: 40 (million)
% 14.42/3.40 % (3684)------------------------------
% 14.42/3.40 % (3684)------------------------------
% 14.42/3.41 % (3686)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_3263 for (2983ds/187Mi)
% 14.42/3.46 % (3686)Instruction limit reached!
% 14.42/3.46 % (3686)------------------------------
% 14.42/3.46 % (3686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.46 % (3686)Termination reason: Unknown
% 14.42/3.46 % (3686)Termination phase: Function definition elimination
% 14.42/3.46
% 14.42/3.46 % (3686)Memory used [KB]: 7164
% 14.42/3.46 % (3686)Time elapsed: 0.056 s
% 14.42/3.46 % (3686)Instructions burned: 188 (million)
% 14.42/3.46 % (3686)------------------------------
% 14.42/3.46 % (3686)------------------------------
% 14.42/3.47 % (3685)Instruction limit reached!
% 14.42/3.47 % (3685)------------------------------
% 14.42/3.47 % (3685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.47 % (3685)Termination reason: Unknown
% 14.42/3.47 % (3685)Termination phase: Saturation
% 14.42/3.47
% 14.42/3.47 % (3685)Memory used [KB]: 12281
% 14.42/3.47 % (3685)Time elapsed: 0.080 s
% 14.42/3.47 % (3685)Instructions burned: 295 (million)
% 14.42/3.47 % (3685)------------------------------
% 14.42/3.47 % (3685)------------------------------
% 14.42/3.47 % (3687)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3263 for (2982ds/371Mi)
% 14.42/3.48 % (3683)Instruction limit reached!
% 14.42/3.48 % (3683)------------------------------
% 14.42/3.48 % (3683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.48 % (3683)Termination reason: Unknown
% 14.42/3.48 % (3683)Termination phase: Saturation
% 14.42/3.48
% 14.42/3.48 % (3683)Memory used [KB]: 19573
% 14.42/3.48 % (3683)Time elapsed: 0.187 s
% 14.42/3.48 % (3683)Instructions burned: 669 (million)
% 14.42/3.48 % (3683)------------------------------
% 14.42/3.48 % (3683)------------------------------
% 14.42/3.48 % (3688)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3263 for (2982ds/1827Mi)
% 14.42/3.49 % (3689)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_3263 for (2982ds/70Mi)
% 14.42/3.50 % (3682)Instruction limit reached!
% 14.42/3.50 % (3682)------------------------------
% 14.42/3.50 % (3682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.50 % (3682)Termination reason: Unknown
% 14.42/3.50 % (3682)Termination phase: Saturation
% 14.42/3.50
% 14.42/3.50 % (3682)Memory used [KB]: 13816
% 14.42/3.50 % (3682)Time elapsed: 0.250 s
% 14.42/3.50 % (3682)Instructions burned: 832 (million)
% 14.42/3.50 % (3682)------------------------------
% 14.42/3.50 % (3682)------------------------------
% 15.35/3.51 % (3690)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_3263 for (2982ds/316Mi)
% 15.35/3.51 % (3689)Instruction limit reached!
% 15.35/3.51 % (3689)------------------------------
% 15.35/3.51 % (3689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.35/3.51 % (3689)Termination reason: Unknown
% 15.35/3.51 % (3689)Termination phase: shuffling
% 15.35/3.51
% 15.35/3.51 % (3689)Memory used [KB]: 5756
% 15.35/3.51 % (3689)Time elapsed: 0.022 s
% 15.35/3.51 % (3689)Instructions burned: 72 (million)
% 15.35/3.51 % (3689)------------------------------
% 15.35/3.51 % (3689)------------------------------
% 15.35/3.52 % (3691)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_3263 for (2982ds/932Mi)
% 15.35/3.59 % (3687)Instruction limit reached!
% 15.35/3.59 % (3687)------------------------------
% 15.35/3.59 % (3687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.35/3.59 % (3687)Termination reason: Unknown
% 15.35/3.59 % (3687)Termination phase: Saturation
% 15.35/3.59
% 15.35/3.59 % (3687)Memory used [KB]: 12153
% 15.35/3.59 % (3687)Time elapsed: 0.114 s
% 15.35/3.59 % (3687)Instructions burned: 372 (million)
% 15.35/3.59 % (3687)------------------------------
% 15.35/3.59 % (3687)------------------------------
% 15.35/3.59 % (3690)Instruction limit reached!
% 15.35/3.59 % (3690)------------------------------
% 15.35/3.59 % (3690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.35/3.59 % (3690)Termination reason: Unknown
% 15.35/3.59 % (3690)Termination phase: Property scanning
% 15.35/3.59
% 15.35/3.59 % (3690)Memory used [KB]: 7675
% 15.35/3.59 % (3690)Time elapsed: 0.084 s
% 15.35/3.59 % (3690)Instructions burned: 319 (million)
% 15.35/3.59 % (3690)------------------------------
% 15.35/3.59 % (3690)------------------------------
% 15.35/3.60 % (3692)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_3263 for (2981ds/4714Mi)
% 15.89/3.60 % (3693)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_3263 for (2981ds/8250Mi)
% 16.19/3.73 % (3692)Refutation not found, incomplete strategy
% 16.19/3.73 % (3692)------------------------------
% 16.19/3.73 % (3692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/3.73 % (3692)Termination reason: Refutation not found, incomplete strategy
% 16.19/3.73
% 16.19/3.73
% 16.19/3.73 % (3692)Memory used [KB]: 13432
% 16.19/3.73 % (3692)Time elapsed: 0.136 s
% 16.19/3.73 % (3692)Instructions burned: 484 (million)
% 16.19/3.73 % (3692)------------------------------
% 16.19/3.73 % (3692)------------------------------
% 16.19/3.74 % (3694)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_3263 for (2980ds/770Mi)
% 16.19/3.78 % (3691)Instruction limit reached!
% 16.19/3.78 % (3691)------------------------------
% 16.19/3.78 % (3691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/3.78 % (3691)Termination reason: Unknown
% 16.19/3.78 % (3691)Termination phase: Saturation
% 16.19/3.78
% 16.19/3.78 % (3691)Memory used [KB]: 14200
% 16.19/3.78 % (3691)Time elapsed: 0.265 s
% 16.19/3.78 % (3691)Instructions burned: 935 (million)
% 16.19/3.78 % (3691)------------------------------
% 16.19/3.78 % (3691)------------------------------
% 16.19/3.79 % (3695)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3263 for (2979ds/794Mi)
% 17.23/3.98 % (3694)Instruction limit reached!
% 17.23/3.98 % (3694)------------------------------
% 17.23/3.98 % (3694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.23/3.98 % (3694)Termination reason: Unknown
% 17.23/3.98 % (3694)Termination phase: Saturation
% 17.23/3.98
% 17.23/3.98 % (3694)Memory used [KB]: 12409
% 17.23/3.98 % (3694)Time elapsed: 0.236 s
% 17.23/3.98 % (3694)Instructions burned: 772 (million)
% 17.23/3.98 % (3694)------------------------------
% 17.23/3.98 % (3694)------------------------------
% 17.23/3.99 % (3696)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3263 for (2977ds/464Mi)
% 19.04/4.03 % (3695)Instruction limit reached!
% 19.04/4.03 % (3695)------------------------------
% 19.04/4.03 % (3695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/4.03 % (3695)Termination reason: Unknown
% 19.04/4.03 % (3695)Termination phase: Saturation
% 19.04/4.03
% 19.04/4.03 % (3695)Memory used [KB]: 10618
% 19.04/4.03 % (3695)Time elapsed: 0.242 s
% 19.04/4.03 % (3695)Instructions burned: 795 (million)
% 19.04/4.03 % (3695)------------------------------
% 19.04/4.03 % (3695)------------------------------
% 19.04/4.05 % (3697)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_3263 for (2977ds/1376Mi)
% 19.04/4.07 % (3688)Instruction limit reached!
% 19.04/4.07 % (3688)------------------------------
% 19.04/4.07 % (3688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/4.07 % (3688)Termination reason: Unknown
% 19.04/4.07 % (3688)Termination phase: Saturation
% 19.04/4.07
% 19.04/4.07 % (3688)Memory used [KB]: 15351
% 19.04/4.07 % (3688)Time elapsed: 0.595 s
% 19.04/4.07 % (3688)Instructions burned: 1830 (million)
% 19.04/4.07 % (3688)------------------------------
% 19.04/4.07 % (3688)------------------------------
% 19.04/4.08 % (3667)Instruction limit reached!
% 19.04/4.08 % (3667)------------------------------
% 19.04/4.08 % (3667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/4.08 % (3667)Termination reason: Unknown
% 19.04/4.08 % (3667)Termination phase: Saturation
% 19.04/4.08
% 19.04/4.08 % (3667)Memory used [KB]: 15223
% 19.04/4.08 % (3667)Time elapsed: 1.384 s
% 19.04/4.08 % (3667)Instructions burned: 4436 (million)
% 19.04/4.08 % (3667)------------------------------
% 19.04/4.08 % (3667)------------------------------
% 19.04/4.08 % (3698)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3263 for (2976ds/906Mi)
% 19.04/4.09 % (3699)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_3263 for (2976ds/434Mi)
% 19.04/4.12 % (3696)Instruction limit reached!
% 19.04/4.12 % (3696)------------------------------
% 19.04/4.12 % (3696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/4.12 % (3696)Termination reason: Unknown
% 19.04/4.12 % (3696)Termination phase: Saturation
% 19.04/4.12
% 19.04/4.12 % (3696)Memory used [KB]: 12281
% 19.04/4.12 % (3696)Time elapsed: 0.136 s
% 19.04/4.12 % (3696)Instructions burned: 467 (million)
% 19.04/4.12 % (3696)------------------------------
% 19.04/4.12 % (3696)------------------------------
% 19.65/4.13 % (3700)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_3263 for (2976ds/865Mi)
% 19.65/4.17 % (3672)Instruction limit reached!
% 19.65/4.17 % (3672)------------------------------
% 19.65/4.17 % (3672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.65/4.17 % (3672)Termination reason: Unknown
% 19.65/4.17 % (3672)Termination phase: Saturation
% 19.65/4.17
% 19.65/4.17 % (3672)Memory used [KB]: 16119
% 19.65/4.17 % (3672)Time elapsed: 1.301 s
% 19.65/4.17 % (3672)Instructions burned: 4352 (million)
% 19.65/4.17 % (3672)------------------------------
% 19.65/4.17 % (3672)------------------------------
% 19.65/4.18 % (3701)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_3263 for (2975ds/593Mi)
% 19.87/4.23 % (3699)Instruction limit reached!
% 19.87/4.23 % (3699)------------------------------
% 19.87/4.23 % (3699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.87/4.23 % (3699)Termination reason: Unknown
% 19.87/4.23 % (3699)Termination phase: Saturation
% 19.87/4.23
% 19.87/4.23 % (3699)Memory used [KB]: 12281
% 19.87/4.23 % (3699)Time elapsed: 0.158 s
% 19.87/4.23 % (3699)Instructions burned: 434 (million)
% 19.87/4.23 % (3699)------------------------------
% 19.87/4.23 % (3699)------------------------------
% 19.87/4.24 % (3702)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3263 for (2975ds/443Mi)
% 20.21/4.31 % (3670)Instruction limit reached!
% 20.21/4.31 % (3670)------------------------------
% 20.21/4.31 % (3670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.31 % (3670)Termination reason: Unknown
% 20.21/4.31 % (3670)Termination phase: Saturation
% 20.21/4.31
% 20.21/4.31 % (3670)Memory used [KB]: 20980
% 20.21/4.31 % (3670)Time elapsed: 1.560 s
% 20.21/4.31 % (3670)Instructions burned: 5208 (million)
% 20.21/4.31 % (3670)------------------------------
% 20.21/4.31 % (3670)------------------------------
% 20.21/4.33 % (3703)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_3263 for (2974ds/594Mi)
% 20.21/4.34 % (3701)Instruction limit reached!
% 20.21/4.34 % (3701)------------------------------
% 20.21/4.34 % (3701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.34 % (3701)Termination reason: Unknown
% 20.21/4.34 % (3701)Termination phase: Saturation
% 20.21/4.34
% 20.21/4.34 % (3701)Memory used [KB]: 14711
% 20.21/4.34 % (3701)Time elapsed: 0.163 s
% 20.21/4.34 % (3701)Instructions burned: 594 (million)
% 20.21/4.34 % (3701)------------------------------
% 20.21/4.34 % (3701)------------------------------
% 20.21/4.35 % (3704)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_3263 for (2974ds/327Mi)
% 20.21/4.37 % (3702)Instruction limit reached!
% 20.21/4.37 % (3702)------------------------------
% 20.21/4.37 % (3702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.37 % (3702)Termination reason: Unknown
% 20.21/4.37 % (3702)Termination phase: Saturation
% 20.21/4.37
% 20.21/4.37 % (3702)Memory used [KB]: 12153
% 20.21/4.37 % (3702)Time elapsed: 0.137 s
% 20.21/4.37 % (3702)Instructions burned: 443 (million)
% 20.21/4.37 % (3702)------------------------------
% 20.21/4.37 % (3702)------------------------------
% 20.21/4.38 % (3705)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_3263 for (2973ds/5411Mi)
% 20.21/4.39 % (3700)Instruction limit reached!
% 20.21/4.39 % (3700)------------------------------
% 20.21/4.39 % (3700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.39 % (3700)Termination reason: Unknown
% 20.21/4.39 % (3700)Termination phase: Saturation
% 20.21/4.39
% 20.21/4.39 % (3700)Memory used [KB]: 13688
% 20.21/4.39 % (3700)Time elapsed: 0.257 s
% 20.21/4.39 % (3700)Instructions burned: 866 (million)
% 20.21/4.39 % (3700)------------------------------
% 20.21/4.39 % (3700)------------------------------
% 20.91/4.40 % (3698)Instruction limit reached!
% 20.91/4.40 % (3698)------------------------------
% 20.91/4.40 % (3698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.91/4.40 % (3698)Termination reason: Unknown
% 20.91/4.40 % (3698)Termination phase: Saturation
% 20.91/4.40
% 20.91/4.40 % (3698)Memory used [KB]: 17270
% 20.91/4.40 % (3698)Time elapsed: 0.340 s
% 20.91/4.40 % (3698)Instructions burned: 907 (million)
% 20.91/4.40 % (3698)------------------------------
% 20.91/4.40 % (3698)------------------------------
% 20.91/4.40 % (3706)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_3263 for (2973ds/1762Mi)
% 20.91/4.41 % (3707)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_3263 for (2973ds/96Mi)
% 20.91/4.43 % (3697)Instruction limit reached!
% 20.91/4.43 % (3697)------------------------------
% 20.91/4.43 % (3697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.91/4.43 % (3697)Termination reason: Unknown
% 20.91/4.43 % (3697)Termination phase: Saturation
% 20.91/4.43
% 20.91/4.43 % (3697)Memory used [KB]: 16502
% 20.91/4.43 % (3697)Time elapsed: 0.414 s
% 20.91/4.43 % (3697)Instructions burned: 1377 (million)
% 20.91/4.43 % (3697)------------------------------
% 20.91/4.43 % (3697)------------------------------
% 20.91/4.44 % (3707)Instruction limit reached!
% 20.91/4.44 % (3707)------------------------------
% 20.91/4.44 % (3707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.91/4.44 % (3707)Termination reason: Unknown
% 20.91/4.44 % (3707)Termination phase: shuffling
% 20.91/4.44
% 20.91/4.44 % (3707)Memory used [KB]: 6396
% 20.91/4.44 % (3707)Time elapsed: 0.029 s
% 20.91/4.44 % (3707)Instructions burned: 99 (million)
% 20.91/4.44 % (3707)------------------------------
% 20.91/4.44 % (3707)------------------------------
% 20.91/4.44 % (3708)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_3263 for (2973ds/503Mi)
% 20.91/4.45 % (3709)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_3263 for (2973ds/90Mi)
% 20.91/4.45 % (3704)Instruction limit reached!
% 20.91/4.45 % (3704)------------------------------
% 20.91/4.45 % (3704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.91/4.45 % (3704)Termination reason: Unknown
% 20.91/4.45 % (3704)Termination phase: Saturation
% 20.91/4.45
% 20.91/4.45 % (3704)Memory used [KB]: 12153
% 20.91/4.45 % (3704)Time elapsed: 0.099 s
% 20.91/4.45 % (3704)Instructions burned: 329 (million)
% 20.91/4.45 % (3704)------------------------------
% 20.91/4.45 % (3704)------------------------------
% 20.91/4.46 % (3710)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3263 for (2973ds/593Mi)
% 20.91/4.48 % (3709)Instruction limit reached!
% 20.91/4.48 % (3709)------------------------------
% 20.91/4.48 % (3709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.91/4.48 % (3709)Termination reason: Unknown
% 20.91/4.48 % (3709)Termination phase: Property scanning
% 20.91/4.48
% 20.91/4.48 % (3709)Memory used [KB]: 5500
% 20.91/4.48 % (3709)Time elapsed: 0.031 s
% 20.91/4.48 % (3709)Instructions burned: 92 (million)
% 20.91/4.48 % (3709)------------------------------
% 20.91/4.48 % (3709)------------------------------
% 20.91/4.49 % (3711)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_3263 for (2972ds/1512Mi)
% 21.93/4.51 % (3703)Instruction limit reached!
% 21.93/4.51 % (3703)------------------------------
% 21.93/4.51 % (3703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.51 % (3703)Termination reason: Unknown
% 21.93/4.51 % (3703)Termination phase: Saturation
% 21.93/4.51
% 21.93/4.51 % (3703)Memory used [KB]: 12281
% 21.93/4.51 % (3703)Time elapsed: 0.183 s
% 21.93/4.51 % (3703)Instructions burned: 595 (million)
% 21.93/4.51 % (3703)------------------------------
% 21.93/4.51 % (3703)------------------------------
% 21.93/4.52 % (3712)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3263 for (2972ds/569Mi)
% 21.93/4.57 % (3705)First to succeed.
% 21.93/4.57 % (3705)Refutation found. Thanks to Tanya!
% 21.93/4.57 % SZS status Theorem for DTF2THF_3263
% 21.93/4.57 % SZS output start Proof for DTF2THF_3263
% 21.93/4.57 thf(type_def_5, type, com: $tType).
% 21.93/4.57 thf(type_def_7, type, pname: $tType).
% 21.93/4.57 thf(type_def_8, type, option_com: $tType).
% 21.93/4.57 thf(type_def_9, type, state: $tType).
% 21.93/4.57 thf(type_def_10, type, hoare_1167836817_state: $tType).
% 21.93/4.57 thf(type_def_11, type, option_pname: $tType).
% 21.93/4.57 thf(type_def_12, type, option1574264306_state: $tType).
% 21.93/4.57 thf(func_def_0, type, com: $tType).
% 21.93/4.57 thf(func_def_1, type, pname: $tType).
% 21.93/4.57 thf(func_def_2, type, state: $tType).
% 21.93/4.57 thf(func_def_3, type, hoare_1167836817_state: $tType).
% 21.93/4.57 thf(func_def_4, type, option_com: $tType).
% 21.93/4.57 thf(func_def_5, type, option_pname: $tType).
% 21.93/4.57 thf(func_def_6, type, option1574264306_state: $tType).
% 21.93/4.57 thf(func_def_7, type, wt: com > $o).
% 21.93/4.57 thf(func_def_9, type, body: pname > option_com).
% 21.93/4.57 thf(func_def_10, type, body_1: pname > com).
% 21.93/4.57 thf(func_def_11, type, skip: com).
% 21.93/4.57 thf(func_def_12, type, semi: com > com > com).
% 21.93/4.57 thf(func_def_13, type, while: (state > $o) > com > com).
% 21.93/4.57 thf(func_def_14, type, finite1066544169me_o_o: (((pname > $o) > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_15, type, finite33115244te_o_o: (((hoare_1167836817_state > $o) > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_16, type, finite297249702name_o: ((pname > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_17, type, finite1380128977tate_o: ((hoare_1167836817_state > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_18, type, finite_finite_pname: (pname > $o) > $o).
% 21.93/4.57 thf(func_def_19, type, finite1084549118_state: (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_20, type, finite349908348name_o: ((pname > $o) > (pname > $o) > pname > $o) > (((pname > $o) > $o) > pname > $o) > $o).
% 21.93/4.57 thf(func_def_21, type, finite979047547tate_o: ((hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > (((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_22, type, finite1282449217_pname: (pname > pname > pname) > ((pname > $o) > pname) > $o).
% 21.93/4.57 thf(func_def_23, type, finite1074406356_state: (hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state) > ((hoare_1167836817_state > $o) > hoare_1167836817_state) > $o).
% 21.93/4.57 thf(func_def_24, type, finite697516351name_o: ((pname > $o) > (pname > $o) > pname > $o) > (((pname > $o) > $o) > pname > $o) > $o).
% 21.93/4.57 thf(func_def_25, type, finite671847800tate_o: ((hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > (((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_26, type, finite89670078_pname: (pname > pname > pname) > ((pname > $o) > pname) > $o).
% 21.93/4.57 thf(func_def_27, type, finite806517911_state: (hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state) > ((hoare_1167836817_state > $o) > hoare_1167836817_state) > $o).
% 21.93/4.57 thf(func_def_28, type, minus_1480864103me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_29, type, minus_1708687022te_o_o: ((hoare_1167836817_state > $o) > $o) > ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_30, type, minus_minus_pname_o: (pname > $o) > (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_31, type, minus_2107060239tate_o: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_32, type, the_pname: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_33, type, the_Ho310147232_state: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_34, type, hoare_Mirabelle_MGT: com > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_35, type, hoare_123228589_state: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_36, type, hoare_529639851_state: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_38, type, hoare_908217195_state: (state > state > $o) > com > (state > state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_39, type, if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_40, type, if_option_com: $o > option_com > option_com > option_com).
% 21.93/4.57 thf(func_def_41, type, semila2013987940me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_42, type, semila1758709489te_o_o: ((hoare_1167836817_state > $o) > $o) > ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_43, type, semila1673364395name_o: (pname > $o) > (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_44, type, semila179895820tate_o: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_45, type, semila181081674me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_46, type, semila866907787te_o_o: ((hoare_1167836817_state > $o) > $o) > ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_47, type, semila1780557381name_o: (pname > $o) > (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_48, type, semila1172322802tate_o: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_49, type, semila10642723_sup_o: $o > $o > $o).
% 21.93/4.57 thf(func_def_50, type, dom_pname_com: (pname > option_com) > pname > $o).
% 21.93/4.57 thf(func_def_51, type, evalc: com > state > state > $o).
% 21.93/4.57 thf(func_def_52, type, some_com: com > option_com).
% 21.93/4.57 thf(func_def_53, type, some_pname: pname > option_pname).
% 21.93/4.57 thf(func_def_54, type, some_H1433514562_state: hoare_1167836817_state > option1574264306_state).
% 21.93/4.57 thf(func_def_55, type, set_com: option_com > com > $o).
% 21.93/4.57 thf(func_def_56, type, set_pname: option_pname > pname > $o).
% 21.93/4.57 thf(func_def_57, type, set_Ho2131684873_state: option1574264306_state > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_58, type, the_com: option_com > com).
% 21.93/4.57 thf(func_def_59, type, bot_bot_pname_o_o: (pname > $o) > $o).
% 21.93/4.57 thf(func_def_60, type, bot_bo691907561te_o_o: (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_61, type, bot_bot_com_o: com > $o).
% 21.93/4.57 thf(func_def_62, type, bot_bot_pname_o: pname > $o).
% 21.93/4.57 thf(func_def_63, type, bot_bo70021908tate_o: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_65, type, ord_le1205211808me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_66, type, ord_le741939125te_o_o: ((hoare_1167836817_state > $o) > $o) > ((hoare_1167836817_state > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_67, type, ord_less_eq_pname_o: (pname > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_68, type, ord_le827224136tate_o: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_69, type, ord_less_eq_o: $o > $o > $o).
% 21.93/4.57 thf(func_def_70, type, collect_pname_o_o: (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_71, type, collec1218656682te_o_o: (((hoare_1167836817_state > $o) > $o) > $o) > ((hoare_1167836817_state > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_72, type, collect_pname_o: ((pname > $o) > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_73, type, collec269976083tate_o: ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_74, type, collect_pname: (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_75, type, collec1027672124_state: (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_76, type, image_1085733413name_o: ((pname > $o) > pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_77, type, image_pname_o_pname: ((pname > $o) > pname) > ((pname > $o) > $o) > pname > $o).
% 21.93/4.57 thf(func_def_78, type, image_1381916541_state: ((pname > $o) > hoare_1167836817_state) > ((pname > $o) > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_79, type, image_1488525317tate_o: ((hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_80, type, image_980295115_pname: ((hoare_1167836817_state > $o) > pname) > ((hoare_1167836817_state > $o) > $o) > pname > $o).
% 21.93/4.57 thf(func_def_81, type, image_635813834_state: ((hoare_1167836817_state > $o) > hoare_1167836817_state) > ((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_82, type, image_pname_pname_o: (pname > pname > $o) > (pname > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_83, type, image_475339327tate_o: (pname > hoare_1167836817_state > $o) > (pname > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_84, type, image_pname_pname: (pname > pname) > (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_85, type, image_575578384_state: (pname > hoare_1167836817_state) > (pname > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_86, type, image_2066861949name_o: (hoare_1167836817_state > pname > $o) > (hoare_1167836817_state > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_87, type, image_1745649338tate_o: (hoare_1167836817_state > hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_88, type, image_8178176_pname: (hoare_1167836817_state > pname) > (hoare_1167836817_state > $o) > pname > $o).
% 21.93/4.57 thf(func_def_89, type, image_31595733_state: (hoare_1167836817_state > hoare_1167836817_state) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_90, type, insert_pname_o: (pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_91, type, insert999278200tate_o: (hoare_1167836817_state > $o) > ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_92, type, insert_com: com > (com > $o) > com > $o).
% 21.93/4.57 thf(func_def_93, type, insert_pname: pname > (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_94, type, insert2134838167_state: hoare_1167836817_state > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_95, type, the_elem_pname: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_96, type, the_el323660082_state: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_97, type, fequal_pname_o: (pname > $o) > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_98, type, fequal1486222077tate_o: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_99, type, fequal_pname: pname > pname > $o).
% 21.93/4.57 thf(func_def_100, type, fequal_state: state > state > $o).
% 21.93/4.57 thf(func_def_101, type, fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_102, type, member_pname_o: (pname > $o) > ((pname > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_103, type, member864234961tate_o: (hoare_1167836817_state > $o) > ((hoare_1167836817_state > $o) > $o) > $o).
% 21.93/4.57 thf(func_def_104, type, member_com: com > (com > $o) > $o).
% 21.93/4.57 thf(func_def_105, type, member_pname: pname > (pname > $o) > $o).
% 21.93/4.57 thf(func_def_106, type, member2058392318_state: hoare_1167836817_state > (hoare_1167836817_state > $o) > $o).
% 21.93/4.57 thf(func_def_107, type, fa: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_108, type, pn: pname).
% 21.93/4.57 thf(func_def_109, type, y: com).
% 21.93/4.57 thf(func_def_123, type, sK0: ((pname > $o) > pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_124, type, sK1: ((pname > $o) > pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_125, type, sK2: (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_126, type, sK3: (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_127, type, sK4: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_128, type, sK5: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_129, type, sK6: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_130, type, sK7: (hoare_1167836817_state > $o) > (pname > $o) > (pname > hoare_1167836817_state) > pname).
% 21.93/4.57 thf(func_def_131, type, sK8: ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_132, type, sK9: ((hoare_1167836817_state > $o) > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_133, type, sK10: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_134, type, sK11: ((hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_135, type, sK12: ((hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_136, type, sK13: (hoare_1167836817_state > $o) > (pname > $o) > (pname > hoare_1167836817_state) > pname > $o).
% 21.93/4.57 thf(func_def_137, type, sK14: ((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_138, type, sK15: ((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_139, type, sK16: ((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_140, type, sK17: (state > state > $o) > (state > state > $o) > (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_141, type, sK18: (state > state > $o) > (state > state > $o) > (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_142, type, sK19: (state > state > $o) > (state > state > $o) > (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_143, type, sK20: ((pname > $o) > $o) > pname).
% 21.93/4.57 thf(func_def_144, type, sK21: ((pname > $o) > $o) > pname > $o).
% 21.93/4.57 thf(func_def_145, type, sK22: ((pname > $o) > $o) > pname).
% 21.93/4.57 thf(func_def_146, type, sK23: state > state).
% 21.93/4.57 thf(func_def_147, type, sK24: ((pname > $o) > $o) > pname).
% 21.93/4.57 thf(func_def_148, type, sK25: ((pname > $o) > $o) > pname > $o).
% 21.93/4.57 thf(func_def_149, type, sK26: ((pname > $o) > $o) > (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_150, type, sK27: ((pname > $o) > $o) > (pname > $o) > pname).
% 21.93/4.57 thf(func_def_151, type, sK28: (pname > state > state > $o) > (pname > state > state > $o) > (pname > state > state > $o) > (hoare_1167836817_state > $o) > (pname > com) > (pname > state > state > $o) > pname).
% 21.93/4.57 thf(func_def_152, type, sK29: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_153, type, sK30: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_154, type, sK31: hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_155, type, sK32: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_156, type, sK33: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_157, type, sK34: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_158, type, sK35: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_159, type, sK36: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_160, type, sK37: (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_161, type, sK38: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_162, type, sK39: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_163, type, sK40: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_164, type, sK41: state > com > state > (state > $o) > state).
% 21.93/4.57 thf(func_def_165, type, sK42: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_166, type, sK43: (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_167, type, sK44: ((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_168, type, sK45: ((hoare_1167836817_state > $o) > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_169, type, sK46: (pname > $o) > (pname > hoare_1167836817_state) > hoare_1167836817_state > pname).
% 21.93/4.57 thf(func_def_170, type, sK47: (hoare_1167836817_state > $o) > hoare_1167836817_state > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_171, type, sK48: (hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_172, type, sK49: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_173, type, sK50: (hoare_1167836817_state > $o) > hoare_1167836817_state > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_174, type, sK51: hoare_1167836817_state > (pname > hoare_1167836817_state) > (pname > $o) > pname).
% 21.93/4.57 thf(func_def_175, type, sK52: ((pname > $o) > pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_176, type, sK53: ((pname > $o) > pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_177, type, sK54: (pname > $o) > (pname > $o) > pname).
% 21.93/4.57 thf(func_def_178, type, sK55: (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_179, type, sK56: hoare_1167836817_state > com).
% 21.93/4.57 thf(func_def_180, type, sK57: hoare_1167836817_state > state > state > $o).
% 21.93/4.57 thf(func_def_181, type, sK58: hoare_1167836817_state > state > state > $o).
% 21.93/4.57 thf(func_def_182, type, sK59: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_183, type, sK60: (pname > $o) > pname > pname > $o).
% 21.93/4.57 thf(func_def_184, type, sK61: (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_185, type, sK62: (state > state > $o) > (state > state > $o) > state).
% 21.93/4.57 thf(func_def_186, type, sK63: ((hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_187, type, sK64: ((hoare_1167836817_state > $o) > hoare_1167836817_state > $o) > hoare_1167836817_state > $o).
% 21.93/4.57 thf(func_def_188, type, sK65: pname > (pname > option_com) > com).
% 21.93/4.57 thf(func_def_189, type, sK66: (pname > hoare_1167836817_state) > (pname > $o) > (hoare_1167836817_state > $o) > pname > $o).
% 21.93/4.57 thf(func_def_190, type, sK67: (pname > $o) > (pname > $o) > pname).
% 21.93/4.57 thf(func_def_191, type, sK68: (state > state > $o) > (state > state > $o) > (hoare_1167836817_state > $o) > com > state).
% 21.93/4.57 thf(func_def_192, type, sK69: (state > state > $o) > (state > state > $o) > (hoare_1167836817_state > $o) > com > state).
% 21.93/4.57 thf(func_def_193, type, sK70: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_194, type, sK71: (pname > $o) > (pname > hoare_1167836817_state) > (pname > hoare_1167836817_state) > pname).
% 21.93/4.57 thf(func_def_195, type, sK72: (pname > $o) > pname > $o).
% 21.93/4.57 thf(func_def_196, type, sK73: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_197, type, sK74: (pname > $o) > (pname > $o) > pname).
% 21.93/4.57 thf(func_def_198, type, sK75: (pname > $o) > (pname > $o) > pname).
% 21.93/4.57 thf(func_def_199, type, sK76: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_200, type, sK77: (pname > $o) > pname > pname > $o).
% 21.93/4.57 thf(func_def_201, type, sK78: (hoare_1167836817_state > $o) > pname).
% 21.93/4.57 thf(func_def_202, type, sK79: pname > com).
% 21.93/4.57 thf(func_def_203, type, sK80: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_204, type, sK81: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_205, type, sK82: (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > (hoare_1167836817_state > $o) > hoare_1167836817_state).
% 21.93/4.57 thf(func_def_206, type, sK83: state).
% 21.93/4.57 thf(func_def_207, type, sK84: state).
% 21.93/4.57 thf(func_def_208, type, sK85: (pname > $o) > pname).
% 21.93/4.57 thf(func_def_210, type, ph87: !>[X0: $tType]:(X0)).
% 21.93/4.57 thf(f3924,plain,(
% 21.93/4.57 $false),
% 21.93/4.57 inference(subsumption_resolution,[status(thm)],[f3923,f3388])).
% 21.93/4.57 thf(f3388,plain,(
% 21.93/4.57 ($true = (wt @ y))),
% 21.93/4.57 inference(equality_resolution,[status(thm)],[f3381])).
% 21.93/4.57 thf(f3381,plain,(
% 21.93/4.57 ( ! [X0 : com] : (((some_com @ y) != (some_com @ X0)) | ($true = (wt @ X0))) )),
% 21.93/4.57 inference(superposition,[status(thm)],[f3367,f2780])).
% 21.93/4.57 thf(f2780,plain,(
% 21.93/4.57 ((body @ pn) = (some_com @ y))),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f721])).
% 21.93/4.57 thf(f721,axiom,(
% 21.93/4.57 ((body @ pn) = (some_com @ y))),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_5)).
% 21.93/4.57 thf(f3367,plain,(
% 21.93/4.57 ( ! [X0 : pname,X1 : com] : (((some_com @ X1) != (body @ X0)) | ($true = (wt @ X1))) )),
% 21.93/4.57 inference(trivial_inequality_removal,[status(thm)],[f3256])).
% 21.93/4.57 thf(f3256,plain,(
% 21.93/4.57 ( ! [X0 : pname,X1 : com] : (($true != $true) | ($true = (wt @ X1)) | ((some_com @ X1) != (body @ X0))) )),
% 21.93/4.57 inference(definition_unfolding,[status(thm)],[f2849,f2662])).
% 21.93/4.57 thf(f2662,plain,(
% 21.93/4.57 (wT_bodies = $true)),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f1563])).
% 21.93/4.57 thf(f1563,plain,(
% 21.93/4.57 (wT_bodies = $true)),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f1562])).
% 21.93/4.57 thf(f1562,plain,(
% 21.93/4.57 wT_bodies),
% 21.93/4.57 inference(rectify,[status(thm)],[f717])).
% 21.93/4.57 thf(f717,axiom,(
% 21.93/4.57 wT_bodies),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_1)).
% 21.93/4.57 thf(f2849,plain,(
% 21.93/4.57 ( ! [X0 : pname,X1 : com] : (($true = (wt @ X1)) | ((some_com @ X1) != (body @ X0)) | (wT_bodies != $true)) )),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f2363])).
% 21.93/4.57 thf(f2363,plain,(
% 21.93/4.57 ! [X0 : pname,X1 : com] : (($true = (wt @ X1)) | ((some_com @ X1) != (body @ X0)) | (wT_bodies != $true))),
% 21.93/4.57 inference(flattening,[status(thm)],[f2362])).
% 21.93/4.57 thf(f2362,plain,(
% 21.93/4.57 ! [X0 : pname,X1 : com] : ((($true = (wt @ X1)) | ((some_com @ X1) != (body @ X0))) | (wT_bodies != $true))),
% 21.93/4.57 inference(ennf_transformation,[status(thm)],[f1051])).
% 21.93/4.57 thf(f1051,plain,(
% 21.93/4.57 ! [X0 : pname,X1 : com] : ((wT_bodies = $true) => (((some_com @ X1) = (body @ X0)) => ($true = (wt @ X1))))),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f1050])).
% 21.93/4.57 thf(f1050,plain,(
% 21.93/4.57 ! [X0 : pname,X1 : com] : (wT_bodies => (((some_com @ X1) = (body @ X0)) => (wt @ X1)))),
% 21.93/4.57 inference(rectify,[status(thm)],[f216])).
% 21.93/4.57 thf(f216,axiom,(
% 21.93/4.57 ! [X18 : pname,X192 : com] : (wT_bodies => (((body @ X18) = (some_com @ X192)) => (wt @ X192)))),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_215_WT__bodiesD)).
% 21.93/4.57 thf(f3923,plain,(
% 21.93/4.57 ($true != (wt @ y))),
% 21.93/4.57 inference(trivial_inequality_removal,[status(thm)],[f3915])).
% 21.93/4.57 thf(f3915,plain,(
% 21.93/4.57 ($true != (wt @ y)) | ($true != $true)),
% 21.93/4.57 inference(superposition,[status(thm)],[f3810,f3362])).
% 21.93/4.57 thf(f3362,plain,(
% 21.93/4.57 ( ! [X0 : com] : (($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o))) | ($true != (wt @ X0))) )),
% 21.93/4.57 inference(trivial_inequality_removal,[status(thm)],[f3361])).
% 21.93/4.57 thf(f3361,plain,(
% 21.93/4.57 ( ! [X0 : com] : (($true != (wt @ X0)) | ($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o))) | ($true != $true)) )),
% 21.93/4.57 inference(duplicate_literal_removal,[status(thm)],[f3257])).
% 21.93/4.57 thf(f3257,plain,(
% 21.93/4.57 ( ! [X0 : com] : (($true != $true) | ($true != (wt @ X0)) | ($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o))) | ($true != $true)) )),
% 21.93/4.57 inference(definition_unfolding,[status(thm)],[f3070,f2662,f2813])).
% 21.93/4.57 thf(f2813,plain,(
% 21.93/4.57 (hoare_1201148605gleton = $true)),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f1849])).
% 21.93/4.57 thf(f1849,plain,(
% 21.93/4.57 (hoare_1201148605gleton = $true)),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f1848])).
% 21.93/4.57 thf(f1848,plain,(
% 21.93/4.57 hoare_1201148605gleton),
% 21.93/4.57 inference(rectify,[status(thm)],[f716])).
% 21.93/4.57 thf(f716,axiom,(
% 21.93/4.57 hoare_1201148605gleton),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_0)).
% 21.93/4.57 thf(f3070,plain,(
% 21.93/4.57 ( ! [X0 : com] : ((wT_bodies != $true) | (hoare_1201148605gleton != $true) | ($true != (wt @ X0)) | ($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o)))) )),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f2091])).
% 21.93/4.57 thf(f2091,plain,(
% 21.93/4.57 ! [X0 : com] : ((wT_bodies != $true) | (hoare_1201148605gleton != $true) | ($true != (wt @ X0)) | ($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o))))),
% 21.93/4.57 inference(flattening,[status(thm)],[f2090])).
% 21.93/4.57 thf(f2090,plain,(
% 21.93/4.57 ! [X0 : com] : (((($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o))) | ($true != (wt @ X0))) | (wT_bodies != $true)) | (hoare_1201148605gleton != $true))),
% 21.93/4.57 inference(ennf_transformation,[status(thm)],[f1789])).
% 21.93/4.57 thf(f1789,plain,(
% 21.93/4.57 ! [X0 : com] : ((hoare_1201148605gleton = $true) => ((wT_bodies = $true) => (($true = (wt @ X0)) => ($true = (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o))))))),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f1788])).
% 21.93/4.57 thf(f1788,plain,(
% 21.93/4.57 ! [X0 : com] : (hoare_1201148605gleton => (wT_bodies => ((wt @ X0) => (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo70021908tate_o)))))),
% 21.93/4.57 inference(rectify,[status(thm)],[f54])).
% 21.93/4.57 thf(f54,axiom,(
% 21.93/4.57 ! [X42 : com] : (hoare_1201148605gleton => (wT_bodies => ((wt @ X42) => (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ X42) @ bot_bo70021908tate_o)))))),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_53_MGF)).
% 21.93/4.57 thf(f3810,plain,(
% 21.93/4.57 ($true != (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o)))),
% 21.93/4.57 inference(trivial_inequality_removal,[status(thm)],[f3800])).
% 21.93/4.57 thf(f3800,plain,(
% 21.93/4.57 ($true != $true) | ($true != (hoare_123228589_state @ bot_bo70021908tate_o @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o)))),
% 21.93/4.57 inference(superposition,[status(thm)],[f3465,f3164])).
% 21.93/4.57 thf(f3164,plain,(
% 21.93/4.57 ( ! [X0 : hoare_1167836817_state > $o] : (((hoare_123228589_state @ X0 @ bot_bo70021908tate_o) = $true)) )),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f833])).
% 21.93/4.57 thf(f833,plain,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o] : ((hoare_123228589_state @ X0 @ bot_bo70021908tate_o) = $true)),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f832])).
% 21.93/4.57 thf(f832,plain,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o] : (hoare_123228589_state @ X0 @ bot_bo70021908tate_o)),
% 21.93/4.57 inference(rectify,[status(thm)],[f1])).
% 21.93/4.57 thf(f1,axiom,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o] : (hoare_123228589_state @ X0 @ bot_bo70021908tate_o)),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_0_empty)).
% 21.93/4.57 thf(f3465,plain,(
% 21.93/4.57 ( ! [X0 : hoare_1167836817_state > $o] : (($true != (hoare_123228589_state @ (image_575578384_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ X0)) | ($true != (hoare_123228589_state @ X0 @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o)))) )),
% 21.93/4.57 inference(trivial_inequality_removal,[status(thm)],[f3454])).
% 21.93/4.57 thf(f3454,plain,(
% 21.93/4.57 ( ! [X0 : hoare_1167836817_state > $o] : (($true != (hoare_123228589_state @ X0 @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o))) | ($true != (hoare_123228589_state @ (image_575578384_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ X0)) | ($true != $true)) )),
% 21.93/4.57 inference(superposition,[status(thm)],[f3149,f3002])).
% 21.93/4.57 thf(f3002,plain,(
% 21.93/4.57 ( ! [X2 : hoare_1167836817_state > $o,X0 : hoare_1167836817_state > $o,X1 : hoare_1167836817_state > $o] : (($true = (hoare_123228589_state @ X1 @ X0)) | ($true != (hoare_123228589_state @ X1 @ X2)) | ((hoare_123228589_state @ X2 @ X0) != $true)) )),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f2193])).
% 21.93/4.57 thf(f2193,plain,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o,X1 : hoare_1167836817_state > $o,X2 : hoare_1167836817_state > $o] : (($true != (hoare_123228589_state @ X1 @ X2)) | ($true = (hoare_123228589_state @ X1 @ X0)) | ((hoare_123228589_state @ X2 @ X0) != $true))),
% 21.93/4.57 inference(flattening,[status(thm)],[f2192])).
% 21.93/4.57 thf(f2192,plain,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o,X1 : hoare_1167836817_state > $o,X2 : hoare_1167836817_state > $o] : ((($true = (hoare_123228589_state @ X1 @ X0)) | ($true != (hoare_123228589_state @ X1 @ X2))) | ((hoare_123228589_state @ X2 @ X0) != $true))),
% 21.93/4.57 inference(ennf_transformation,[status(thm)],[f891])).
% 21.93/4.57 thf(f891,plain,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o,X1 : hoare_1167836817_state > $o,X2 : hoare_1167836817_state > $o] : (((hoare_123228589_state @ X2 @ X0) = $true) => (($true = (hoare_123228589_state @ X1 @ X2)) => ($true = (hoare_123228589_state @ X1 @ X0))))),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f890])).
% 21.93/4.57 thf(f890,plain,(
% 21.93/4.57 ! [X0 : hoare_1167836817_state > $o,X1 : hoare_1167836817_state > $o,X2 : hoare_1167836817_state > $o] : ((hoare_123228589_state @ X2 @ X0) => ((hoare_123228589_state @ X1 @ X2) => (hoare_123228589_state @ X1 @ X0)))),
% 21.93/4.57 inference(rectify,[status(thm)],[f5])).
% 21.93/4.57 thf(f5,axiom,(
% 21.93/4.57 ! [X11 : hoare_1167836817_state > $o,X9 : hoare_1167836817_state > $o,X10 : hoare_1167836817_state > $o] : ((hoare_123228589_state @ X10 @ X11) => ((hoare_123228589_state @ X9 @ X10) => (hoare_123228589_state @ X9 @ X11)))),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',fact_4_cut)).
% 21.93/4.57 thf(f3149,plain,(
% 21.93/4.57 ($true != (hoare_123228589_state @ (image_575578384_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o)))),
% 21.93/4.57 inference(cnf_transformation,[status(thm)],[f1934])).
% 21.93/4.57 thf(f1934,plain,(
% 21.93/4.57 ($true != (hoare_123228589_state @ (image_575578384_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o)))),
% 21.93/4.57 inference(flattening,[status(thm)],[f1721])).
% 21.93/4.57 thf(f1721,plain,(
% 21.93/4.57 ~($true = (hoare_123228589_state @ (image_575578384_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o)))),
% 21.93/4.57 inference(fool_elimination,[status(thm)],[f1720])).
% 21.93/4.57 thf(f1720,plain,(
% 21.93/4.57 ~(hoare_123228589_state @ (image_575578384_state @ (^[X0 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X0))) @ (dom_pname_com @ body)) @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o))),
% 21.93/4.57 inference(rectify,[status(thm)],[f724])).
% 21.93/4.57 thf(f724,negated_conjecture,(
% 21.93/4.57 ~(hoare_123228589_state @ (image_575578384_state @ (^[X217 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X217))) @ (dom_pname_com @ body)) @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o))),
% 21.93/4.57 inference(negated_conjecture,[status(cth)],[f723])).
% 21.93/4.57 thf(f723,conjecture,(
% 21.93/4.57 (hoare_123228589_state @ (image_575578384_state @ (^[X217 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X217))) @ (dom_pname_com @ body)) @ (insert2134838167_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo70021908tate_o))),
% 21.93/4.57 file('/export/starexec/sandbox/tmp/tmp.mucXTLhVAV/DTF2THF_3263.p',conj_7)).
% 21.93/4.57 % SZS output end Proof for DTF2THF_3263
% 21.93/4.57 % (3705)------------------------------
% 21.93/4.57 % (3705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.57 % (3705)Termination reason: Refutation
% 21.93/4.57
% 21.93/4.57 % (3705)Memory used [KB]: 12153
% 21.93/4.57 % (3705)Time elapsed: 0.187 s
% 21.93/4.57 % (3705)Instructions burned: 606 (million)
% 21.93/4.57 % (3705)------------------------------
% 21.93/4.57 % (3705)------------------------------
% 21.93/4.57 % (3570)Success in time 2.815 s
%------------------------------------------------------------------------------