%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP143^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 08:55:53 AM UTC 2026
% Result : Theorem 40.46s 7.16s
% Output : Refutation 40.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 95 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 645 ( 47 ~; 26 |; 15 &; 532 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 37 ( 36 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 247 ( 244 usr; 13 con; 0-5 aty)
% Number of variables : 90 ( 14 ^; 69 !; 7 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
list_list_com: $tType ).
thf(type_def_8,type,
list_com: $tType ).
thf(type_def_9,type,
list_P1040014977_state: $tType ).
thf(type_def_10,type,
com: $tType ).
thf(type_def_11,type,
list_state: $tType ).
thf(type_def_12,type,
set_Pr1822651163om_com: $tType ).
thf(type_def_13,type,
set_Pr602326075st_com: $tType ).
thf(type_def_14,type,
set_Pr1165141447_state: $tType ).
thf(type_def_15,type,
set_Pr1142642759_state: $tType ).
thf(type_def_16,type,
state: $tType ).
thf(type_def_17,type,
produc2041926651_state: $tType ).
thf(type_def_18,type,
set_Pr849496667_state: $tType ).
thf(type_def_19,type,
set_Pr391631483_state: $tType ).
thf(type_def_20,type,
set_nat: $tType ).
thf(type_def_21,type,
set_state: $tType ).
thf(type_def_22,type,
produc2058209240st_com: $tType ).
thf(type_def_23,type,
produc1393453339_state: $tType ).
thf(type_def_24,type,
produc258871771st_com: $tType ).
thf(type_def_25,type,
produc1225889383_state: $tType ).
thf(type_def_26,type,
product_prod_com_com: $tType ).
thf(type_def_27,type,
produc1115495963_state: $tType ).
thf(type_def_28,type,
produc1440412305st_com: $tType ).
thf(type_def_29,type,
produc392316135_state: $tType ).
thf(type_def_30,type,
produc1762014951st_com: $tType ).
thf(type_def_31,type,
produc410756839_state: $tType ).
thf(type_def_32,type,
produc1519776487_state: $tType ).
thf(type_def_33,type,
produc1065433319om_com: $tType ).
thf(type_def_34,type,
produc186437863_state: $tType ).
thf(type_def_35,type,
set_Pr135335153st_com: $tType ).
thf(type_def_36,type,
set_Pr1419004359_state: $tType ).
thf(type_def_37,type,
set_Pr2083163591st_com: $tType ).
thf(type_def_38,type,
set_Pr1847866567_state: $tType ).
thf(type_def_39,type,
set_Pr1675528647om_com: $tType ).
thf(type_def_40,type,
set_Pr2096893127_state: $tType ).
thf(type_def_41,type,
set_Pr795498619_state: $tType ).
thf(func_def_0,type,
set_Pr1847866567_state: $tType ).
thf(func_def_1,type,
produc1519776487_state: $tType ).
thf(func_def_2,type,
set_Pr2096893127_state: $tType ).
thf(func_def_3,type,
produc186437863_state: $tType ).
thf(func_def_4,type,
set_Pr1419004359_state: $tType ).
thf(func_def_5,type,
set_Pr135335153st_com: $tType ).
thf(func_def_6,type,
produc392316135_state: $tType ).
thf(func_def_7,type,
produc1440412305st_com: $tType ).
thf(func_def_8,type,
set_Pr1142642759_state: $tType ).
thf(func_def_9,type,
set_Pr2083163591st_com: $tType ).
thf(func_def_10,type,
produc1225889383_state: $tType ).
thf(func_def_11,type,
produc1762014951st_com: $tType ).
thf(func_def_12,type,
set_Pr1165141447_state: $tType ).
thf(func_def_13,type,
produc410756839_state: $tType ).
thf(func_def_14,type,
set_Pr1675528647om_com: $tType ).
thf(func_def_15,type,
produc1065433319om_com: $tType ).
thf(func_def_16,type,
set_Pr391631483_state: $tType ).
thf(func_def_17,type,
produc1393453339_state: $tType ).
thf(func_def_18,type,
produc2058209240st_com: $tType ).
thf(func_def_19,type,
set_Pr602326075st_com: $tType ).
thf(func_def_20,type,
list_P1040014977_state: $tType ).
thf(func_def_21,type,
set_Pr849496667_state: $tType ).
thf(func_def_22,type,
produc258871771st_com: $tType ).
thf(func_def_23,type,
set_Pr795498619_state: $tType ).
thf(func_def_24,type,
produc2041926651_state: $tType ).
thf(func_def_25,type,
set_Pr1822651163om_com: $tType ).
thf(func_def_26,type,
produc1115495963_state: $tType ).
thf(func_def_27,type,
product_prod_com_com: $tType ).
thf(func_def_28,type,
list_list_com: $tType ).
thf(func_def_29,type,
list_state: $tType ).
thf(func_def_30,type,
set_state: $tType ).
thf(func_def_31,type,
list_com: $tType ).
thf(func_def_32,type,
set_nat: $tType ).
thf(func_def_33,type,
state: $tType ).
thf(func_def_34,type,
com: $tType ).
thf(func_def_35,type,
nat: $tType ).
thf(func_def_36,type,
zero_zero_nat: nat ).
thf(func_def_37,type,
append_list_com: list_list_com > list_list_com > list_list_com ).
thf(func_def_38,type,
append_com: list_com > list_com > list_com ).
thf(func_def_39,type,
append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state ).
thf(func_def_40,type,
bind_com_com: list_com > ( com > list_com ) > list_com ).
thf(func_def_41,type,
concat_com: list_list_com > list_com ).
thf(func_def_42,type,
gen_length_list_com: nat > list_list_com > nat ).
thf(func_def_43,type,
gen_length_com: nat > list_com > nat ).
thf(func_def_44,type,
gen_length_state: nat > list_state > nat ).
thf(func_def_45,type,
gen_le1266608782_state: nat > list_P1040014977_state > nat ).
thf(func_def_46,type,
insert_com: com > list_com > list_com ).
thf(func_def_47,type,
lenlex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_48,type,
lenlex295247238_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_49,type,
lex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_50,type,
lex_Pr570247525_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_51,type,
lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_52,type,
lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_53,type,
cons_list_com: list_com > list_list_com > list_list_com ).
thf(func_def_54,type,
cons_com: com > list_com > list_com ).
thf(func_def_55,type,
cons_state: state > list_state > list_state ).
thf(func_def_56,type,
cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state ).
thf(func_def_57,type,
nil_list_com: list_list_com ).
thf(func_def_58,type,
nil_com: list_com ).
thf(func_def_59,type,
nil_state: list_state ).
thf(func_def_60,type,
nil_Pr1844458753_state: list_P1040014977_state ).
thf(func_def_61,type,
listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_62,type,
listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_63,type,
listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state ).
thf(func_def_64,type,
listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_65,type,
listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_66,type,
maps_com_com: ( com > list_com ) > list_com > list_com ).
thf(func_def_67,type,
n_lists_com: nat > list_com > list_list_com ).
thf(func_def_68,type,
nths_com: list_com > set_nat > list_com ).
thf(func_def_69,type,
product_lists_com: list_list_com > list_list_com ).
thf(func_def_70,type,
rotate1_com: list_com > list_com ).
thf(func_def_71,type,
subseqs_com: list_com > list_list_com ).
thf(func_def_72,type,
suc: nat > nat ).
thf(func_def_73,type,
size_size_list_com: list_com > nat ).
thf(func_def_74,type,
size_s213202669_state: list_P1040014977_state > nat ).
thf(func_def_75,type,
pHoare259243666_exec1: set_Pr1165141447_state ).
thf(func_def_76,type,
pHoare202237534exec1p: list_com > state > list_com > state > $o ).
thf(func_def_77,type,
pHoare259243732_execs: state > list_com > state > $o ).
thf(func_def_78,type,
pHoare2126160787le_inf: list_com > state > $o ).
thf(func_def_79,type,
pHoare806997636termis: list_com > state > $o ).
thf(func_def_80,type,
cond: ( state > $o ) > com > com > com ).
thf(func_def_81,type,
do: ( state > set_state ) > com ).
thf(func_def_82,type,
semi: com > com > com ).
thf(func_def_83,type,
while: ( state > $o ) > com > com ).
thf(func_def_84,type,
exec: state > com > state > $o ).
thf(func_def_85,type,
termi: com > state > $o ).
thf(func_def_86,type,
produc1914379986st_com: ( com > com > $o ) > list_com > produc2058209240st_com ).
thf(func_def_87,type,
produc1742567891_state: list_list_com > list_state > produc1393453339_state ).
thf(func_def_88,type,
produc1307105171st_com: list_com > list_com > produc258871771st_com ).
thf(func_def_89,type,
produc1204172211_state: list_com > state > produc2041926651_state ).
thf(func_def_90,type,
produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state ).
thf(func_def_91,type,
product_Pair_com_com: com > com > product_prod_com_com ).
thf(func_def_92,type,
produc64584659_state: state > state > produc1115495963_state ).
thf(func_def_93,type,
produc67337417st_com: produc2058209240st_com > produc2058209240st_com > produc1440412305st_com ).
thf(func_def_94,type,
produc67381847_state: produc1393453339_state > produc1393453339_state > produc392316135_state ).
thf(func_def_95,type,
produc313736791st_com: produc258871771st_com > produc258871771st_com > produc1762014951st_com ).
thf(func_def_96,type,
produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).
thf(func_def_97,type,
produc984060759_state: produc1225889383_state > produc1225889383_state > produc1519776487_state ).
thf(func_def_98,type,
produc1140939351om_com: product_prod_com_com > product_prod_com_com > produc1065433319om_com ).
thf(func_def_99,type,
produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state ).
thf(func_def_100,type,
irrefl_com: set_Pr1822651163om_com > $o ).
thf(func_def_101,type,
irrefl654089520_state: set_Pr1165141447_state > $o ).
thf(func_def_102,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_103,type,
collect_state: ( state > $o ) > set_state ).
thf(func_def_104,type,
collec924674566_state: ( produc1393453339_state > $o ) > set_Pr391631483_state ).
thf(func_def_105,type,
collec328862150st_com: ( produc258871771st_com > $o ) > set_Pr602326075st_com ).
thf(func_def_106,type,
collec1409185766_state: ( produc2041926651_state > $o ) > set_Pr849496667_state ).
thf(func_def_107,type,
collec183560402_state: ( produc1225889383_state > $o ) > set_Pr1142642759_state ).
thf(func_def_108,type,
collec300063826_state: ( produc410756839_state > $o ) > set_Pr1165141447_state ).
thf(func_def_109,type,
transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com ).
thf(func_def_110,type,
transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state ).
thf(func_def_111,type,
transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com ).
thf(func_def_112,type,
transi1592315797st_com: set_Pr135335153st_com > set_Pr135335153st_com ).
thf(func_def_113,type,
transi89280670_state: set_Pr1419004359_state > set_Pr1419004359_state ).
thf(func_def_114,type,
transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com ).
thf(func_def_115,type,
transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(func_def_116,type,
transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state ).
thf(func_def_117,type,
transi1042416958om_com: set_Pr1675528647om_com > set_Pr1675528647om_com ).
thf(func_def_118,type,
transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).
thf(func_def_119,type,
same_f855297288_state: ( list_com > $o ) > ( list_com > set_Pr795498619_state ) > set_Pr1165141447_state ).
thf(func_def_120,type,
same_f1258458156_state: ( produc2041926651_state > $o ) > ( produc2041926651_state > set_Pr1165141447_state ) > set_Pr2096893127_state ).
thf(func_def_121,type,
member_nat: nat > set_nat > $o ).
thf(func_def_122,type,
member_state: state > set_state > $o ).
thf(func_def_123,type,
member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
thf(func_def_124,type,
member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
thf(func_def_125,type,
member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
thf(func_def_126,type,
member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).
thf(func_def_127,type,
member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
thf(func_def_128,type,
member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o ).
thf(func_def_129,type,
member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o ).
thf(func_def_130,type,
member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o ).
thf(func_def_131,type,
member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o ).
thf(func_def_132,type,
member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
thf(func_def_133,type,
member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o ).
thf(func_def_134,type,
member2105207824om_com: produc1065433319om_com > set_Pr1675528647om_com > $o ).
thf(func_def_135,type,
member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
thf(func_def_136,type,
a: list_com ).
thf(func_def_137,type,
b: state > $o ).
thf(func_def_138,type,
ba: state ).
thf(func_def_139,type,
c: com ).
thf(func_def_140,type,
cs: list_com ).
thf(func_def_141,type,
f: nat > produc2041926651_state ).
thf(func_def_142,type,
s: state ).
thf(func_def_162,type,
sK0: list_com > list_com ).
thf(func_def_163,type,
sK1: list_com > com ).
thf(func_def_164,type,
sK2: list_com > com ).
thf(func_def_165,type,
sK3: list_com > com ).
thf(func_def_166,type,
sK4: ( nat > nat > $o ) > nat ).
thf(func_def_167,type,
sK5: ( nat > nat > $o ) > nat ).
thf(func_def_168,type,
sK6: ( nat > nat > $o ) > nat ).
thf(func_def_169,type,
sK7: ( nat > nat > $o ) > nat ).
thf(func_def_170,type,
sK8: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_171,type,
sK9: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_172,type,
sK10: produc410756839_state > produc2041926651_state ).
thf(func_def_173,type,
sK11: produc410756839_state > list_com ).
thf(func_def_174,type,
sK12: produc410756839_state > state ).
thf(func_def_175,type,
sK13: set_Pr1165141447_state > produc2041926651_state > ( nat > produc2041926651_state ) > nat ).
thf(func_def_176,type,
sK14: set_Pr1165141447_state > produc2041926651_state > nat > produc2041926651_state ).
thf(func_def_177,type,
sK15: ( list_com > state > $o ) > set_Pr1165141447_state > list_com > state > list_com ).
thf(func_def_178,type,
sK16: ( list_com > state > $o ) > set_Pr1165141447_state > list_com > state > state ).
thf(func_def_179,type,
sK17: ( list_com > state > $o ) > set_Pr1165141447_state > list_com > state > state ).
thf(func_def_180,type,
sK18: ( list_com > state > $o ) > set_Pr1165141447_state > list_com > state > list_com ).
thf(func_def_181,type,
sK19: produc2041926651_state > list_com ).
thf(func_def_182,type,
sK20: produc2041926651_state > state ).
thf(func_def_183,type,
sK21: list_com > list_com ).
thf(func_def_184,type,
sK22: list_com > com ).
thf(func_def_185,type,
sK23: ( list_com > $o ) > com ).
thf(func_def_186,type,
sK24: ( list_com > $o ) > com ).
thf(func_def_187,type,
sK25: ( list_com > $o ) > com ).
thf(func_def_188,type,
sK26: ( list_com > $o ) > list_com ).
thf(func_def_189,type,
sK27: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_190,type,
sK28: ( produc410756839_state > $o ) > list_com ).
thf(func_def_191,type,
sK29: ( produc410756839_state > $o ) > state ).
thf(func_def_192,type,
sK30: set_Pr1165141447_state > ( produc2041926651_state > $o ) > produc2041926651_state > produc2041926651_state ).
thf(func_def_193,type,
sK31: set_Pr1165141447_state > ( produc2041926651_state > $o ) > produc2041926651_state > produc2041926651_state ).
thf(func_def_194,type,
sK32: ( produc258871771st_com > $o ) > list_com ).
thf(func_def_195,type,
sK33: ( produc258871771st_com > $o ) > list_com ).
thf(func_def_196,type,
sK34: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_197,type,
sK35: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_198,type,
sK36: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_199,type,
sK37: ( produc2041926651_state > $o ) > state ).
thf(func_def_200,type,
sK38: ( produc2041926651_state > $o ) > list_com ).
thf(func_def_201,type,
sK39: ( produc2041926651_state > $o ) > state ).
thf(func_def_202,type,
sK40: ( produc2041926651_state > $o ) > list_com ).
thf(func_def_203,type,
sK41: ( produc258871771st_com > $o ) > list_com ).
thf(func_def_204,type,
sK42: ( produc258871771st_com > $o ) > list_com ).
thf(func_def_205,type,
sK43: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_206,type,
sK44: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_207,type,
sK45: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_208,type,
sK46: ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_209,type,
sK47: nat > nat ).
thf(func_def_210,type,
sK48: ( list_com > list_com > $o ) > list_com ).
thf(func_def_211,type,
sK49: ( list_com > list_com > $o ) > list_com ).
thf(func_def_212,type,
sK50: ( list_com > list_com > $o ) > list_com ).
thf(func_def_213,type,
sK51: ( list_com > list_com > $o ) > list_com ).
thf(func_def_214,type,
sK52: ( list_com > list_com > $o ) > com ).
thf(func_def_215,type,
sK53: ( list_com > list_com > $o ) > com ).
thf(func_def_216,type,
sK54: produc258871771st_com > list_com ).
thf(func_def_217,type,
sK55: produc258871771st_com > list_com ).
thf(func_def_218,type,
sK56: produc258871771st_com > list_com ).
thf(func_def_219,type,
sK57: produc258871771st_com > com ).
thf(func_def_220,type,
sK58: produc258871771st_com > com ).
thf(func_def_221,type,
sK59: produc258871771st_com > list_com ).
thf(func_def_222,type,
sK60: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_223,type,
sK61: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_224,type,
sK62: ( list_com > $o ) > com ).
thf(func_def_225,type,
sK63: ( list_com > $o ) > list_com ).
thf(func_def_226,type,
sK64: ( list_com > $o ) > com ).
thf(func_def_227,type,
sK65: list_com > list_com ).
thf(func_def_228,type,
sK66: list_com > com ).
thf(func_def_229,type,
sK67: produc2041926651_state > list_com ).
thf(func_def_230,type,
sK68: produc2041926651_state > state ).
thf(func_def_231,type,
sK69: set_Pr1165141447_state > state > ( list_com > state > $o ) > list_com > state ).
thf(func_def_232,type,
sK70: set_Pr1165141447_state > state > ( list_com > state > $o ) > list_com > list_com ).
thf(func_def_233,type,
sK71: set_Pr1165141447_state > state > ( list_com > state > $o ) > list_com > list_com ).
thf(func_def_234,type,
sK72: set_Pr1165141447_state > state > ( list_com > state > $o ) > list_com > state ).
thf(func_def_235,type,
sK73: ( nat > produc2041926651_state ) > nat ).
thf(func_def_236,type,
sK74: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_237,type,
sK75: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_238,type,
sK76: ( ( com > com > $o ) > list_com > $o ) > list_com ).
thf(func_def_239,type,
sK77: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_240,type,
sK78: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_241,type,
sK79: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_242,type,
sK80: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_243,type,
sK81: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_244,type,
sK82: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_245,type,
sK83: ( ( com > com > $o ) > list_com > $o ) > list_com ).
thf(func_def_246,type,
sK84: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_247,type,
sK85: ( nat > $o ) > nat ).
thf(func_def_248,type,
sK86: state > list_com > list_com > set_Pr1165141447_state > state > list_com ).
thf(func_def_249,type,
sK87: state > list_com > list_com > set_Pr1165141447_state > state > state ).
thf(func_def_250,type,
sK88: ( list_com > $o ) > com ).
thf(func_def_251,type,
sK89: ( list_com > $o ) > list_com ).
thf(func_def_252,type,
sK90: produc410756839_state > produc2041926651_state ).
thf(func_def_253,type,
sK91: produc410756839_state > produc2041926651_state ).
thf(func_def_254,type,
sK92: ( list_com > list_com > $o ) > com ).
thf(func_def_255,type,
sK93: ( list_com > list_com > $o ) > list_com ).
thf(func_def_256,type,
sK94: ( list_com > list_com > $o ) > list_com ).
thf(func_def_257,type,
sK95: ( list_com > list_com > $o ) > com ).
thf(func_def_258,type,
sK96: ( list_com > list_com > $o ) > com ).
thf(func_def_259,type,
sK97: ( list_com > list_com > $o ) > list_com ).
thf(func_def_260,type,
sK98: ( list_com > list_com > $o ) > com ).
thf(func_def_261,type,
sK99: ( list_com > list_com > $o ) > list_com ).
thf(func_def_262,type,
sK100: nat > nat ).
thf(func_def_263,type,
sK101: ( list_com > $o ) > com ).
thf(func_def_264,type,
sK102: ( list_com > $o ) > list_com ).
thf(func_def_265,type,
sK103: ( list_com > $o ) > com ).
thf(func_def_266,type,
sK104: produc258871771st_com > list_com ).
thf(func_def_267,type,
sK105: produc258871771st_com > list_com ).
thf(func_def_268,type,
sK106: ( list_com > $o ) > list_com ).
thf(func_def_269,type,
sK107: ( list_com > $o ) > com ).
thf(func_def_270,type,
sK108: ( list_com > list_com > $o ) > list_com ).
thf(func_def_271,type,
sK109: ( list_com > list_com > $o ) > com ).
thf(func_def_272,type,
sK110: ( list_com > list_com > $o ) > list_com ).
thf(func_def_273,type,
sK111: ( list_com > list_com > $o ) > list_com ).
thf(func_def_274,type,
sK112: ( nat > $o ) > nat ).
thf(func_def_275,type,
sK113: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_276,type,
sK114: produc2041926651_state > ( nat > produc2041926651_state ) > set_Pr1165141447_state > nat ).
thf(func_def_277,type,
sK115: produc2041926651_state > set_Pr1165141447_state > nat > produc2041926651_state ).
thf(func_def_278,type,
sK116: produc410756839_state > produc2041926651_state ).
thf(func_def_279,type,
sK117: produc410756839_state > produc2041926651_state ).
thf(func_def_280,type,
sK118: produc258871771st_com > list_com ).
thf(func_def_281,type,
sK119: produc258871771st_com > com ).
thf(func_def_282,type,
sK120: produc258871771st_com > list_com ).
thf(func_def_283,type,
sK121: produc258871771st_com > list_com ).
thf(func_def_284,type,
sK122: ( ( com > com ) > list_com > list_com > $o ) > com > com ).
thf(func_def_285,type,
sK123: ( ( com > com ) > list_com > list_com > $o ) > list_com ).
thf(func_def_286,type,
sK124: ( ( com > com ) > list_com > list_com > $o ) > com ).
thf(func_def_287,type,
sK125: ( ( com > com ) > list_com > list_com > $o ) > list_com ).
thf(func_def_288,type,
sK126: ( ( com > com ) > list_com > list_com > $o ) > list_com ).
thf(func_def_289,type,
sK127: ( ( com > com ) > list_com > list_com > $o ) > com > com ).
thf(func_def_290,type,
sK128: ( nat > $o ) > nat ).
thf(func_def_291,type,
sK129: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_292,type,
sK130: produc258871771st_com > list_com ).
thf(func_def_293,type,
sK131: produc258871771st_com > list_com ).
thf(func_def_294,type,
sK132: ( list_com > $o ) > com ).
thf(func_def_295,type,
sK133: ( list_com > $o ) > com ).
thf(func_def_296,type,
sK134: ( list_com > $o ) > list_com ).
thf(func_def_297,type,
sK135: ( list_com > $o ) > com ).
thf(func_def_299,type,
ph137:
!>[X0: $tType] : X0 ).
thf(f1723,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1719]) ).
thf(f1719,plain,
( ( produc1204172211_state @ a @ s )
!= ( produc1204172211_state @ a @ s ) ),
inference(backward_demodulation,[status(thm)],[f1696,f1713]) ).
thf(f1713,plain,
( a
= ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1711]) ).
thf(f1711,plain,
( ( $true != $true )
| ( a
= ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) ) ),
inference(superposition,[status(thm)],[f1625,f1632]) ).
thf(f1632,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ a @ s ) ) @ pHoare259243666_exec1 )
= $true ),
inference(backward_demodulation,[status(thm)],[f1314,f1630]) ).
thf(f1630,plain,
s = ba,
inference(trivial_inequality_removal,[status(thm)],[f1629]) ).
thf(f1629,plain,
( ( s = ba )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1624,f1314]) ).
thf(f1624,plain,
! [X0: list_com,X1: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ X0 @ X1 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( s = X1 ) ),
inference(subsumption_resolution,[status(thm)],[f1615,f1217]) ).
thf(f1217,plain,
( ( b @ s )
= $true ),
inference(cnf_transformation,[status(thm)],[f1080]) ).
thf(f1080,plain,
( ( ( b @ s )
= $true )
& ! [X0: nat > produc2041926651_state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ ( sK73 @ X0 ) ) @ ( X0 @ ( suc @ ( sK73 @ X0 ) ) ) ) @ pHoare259243666_exec1 )
!= $true )
| ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
!= ( X0 @ zero_zero_nat ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f974,f1079]) ).
thf(f1079,plain,
! [X0: nat > produc2041926651_state] :
( ? [X1: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ X1 ) @ ( X0 @ ( suc @ X1 ) ) ) @ pHoare259243666_exec1 )
!= $true )
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ ( sK73 @ X0 ) ) @ ( X0 @ ( suc @ ( sK73 @ X0 ) ) ) ) @ pHoare259243666_exec1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f974,plain,
( ( ( b @ s )
= $true )
& ! [X0: nat > produc2041926651_state] :
( ? [X1: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ X1 ) @ ( X0 @ ( suc @ X1 ) ) ) @ pHoare259243666_exec1 )
!= $true )
| ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
!= ( X0 @ zero_zero_nat ) ) ) ),
inference(ennf_transformation,[status(thm)],[f865]) ).
thf(f865,plain,
~ ( ( ( b @ s )
!= $true )
| ? [X0: nat > produc2041926651_state] :
( ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
= ( X0 @ zero_zero_nat ) )
& ! [X1: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ X1 ) @ ( X0 @ ( suc @ X1 ) ) ) @ pHoare259243666_exec1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f756]) ).
thf(f756,plain,
~ ( ( ( b @ s )
!= $true )
| ? [X0: nat > produc2041926651_state] :
( ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
= ( X0 @ zero_zero_nat ) )
& ! [X1: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ X1 ) @ ( X0 @ ( suc @ X1 ) ) ) @ pHoare259243666_exec1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f755]) ).
thf(f755,plain,
~ ( ~ ( b @ s )
| ? [X0: nat > produc2041926651_state] :
( ! [X1: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ X1 ) @ ( X0 @ ( suc @ X1 ) ) ) @ pHoare259243666_exec1 )
& ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
= ( X0 @ zero_zero_nat ) ) ) ),
inference(rectify,[status(thm)],[f355]) ).
thf(f355,negated_conjecture,
~ ( ~ ( b @ s )
| ? [X139: nat > produc2041926651_state] :
( ! [X58: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( X139 @ X58 ) @ ( X139 @ ( suc @ X58 ) ) ) @ pHoare259243666_exec1 )
& ( ( X139 @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s ) ) ) ),
inference(negated_conjecture,[status(cth)],[f354]) ).
thf(f354,conjecture,
( ~ ( b @ s )
| ? [X139: nat > produc2041926651_state] :
( ! [X58: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( X139 @ X58 ) @ ( X139 @ ( suc @ X58 ) ) ) @ pHoare259243666_exec1 )
& ( ( X139 @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_4) ).
thf(f1615,plain,
! [X0: list_com,X1: state] :
( ( ( b @ s )
!= $true )
| ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ X0 @ X1 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( s = X1 ) ),
inference(superposition,[status(thm)],[f1286,f1301]) ).
thf(f1301,plain,
( ( f @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ ( while @ b @ c ) @ cs ) @ s ) ),
inference(cnf_transformation,[status(thm)],[f350]) ).
thf(f350,axiom,
( ( f @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ ( while @ b @ c ) @ cs ) @ s ) ),
file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_0) ).
thf(f1286,plain,
! [X2: state > $o,X3: com,X0: list_com,X1: list_com,X4: state,X5: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( X4 = X5 )
| ( ( X2 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f996]) ).
thf(f996,plain,
! [X0: list_com,X1: list_com,X2: state > $o,X3: com,X4: state,X5: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( ( ( X2 @ X4 )
= $true )
& ( ( cons_com @ X3 @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) )
= X0 )
& ( X4 = X5 ) )
| ( ( X0 = X1 )
& ( X4 = X5 )
& ( ( X2 @ X4 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f995]) ).
thf(f995,plain,
! [X0: list_com,X1: list_com,X2: state > $o,X3: com,X4: state,X5: state] :
( ( ( ( X2 @ X4 )
= $true )
& ( X4 = X5 )
& ( ( cons_com @ X3 @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) )
= X0 ) )
| ( ( ( X2 @ X4 )
!= $true )
& ( X4 = X5 )
& ( X0 = X1 ) )
| ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f883]) ).
thf(f883,plain,
! [X0: list_com,X1: list_com,X2: state > $o,X3: com,X4: state,X5: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
= $true )
=> ( ( ( X0 = X1 )
=> ( ( X4 = X5 )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ~ ( ( ( cons_com @ X3 @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) )
= X0 )
=> ( ( X4 = X5 )
=> ( ( X2 @ X4 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f410]) ).
thf(f410,plain,
! [X0: list_com,X1: list_com,X2: state > $o,X3: com,X4: state,X5: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
= $true )
=> ( ( ( X0 = X1 )
=> ( ( X4 = X5 )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ~ ( ( ( cons_com @ X3 @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) )
= X0 )
=> ( ( X4 = X5 )
=> ( ( X2 @ X4 )
!= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f409]) ).
thf(f409,plain,
! [X0: list_com,X1: list_com,X2: state > $o,X3: com,X4: state,X5: state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
=> ( ( ( X0 = X1 )
=> ( ( X4 = X5 )
=> ( X2 @ X4 ) ) )
=> ~ ( ( ( cons_com @ X3 @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) )
= X0 )
=> ( ( X4 = X5 )
=> ~ ( X2 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X4: list_com,X2: list_com,X0: state > $o,X1: com,X3: state,X5: state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X0 @ X1 ) @ X2 ) @ X3 ) @ ( produc1204172211_state @ X4 @ X5 ) ) @ pHoare259243666_exec1 )
=> ( ( ( X2 = X4 )
=> ( ( X3 = X5 )
=> ( X0 @ X3 ) ) )
=> ~ ( ( ( cons_com @ X1 @ ( cons_com @ ( while @ X0 @ X1 ) @ X2 ) )
= X4 )
=> ( ( X3 = X5 )
=> ~ ( X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',fact_0_exec1E_I5_J) ).
thf(f1314,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ a @ ba ) ) @ pHoare259243666_exec1 )
= $true ),
inference(forward_demodulation,[status(thm)],[f1143,f1233]) ).
thf(f1233,plain,
( ( f @ ( suc @ zero_zero_nat ) )
= ( produc1204172211_state @ a @ ba ) ),
inference(cnf_transformation,[status(thm)],[f353]) ).
thf(f353,axiom,
( ( f @ ( suc @ zero_zero_nat ) )
= ( produc1204172211_state @ a @ ba ) ),
file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_3) ).
thf(f1143,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ zero_zero_nat ) ) ) @ pHoare259243666_exec1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f358]) ).
thf(f358,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ zero_zero_nat ) ) ) @ pHoare259243666_exec1 )
= $true ),
inference(fool_elimination,[status(thm)],[f357]) ).
thf(f357,plain,
member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ zero_zero_nat ) ) ) @ pHoare259243666_exec1,
inference(rectify,[status(thm)],[f352]) ).
thf(f352,axiom,
member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ zero_zero_nat ) ) ) @ pHoare259243666_exec1,
file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_2) ).
thf(f1625,plain,
! [X0: list_com,X1: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ X0 @ X1 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) )
= X0 ) ),
inference(subsumption_resolution,[status(thm)],[f1617,f1217]) ).
thf(f1617,plain,
! [X0: list_com,X1: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ X0 @ X1 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) )
= X0 )
| ( ( b @ s )
!= $true ) ),
inference(superposition,[status(thm)],[f1289,f1301]) ).
thf(f1289,plain,
! [X2: state > $o,X3: com,X0: list_com,X1: list_com,X4: state,X5: state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) @ X4 ) @ ( produc1204172211_state @ X0 @ X5 ) ) @ pHoare259243666_exec1 )
!= $true )
| ( ( X2 @ X4 )
!= $true )
| ( ( cons_com @ X3 @ ( cons_com @ ( while @ X2 @ X3 ) @ X1 ) )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f996]) ).
thf(f1696,plain,
( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
!= ( produc1204172211_state @ a @ s ) ),
inference(subsumption_resolution,[status(thm)],[f1693,f1299]) ).
thf(f1299,plain,
! [X0: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ X0 ) @ ( f @ ( suc @ X0 ) ) ) @ pHoare259243666_exec1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f680]) ).
thf(f680,plain,
! [X0: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ X0 ) @ ( f @ ( suc @ X0 ) ) ) @ pHoare259243666_exec1 )
= $true ),
inference(fool_elimination,[status(thm)],[f679]) ).
thf(f679,plain,
! [X0: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X0 ) @ ( f @ ( suc @ X0 ) ) ) @ pHoare259243666_exec1 ),
inference(rectify,[status(thm)],[f351]) ).
thf(f351,axiom,
! [X60: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X60 ) @ ( f @ ( suc @ X60 ) ) ) @ pHoare259243666_exec1 ),
file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_1) ).
thf(f1693,plain,
( ( ( member1069318160_state
@ ( produc1909270103_state
@ ( f
@ ( suc
@ ( sK73
@ ^ [Y0: nat] : ( f @ ( suc @ Y0 ) ) ) ) )
@ ( f
@ ( suc
@ ( suc
@ ( sK73
@ ^ [Y0: nat] : ( f @ ( suc @ Y0 ) ) ) ) ) ) )
@ pHoare259243666_exec1 )
!= $true )
| ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
!= ( produc1204172211_state @ a @ s ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1688]) ).
thf(f1688,plain,
( ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
!= ( produc1204172211_state @ a @ s ) )
| ( ( member1069318160_state
@ ( produc1909270103_state
@ ( ^ [Y0: nat] :
( f
@ ( ^ [Y1: nat] :
( suc
@ ( ^ [Y2: nat] : Y2
@ Y1 ) )
@ Y0 ) )
@ ( sK73
@ ^ [Y0: nat] :
( f
@ ( ^ [Y1: nat] :
( suc
@ ( ^ [Y2: nat] : Y2
@ Y1 ) )
@ Y0 ) ) ) )
@ ( ^ [Y0: nat] :
( f
@ ( ^ [Y1: nat] :
( suc
@ ( ^ [Y2: nat] : Y2
@ Y1 ) )
@ Y0 ) )
@ ( suc
@ ( sK73
@ ^ [Y0: nat] :
( f
@ ( ^ [Y1: nat] :
( suc
@ ( ^ [Y2: nat] : Y2
@ Y1 ) )
@ Y0 ) ) ) ) ) )
@ pHoare259243666_exec1 )
!= $true ) ),
inference(superposition,[status(thm)],[f1216,f1631]) ).
thf(f1631,plain,
( ( f @ ( suc @ zero_zero_nat ) )
= ( produc1204172211_state @ a @ s ) ),
inference(backward_demodulation,[status(thm)],[f1233,f1630]) ).
thf(f1216,plain,
! [X0: nat > produc2041926651_state] :
( ( ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s )
!= ( X0 @ zero_zero_nat ) )
| ( ( member1069318160_state @ ( produc1909270103_state @ ( X0 @ ( sK73 @ X0 ) ) @ ( X0 @ ( suc @ ( sK73 @ X0 ) ) ) ) @ pHoare259243666_exec1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP143^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:27:44 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : ITP143^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.45 % Domain : Interactive Theorem Proving
% 0.19/0.45 % Problem : Sledgehammer PHoareTotal problem prob_402__3262836_1
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Des21]
% 0.19/0.45 % Names : PHoareTotal/prob_402__3262836_1 [Des21]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.82 v7.5.0
% 0.19/0.45 % Syntax : Number of formulae : 497 ( 165 unt; 143 typ; 0 def)
% 0.19/0.45 % Number of atoms : 909 ( 473 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.19/0.45 % Number of connectives : 4557 ( 201 ~; 23 |; 103 &;3731 @)
% 0.19/0.45 % ( 0 <=>; 499 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 22 ( 9 avg)
% 0.19/0.45 % Number of types : 37 ( 36 usr)
% 0.19/0.45 % Number of type conns : 417 ( 417 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 108 ( 107 usr; 11 con; 0-4 aty)
% 0.19/0.45 % Number of variables : 1477 ( 13 ^;1396 !; 68 ?;1477 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:28.516
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % Could-be-implicit typings (36)
% 0.19/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J_J,type,
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% 0.19/0.45 produc1519776487_state: $tType ).
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% 0.19/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.19/0.45 set_Pr2096893127_state: $tType ).
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% 0.19/0.45 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.19/0.45 produc186437863_state: $tType ).
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% 0.19/0.45 set_Pr135335153st_com: $tType ).
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% 0.19/0.45 produc392316135_state: $tType ).
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% 0.19/0.45 produc1440412305st_com: $tType ).
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% 0.19/0.45 set_Pr1142642759_state: $tType ).
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% 0.19/0.45 thf(ty_n_t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
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% 0.19/0.45 thf(ty_n_t__List__Olist_It__PLang__Ocom_J,type,
% 0.19/0.45 list_com: $tType ).
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% 0.19/0.45 thf(ty_n_t__PLang__Ocom,type,
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% 0.19/0.45 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.19/0.45 transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.19/0.45 transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.19/0.45 transi1042416958om_com: set_Pr1675528647om_com > set_Pr1675528647om_com ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.19/0.45 transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Wfrec_Osame__fst_001t__List__Olist_It__PLang__Ocom_J_001t__PLang__Ostate,type,
% 0.19/0.45 same_f855297288_state: ( list_com > $o ) > ( list_com > set_Pr795498619_state ) > set_Pr1165141447_state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Wfrec_Osame__fst_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.19/0.45 same_f1258458156_state: ( produc2041926651_state > $o ) > ( produc2041926651_state > set_Pr1165141447_state ) > set_Pr2096893127_state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Nat__Onat,type,
% 0.19/0.45 member_nat: nat > set_nat > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__PLang__Ostate,type,
% 0.19/0.45 member_state: state > set_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.19/0.45 member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.19/0.45 member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.19/0.45 member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.19/0.45 member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.19/0.45 member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.19/0.45 member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.19/0.45 member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.19/0.45 member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.19/0.45 member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.19/0.45 member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.19/0.45 member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_Mt__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J,type,
% 0.19/0.45 member2105207824om_com: produc1065433319om_com > set_Pr1675528647om_com > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.19/0.45 member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_a,type,
% 0.19/0.45 a: list_com ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_b,type,
% 0.19/0.45 b: state > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_ba,type,
% 0.19/0.45 ba: state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_c,type,
% 0.19/0.45 c: com ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_cs,type,
% 0.19/0.45 cs: list_com ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_f,type,
% 0.19/0.45 f: nat > produc2041926651_state ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_s,type,
% 0.19/0.45 s: state ).
% 0.19/0.45
% 0.19/0.45 % Relevant facts (349)
% 0.19/0.45 thf(fact_0_exec1E_I5_J,axiom,
% 0.19/0.45 ! [B: state > $o,C: com,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.19/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.19/0.45 => ( ( ( Cs2 = Cs )
% 0.19/0.45 => ( ( S2 = S )
% 0.19/0.45 => ( B @ S ) ) )
% 0.19/0.45 => ~ ( ( Cs2
% 0.19/0.45 = ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs ) ) )
% 0.19/0.45 => ( ( S2 = S )
% 0.19/0.45 => ~ ( B @ S ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % exec1E(5)
% 0.19/0.45 thf(fact_1_exec1_OWhileTrue,axiom,
% 0.19/0.45 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.19/0.45 ( ( B @ S )
% 0.19/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % exec1.WhileTrue
% 0.19/0.45 thf(fact_2_exec1_OWhileFalse,axiom,
% 0.19/0.45 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.19/0.45 ( ~ ( B @ S )
% 0.19/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1.WhileFalse
% 0.19/0.46 thf(fact_3_inf__def,axiom,
% 0.19/0.46 ( pHoare2126160787le_inf
% 0.19/0.46 = ( ^ [Cs3: list_com,S3: state] :
% 0.19/0.46 ? [F: nat > produc2041926651_state] :
% 0.19/0.46 ( ( ( F @ zero_zero_nat )
% 0.19/0.46 = ( produc1204172211_state @ Cs3 @ S3 ) )
% 0.19/0.46 & ! [I: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ pHoare259243666_exec1 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % inf_def
% 0.19/0.46 thf(fact_4_com_Oinject_I4_J,axiom,
% 0.19/0.46 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.19/0.46 ( ( ( while @ X41 @ X42 )
% 0.19/0.46 = ( while @ Y41 @ Y42 ) )
% 0.19/0.46 = ( ( X41 = Y41 )
% 0.19/0.46 & ( X42 = Y42 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.inject(4)
% 0.19/0.46 thf(fact_5_nat_Oinject,axiom,
% 0.19/0.46 ! [X2: nat,Y2: nat] :
% 0.19/0.46 ( ( ( suc @ X2 )
% 0.19/0.46 = ( suc @ Y2 ) )
% 0.19/0.46 = ( X2 = Y2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat.inject
% 0.19/0.46 thf(fact_6_old_Onat_Oinject,axiom,
% 0.19/0.46 ! [Nat: nat,Nat2: nat] :
% 0.19/0.46 ( ( ( suc @ Nat )
% 0.19/0.46 = ( suc @ Nat2 ) )
% 0.19/0.46 = ( Nat = Nat2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.inject
% 0.19/0.46 thf(fact_7_list_Oinject,axiom,
% 0.19/0.46 ! [X21: list_com,X22: list_list_com,Y21: list_com,Y22: list_list_com] :
% 0.19/0.46 ( ( ( cons_list_com @ X21 @ X22 )
% 0.19/0.46 = ( cons_list_com @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inject
% 0.19/0.46 thf(fact_8_list_Oinject,axiom,
% 0.19/0.46 ! [X21: produc2041926651_state,X22: list_P1040014977_state,Y21: produc2041926651_state,Y22: list_P1040014977_state] :
% 0.19/0.46 ( ( ( cons_P465369265_state @ X21 @ X22 )
% 0.19/0.46 = ( cons_P465369265_state @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inject
% 0.19/0.46 thf(fact_9_list_Oinject,axiom,
% 0.19/0.46 ! [X21: state,X22: list_state,Y21: state,Y22: list_state] :
% 0.19/0.46 ( ( ( cons_state @ X21 @ X22 )
% 0.19/0.46 = ( cons_state @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inject
% 0.19/0.46 thf(fact_10_list_Oinject,axiom,
% 0.19/0.46 ! [X21: com,X22: list_com,Y21: com,Y22: list_com] :
% 0.19/0.46 ( ( ( cons_com @ X21 @ X22 )
% 0.19/0.46 = ( cons_com @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inject
% 0.19/0.46 thf(fact_11_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: com,X2: com,Y1: com,Y2: com] :
% 0.19/0.46 ( ( ( product_Pair_com_com @ X1 @ X2 )
% 0.19/0.46 = ( product_Pair_com_com @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_12_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,Y1: list_P1040014977_state,Y2: list_P1040014977_state] :
% 0.19/0.46 ( ( ( produc1298457559_state @ X1 @ X2 )
% 0.19/0.46 = ( produc1298457559_state @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_13_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: list_com,X2: list_com,Y1: list_com,Y2: list_com] :
% 0.19/0.46 ( ( ( produc1307105171st_com @ X1 @ X2 )
% 0.19/0.46 = ( produc1307105171st_com @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_14_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: list_list_com,X2: list_state,Y1: list_list_com,Y2: list_state] :
% 0.19/0.46 ( ( ( produc1742567891_state @ X1 @ X2 )
% 0.19/0.46 = ( produc1742567891_state @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_15_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: com > com > $o,X2: list_com,Y1: com > com > $o,Y2: list_com] :
% 0.19/0.46 ( ( ( produc1914379986st_com @ X1 @ X2 )
% 0.19/0.46 = ( produc1914379986st_com @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_16_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: list_com,X2: state,Y1: list_com,Y2: state] :
% 0.19/0.46 ( ( ( produc1204172211_state @ X1 @ X2 )
% 0.19/0.46 = ( produc1204172211_state @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_17_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y2: produc2041926651_state] :
% 0.19/0.46 ( ( ( produc1909270103_state @ X1 @ X2 )
% 0.19/0.46 = ( produc1909270103_state @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_18_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: com,B: com,A2: com,B2: com] :
% 0.19/0.46 ( ( ( product_Pair_com_com @ A @ B )
% 0.19/0.46 = ( product_Pair_com_com @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_19_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: list_P1040014977_state,B: list_P1040014977_state,A2: list_P1040014977_state,B2: list_P1040014977_state] :
% 0.19/0.46 ( ( ( produc1298457559_state @ A @ B )
% 0.19/0.46 = ( produc1298457559_state @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_20_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: list_com,B: list_com,A2: list_com,B2: list_com] :
% 0.19/0.46 ( ( ( produc1307105171st_com @ A @ B )
% 0.19/0.46 = ( produc1307105171st_com @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_21_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: list_list_com,B: list_state,A2: list_list_com,B2: list_state] :
% 0.19/0.46 ( ( ( produc1742567891_state @ A @ B )
% 0.19/0.46 = ( produc1742567891_state @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_22_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: com > com > $o,B: list_com,A2: com > com > $o,B2: list_com] :
% 0.19/0.46 ( ( ( produc1914379986st_com @ A @ B )
% 0.19/0.46 = ( produc1914379986st_com @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_23_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: list_com,B: state,A2: list_com,B2: state] :
% 0.19/0.46 ( ( ( produc1204172211_state @ A @ B )
% 0.19/0.46 = ( produc1204172211_state @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_24_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.19/0.46 ( ( ( produc1909270103_state @ A @ B )
% 0.19/0.46 = ( produc1909270103_state @ A2 @ B2 ) )
% 0.19/0.46 = ( ( A = A2 )
% 0.19/0.46 & ( B = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_25_exec1__pres__termis,axiom,
% 0.19/0.46 ! [Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.19/0.46 => ( ( pHoare806997636termis @ Cs @ S )
% 0.19/0.46 => ( pHoare806997636termis @ Cs2 @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1_pres_termis
% 0.19/0.46 thf(fact_26_prod__cases3,axiom,
% 0.19/0.46 ! [Y: produc410756839_state] :
% 0.19/0.46 ~ ! [A3: produc2041926651_state,B3: list_com,C2: state] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1909270103_state @ A3 @ ( produc1204172211_state @ B3 @ C2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases3
% 0.19/0.46 thf(fact_27_zero__reorient,axiom,
% 0.19/0.46 ! [X: nat] :
% 0.19/0.46 ( ( zero_zero_nat = X )
% 0.19/0.46 = ( X = zero_zero_nat ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_reorient
% 0.19/0.46 thf(fact_28_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: product_prod_com_com > $o,Prod: product_prod_com_com] :
% 0.19/0.46 ( ! [A3: com,B3: com] : ( P @ ( product_Pair_com_com @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_29_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc1225889383_state > $o,Prod: produc1225889383_state] :
% 0.19/0.46 ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state] : ( P @ ( produc1298457559_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_30_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc258871771st_com > $o,Prod: produc258871771st_com] :
% 0.19/0.46 ( ! [A3: list_com,B3: list_com] : ( P @ ( produc1307105171st_com @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_31_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc1393453339_state > $o,Prod: produc1393453339_state] :
% 0.19/0.46 ( ! [A3: list_list_com,B3: list_state] : ( P @ ( produc1742567891_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_32_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc2058209240st_com > $o,Prod: produc2058209240st_com] :
% 0.19/0.46 ( ! [A3: com > com > $o,B3: list_com] : ( P @ ( produc1914379986st_com @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_33_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 0.19/0.46 ( ! [A3: list_com,B3: state] : ( P @ ( produc1204172211_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_34_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 0.19/0.46 ( ! [A3: produc2041926651_state,B3: produc2041926651_state] : ( P @ ( produc1909270103_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_35_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: product_prod_com_com] :
% 0.19/0.46 ~ ! [A3: com,B3: com] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( product_Pair_com_com @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_36_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc1225889383_state] :
% 0.19/0.46 ~ ! [A3: list_P1040014977_state,B3: list_P1040014977_state] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1298457559_state @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_37_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc258871771st_com] :
% 0.19/0.46 ~ ! [A3: list_com,B3: list_com] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1307105171st_com @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_38_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc1393453339_state] :
% 0.19/0.46 ~ ! [A3: list_list_com,B3: list_state] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1742567891_state @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_39_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc2058209240st_com] :
% 0.19/0.46 ~ ! [A3: com > com > $o,B3: list_com] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1914379986st_com @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_40_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc2041926651_state] :
% 0.19/0.46 ~ ! [A3: list_com,B3: state] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1204172211_state @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_41_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc410756839_state] :
% 0.19/0.46 ~ ! [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1909270103_state @ A3 @ B3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_42_Pair__inject,axiom,
% 0.19/0.46 ! [A: com,B: com,A2: com,B2: com] :
% 0.19/0.46 ( ( ( product_Pair_com_com @ A @ B )
% 0.19/0.46 = ( product_Pair_com_com @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_43_Pair__inject,axiom,
% 0.19/0.46 ! [A: list_P1040014977_state,B: list_P1040014977_state,A2: list_P1040014977_state,B2: list_P1040014977_state] :
% 0.19/0.46 ( ( ( produc1298457559_state @ A @ B )
% 0.19/0.46 = ( produc1298457559_state @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_44_Pair__inject,axiom,
% 0.19/0.46 ! [A: list_com,B: list_com,A2: list_com,B2: list_com] :
% 0.19/0.46 ( ( ( produc1307105171st_com @ A @ B )
% 0.19/0.46 = ( produc1307105171st_com @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_45_Pair__inject,axiom,
% 0.19/0.46 ! [A: list_list_com,B: list_state,A2: list_list_com,B2: list_state] :
% 0.19/0.46 ( ( ( produc1742567891_state @ A @ B )
% 0.19/0.46 = ( produc1742567891_state @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_46_Pair__inject,axiom,
% 0.19/0.46 ! [A: com > com > $o,B: list_com,A2: com > com > $o,B2: list_com] :
% 0.19/0.46 ( ( ( produc1914379986st_com @ A @ B )
% 0.19/0.46 = ( produc1914379986st_com @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_47_Pair__inject,axiom,
% 0.19/0.46 ! [A: list_com,B: state,A2: list_com,B2: state] :
% 0.19/0.46 ( ( ( produc1204172211_state @ A @ B )
% 0.19/0.46 = ( produc1204172211_state @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_48_Pair__inject,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.19/0.46 ( ( ( produc1909270103_state @ A @ B )
% 0.19/0.46 = ( produc1909270103_state @ A2 @ B2 ) )
% 0.19/0.46 => ~ ( ( A = A2 )
% 0.19/0.46 => ( B != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_49_prod__cases,axiom,
% 0.19/0.46 ! [P: product_prod_com_com > $o,P2: product_prod_com_com] :
% 0.19/0.46 ( ! [A3: com,B3: com] : ( P @ ( product_Pair_com_com @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_50_prod__cases,axiom,
% 0.19/0.46 ! [P: produc1225889383_state > $o,P2: produc1225889383_state] :
% 0.19/0.46 ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state] : ( P @ ( produc1298457559_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_51_prod__cases,axiom,
% 0.19/0.46 ! [P: produc258871771st_com > $o,P2: produc258871771st_com] :
% 0.19/0.46 ( ! [A3: list_com,B3: list_com] : ( P @ ( produc1307105171st_com @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_52_prod__cases,axiom,
% 0.19/0.46 ! [P: produc1393453339_state > $o,P2: produc1393453339_state] :
% 0.19/0.46 ( ! [A3: list_list_com,B3: list_state] : ( P @ ( produc1742567891_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_53_prod__cases,axiom,
% 0.19/0.46 ! [P: produc2058209240st_com > $o,P2: produc2058209240st_com] :
% 0.19/0.46 ( ! [A3: com > com > $o,B3: list_com] : ( P @ ( produc1914379986st_com @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_54_prod__cases,axiom,
% 0.19/0.46 ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 0.19/0.46 ( ! [A3: list_com,B3: state] : ( P @ ( produc1204172211_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_55_prod__cases,axiom,
% 0.19/0.46 ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 0.19/0.46 ( ! [A3: produc2041926651_state,B3: produc2041926651_state] : ( P @ ( produc1909270103_state @ A3 @ B3 ) )
% 0.19/0.46 => ( P @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_56_surj__pair,axiom,
% 0.19/0.46 ! [P2: product_prod_com_com] :
% 0.19/0.46 ? [X3: com,Y3: com] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( product_Pair_com_com @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_57_surj__pair,axiom,
% 0.19/0.46 ! [P2: produc1225889383_state] :
% 0.19/0.46 ? [X3: list_P1040014977_state,Y3: list_P1040014977_state] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( produc1298457559_state @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_58_surj__pair,axiom,
% 0.19/0.46 ! [P2: produc258871771st_com] :
% 0.19/0.46 ? [X3: list_com,Y3: list_com] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( produc1307105171st_com @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_59_surj__pair,axiom,
% 0.19/0.46 ! [P2: produc1393453339_state] :
% 0.19/0.46 ? [X3: list_list_com,Y3: list_state] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( produc1742567891_state @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_60_surj__pair,axiom,
% 0.19/0.46 ! [P2: produc2058209240st_com] :
% 0.19/0.46 ? [X3: com > com > $o,Y3: list_com] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( produc1914379986st_com @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_61_surj__pair,axiom,
% 0.19/0.46 ! [P2: produc2041926651_state] :
% 0.19/0.46 ? [X3: list_com,Y3: state] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( produc1204172211_state @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_62_surj__pair,axiom,
% 0.19/0.46 ! [P2: produc410756839_state] :
% 0.19/0.46 ? [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.19/0.46 ( P2
% 0.19/0.46 = ( produc1909270103_state @ X3 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_63_not__Cons__self2,axiom,
% 0.19/0.46 ! [X: list_com,Xs: list_list_com] :
% 0.19/0.46 ( ( cons_list_com @ X @ Xs )
% 0.19/0.46 != Xs ) ).
% 0.19/0.46
% 0.19/0.46 % not_Cons_self2
% 0.19/0.46 thf(fact_64_not__Cons__self2,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.19/0.46 ( ( cons_P465369265_state @ X @ Xs )
% 0.19/0.46 != Xs ) ).
% 0.19/0.46
% 0.19/0.46 % not_Cons_self2
% 0.19/0.46 thf(fact_65_not__Cons__self2,axiom,
% 0.19/0.46 ! [X: state,Xs: list_state] :
% 0.19/0.46 ( ( cons_state @ X @ Xs )
% 0.19/0.46 != Xs ) ).
% 0.19/0.46
% 0.19/0.46 % not_Cons_self2
% 0.19/0.46 thf(fact_66_not__Cons__self2,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com] :
% 0.19/0.46 ( ( cons_com @ X @ Xs )
% 0.19/0.46 != Xs ) ).
% 0.19/0.46
% 0.19/0.46 % not_Cons_self2
% 0.19/0.46 thf(fact_67_n__not__Suc__n,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( N
% 0.19/0.46 != ( suc @ N ) ) ).
% 0.19/0.46
% 0.19/0.46 % n_not_Suc_n
% 0.19/0.46 thf(fact_68_Suc__inject,axiom,
% 0.19/0.46 ! [X: nat,Y: nat] :
% 0.19/0.46 ( ( ( suc @ X )
% 0.19/0.46 = ( suc @ Y ) )
% 0.19/0.46 => ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_inject
% 0.19/0.46 thf(fact_69_not0__implies__Suc,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( ( N != zero_zero_nat )
% 0.19/0.46 => ? [M: nat] :
% 0.19/0.46 ( N
% 0.19/0.46 = ( suc @ M ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not0_implies_Suc
% 0.19/0.46 thf(fact_70_old_Onat_Oinducts,axiom,
% 0.19/0.46 ! [P: nat > $o,Nat: nat] :
% 0.19/0.46 ( ( P @ zero_zero_nat )
% 0.19/0.46 => ( ! [Nat3: nat] :
% 0.19/0.46 ( ( P @ Nat3 )
% 0.19/0.46 => ( P @ ( suc @ Nat3 ) ) )
% 0.19/0.46 => ( P @ Nat ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.inducts
% 0.19/0.46 thf(fact_71_old_Onat_Oexhaust,axiom,
% 0.19/0.46 ! [Y: nat] :
% 0.19/0.46 ( ( Y != zero_zero_nat )
% 0.19/0.46 => ~ ! [Nat3: nat] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.exhaust
% 0.19/0.46 thf(fact_72_Zero__not__Suc,axiom,
% 0.19/0.46 ! [M2: nat] :
% 0.19/0.46 ( zero_zero_nat
% 0.19/0.46 != ( suc @ M2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Zero_not_Suc
% 0.19/0.46 thf(fact_73_Zero__neq__Suc,axiom,
% 0.19/0.46 ! [M2: nat] :
% 0.19/0.46 ( zero_zero_nat
% 0.19/0.46 != ( suc @ M2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Zero_neq_Suc
% 0.19/0.46 thf(fact_74_Suc__neq__Zero,axiom,
% 0.19/0.46 ! [M2: nat] :
% 0.19/0.46 ( ( suc @ M2 )
% 0.19/0.46 != zero_zero_nat ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_neq_Zero
% 0.19/0.46 thf(fact_75_zero__induct,axiom,
% 0.19/0.46 ! [P: nat > $o,K: nat] :
% 0.19/0.46 ( ( P @ K )
% 0.19/0.46 => ( ! [N2: nat] :
% 0.19/0.46 ( ( P @ ( suc @ N2 ) )
% 0.19/0.46 => ( P @ N2 ) )
% 0.19/0.46 => ( P @ zero_zero_nat ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_induct
% 0.19/0.46 thf(fact_76_diff__induct,axiom,
% 0.19/0.46 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 0.19/0.46 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.19/0.46 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.19/0.46 => ( ! [X3: nat,Y3: nat] :
% 0.19/0.46 ( ( P @ X3 @ Y3 )
% 0.19/0.46 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.19/0.46 => ( P @ M2 @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_induct
% 0.19/0.46 thf(fact_77_nat__induct,axiom,
% 0.19/0.46 ! [P: nat > $o,N: nat] :
% 0.19/0.46 ( ( P @ zero_zero_nat )
% 0.19/0.46 => ( ! [N2: nat] :
% 0.19/0.46 ( ( P @ N2 )
% 0.19/0.46 => ( P @ ( suc @ N2 ) ) )
% 0.19/0.46 => ( P @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat_induct
% 0.19/0.46 thf(fact_78_nat_OdiscI,axiom,
% 0.19/0.46 ! [Nat: nat,X2: nat] :
% 0.19/0.46 ( ( Nat
% 0.19/0.46 = ( suc @ X2 ) )
% 0.19/0.46 => ( Nat != zero_zero_nat ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat.discI
% 0.19/0.46 thf(fact_79_old_Onat_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [Nat2: nat] :
% 0.19/0.46 ( zero_zero_nat
% 0.19/0.46 != ( suc @ Nat2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.distinct(1)
% 0.19/0.46 thf(fact_80_old_Onat_Odistinct_I2_J,axiom,
% 0.19/0.46 ! [Nat2: nat] :
% 0.19/0.46 ( ( suc @ Nat2 )
% 0.19/0.46 != zero_zero_nat ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.distinct(2)
% 0.19/0.46 thf(fact_81_nat_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X2: nat] :
% 0.19/0.46 ( zero_zero_nat
% 0.19/0.46 != ( suc @ X2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat.distinct(1)
% 0.19/0.46 thf(fact_82_prod__induct3,axiom,
% 0.19/0.46 ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 0.19/0.46 ( ! [A3: produc2041926651_state,B3: list_com,C2: state] : ( P @ ( produc1909270103_state @ A3 @ ( produc1204172211_state @ B3 @ C2 ) ) )
% 0.19/0.46 => ( P @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_induct3
% 0.19/0.46 thf(fact_83_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: produc1225889383_state,P: produc1225889383_state > $o] :
% 0.19/0.46 ( ( member1267359376_state @ A @ ( collec183560402_state @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_84_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,P: produc2041926651_state > $o] :
% 0.19/0.46 ( ( member64234660_state @ A @ ( collec1409185766_state @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_85_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: produc258871771st_com,P: produc258871771st_com > $o] :
% 0.19/0.46 ( ( member32358020st_com @ A @ ( collec328862150st_com @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_86_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: produc1393453339_state,P: produc1393453339_state > $o] :
% 0.19/0.46 ( ( member1442949316_state @ A @ ( collec924674566_state @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_87_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: nat,P: nat > $o] :
% 0.19/0.46 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_88_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: produc410756839_state,P: produc410756839_state > $o] :
% 0.19/0.46 ( ( member1069318160_state @ A @ ( collec300063826_state @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_89_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: state,P: state > $o] :
% 0.19/0.46 ( ( member_state @ A @ ( collect_state @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_90_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_Pr1142642759_state] :
% 0.19/0.46 ( ( collec183560402_state
% 0.19/0.46 @ ^ [X4: produc1225889383_state] : ( member1267359376_state @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_91_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_Pr849496667_state] :
% 0.19/0.46 ( ( collec1409185766_state
% 0.19/0.46 @ ^ [X4: produc2041926651_state] : ( member64234660_state @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_92_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_Pr602326075st_com] :
% 0.19/0.46 ( ( collec328862150st_com
% 0.19/0.46 @ ^ [X4: produc258871771st_com] : ( member32358020st_com @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_93_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_Pr391631483_state] :
% 0.19/0.46 ( ( collec924674566_state
% 0.19/0.46 @ ^ [X4: produc1393453339_state] : ( member1442949316_state @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_94_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_nat] :
% 0.19/0.46 ( ( collect_nat
% 0.19/0.46 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_95_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_Pr1165141447_state] :
% 0.19/0.46 ( ( collec300063826_state
% 0.19/0.46 @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_96_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A4: set_state] :
% 0.19/0.46 ( ( collect_state
% 0.19/0.46 @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_97_Collect__cong,axiom,
% 0.19/0.46 ! [P: state > $o,Q: state > $o] :
% 0.19/0.46 ( ! [X3: state] :
% 0.19/0.46 ( ( P @ X3 )
% 0.19/0.46 = ( Q @ X3 ) )
% 0.19/0.46 => ( ( collect_state @ P )
% 0.19/0.46 = ( collect_state @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_cong
% 0.19/0.46 thf(fact_98_Collect__cong,axiom,
% 0.19/0.46 ! [P: produc410756839_state > $o,Q: produc410756839_state > $o] :
% 0.19/0.46 ( ! [X3: produc410756839_state] :
% 0.19/0.46 ( ( P @ X3 )
% 0.19/0.46 = ( Q @ X3 ) )
% 0.19/0.46 => ( ( collec300063826_state @ P )
% 0.19/0.46 = ( collec300063826_state @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_cong
% 0.19/0.46 thf(fact_99_exec1_OSemi,axiom,
% 0.19/0.46 ! [C1: com,C22: com,Cs: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 0.19/0.46
% 0.19/0.46 % exec1.Semi
% 0.19/0.46 thf(fact_100_exec1E_I3_J,axiom,
% 0.19/0.46 ! [C1: com,C22: com,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.19/0.46 => ~ ( ( Cs2
% 0.19/0.46 = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs ) ) )
% 0.19/0.46 => ( S2 != S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1E(3)
% 0.19/0.46 thf(fact_101_exec1_ODo,axiom,
% 0.19/0.46 ! [T: state,F2: state > set_state,S: state,Cs: list_com] :
% 0.19/0.46 ( ( member_state @ T @ ( F2 @ S ) )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs @ T ) ) @ pHoare259243666_exec1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1.Do
% 0.19/0.46 thf(fact_102_exec1E_I2_J,axiom,
% 0.19/0.46 ! [F2: state > set_state,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.19/0.46 => ~ ( ( Cs2 = Cs )
% 0.19/0.46 => ~ ( member_state @ S2 @ ( F2 @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1E(2)
% 0.19/0.46 thf(fact_103_exec1_OIfFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1.IfFalse
% 0.19/0.46 thf(fact_104_exec1_OIfTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1.IfTrue
% 0.19/0.46 thf(fact_105_exec1E_I4_J,axiom,
% 0.19/0.46 ! [B: state > $o,C1: com,C22: com,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.19/0.46 => ( ( ( Cs2
% 0.19/0.46 = ( cons_com @ C1 @ Cs ) )
% 0.19/0.46 => ( ( S2 = S )
% 0.19/0.46 => ~ ( B @ S ) ) )
% 0.19/0.46 => ~ ( ( Cs2
% 0.19/0.46 = ( cons_com @ C22 @ Cs ) )
% 0.19/0.46 => ( ( S2 = S )
% 0.19/0.46 => ( B @ S ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1E(4)
% 0.19/0.46 thf(fact_106_gen__length__code_I2_J,axiom,
% 0.19/0.46 ! [N: nat,X: list_com,Xs: list_list_com] :
% 0.19/0.46 ( ( gen_length_list_com @ N @ ( cons_list_com @ X @ Xs ) )
% 0.19/0.46 = ( gen_length_list_com @ ( suc @ N ) @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % gen_length_code(2)
% 0.19/0.46 thf(fact_107_gen__length__code_I2_J,axiom,
% 0.19/0.46 ! [N: nat,X: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.19/0.46 ( ( gen_le1266608782_state @ N @ ( cons_P465369265_state @ X @ Xs ) )
% 0.19/0.46 = ( gen_le1266608782_state @ ( suc @ N ) @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % gen_length_code(2)
% 0.19/0.46 thf(fact_108_gen__length__code_I2_J,axiom,
% 0.19/0.46 ! [N: nat,X: state,Xs: list_state] :
% 0.19/0.46 ( ( gen_length_state @ N @ ( cons_state @ X @ Xs ) )
% 0.19/0.46 = ( gen_length_state @ ( suc @ N ) @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % gen_length_code(2)
% 0.19/0.46 thf(fact_109_gen__length__code_I2_J,axiom,
% 0.19/0.46 ! [N: nat,X: com,Xs: list_com] :
% 0.19/0.46 ( ( gen_length_com @ N @ ( cons_com @ X @ Xs ) )
% 0.19/0.46 = ( gen_length_com @ ( suc @ N ) @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % gen_length_code(2)
% 0.19/0.46 thf(fact_110_com_Oinject_I3_J,axiom,
% 0.19/0.46 ! [X31: state > $o,X32: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 0.19/0.46 ( ( ( cond @ X31 @ X32 @ X33 )
% 0.19/0.46 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 0.19/0.46 = ( ( X31 = Y31 )
% 0.19/0.46 & ( X32 = Y32 )
% 0.19/0.46 & ( X33 = Y33 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.inject(3)
% 0.19/0.46 thf(fact_111_com_Oinject_I1_J,axiom,
% 0.19/0.46 ! [X1: state > set_state,Y1: state > set_state] :
% 0.19/0.46 ( ( ( do @ X1 )
% 0.19/0.46 = ( do @ Y1 ) )
% 0.19/0.46 = ( X1 = Y1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.inject(1)
% 0.19/0.46 thf(fact_112_com_Oinject_I2_J,axiom,
% 0.19/0.46 ! [X21: com,X22: com,Y21: com,Y22: com] :
% 0.19/0.46 ( ( ( semi @ X21 @ X22 )
% 0.19/0.46 = ( semi @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.inject(2)
% 0.19/0.46 thf(fact_113_com_Odistinct_I11_J,axiom,
% 0.19/0.46 ! [X21: com,X22: com,X31: state > $o,X32: com,X33: com] :
% 0.19/0.46 ( ( semi @ X21 @ X22 )
% 0.19/0.46 != ( cond @ X31 @ X32 @ X33 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.distinct(11)
% 0.19/0.46 thf(fact_114_com_Odistinct_I3_J,axiom,
% 0.19/0.46 ! [X1: state > set_state,X31: state > $o,X32: com,X33: com] :
% 0.19/0.46 ( ( do @ X1 )
% 0.19/0.46 != ( cond @ X31 @ X32 @ X33 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.distinct(3)
% 0.19/0.46 thf(fact_115_com_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X1: state > set_state,X21: com,X22: com] :
% 0.19/0.46 ( ( do @ X1 )
% 0.19/0.46 != ( semi @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.distinct(1)
% 0.19/0.46 thf(fact_116_com_Odistinct_I19_J,axiom,
% 0.19/0.46 ! [X31: state > $o,X32: com,X33: com,X41: state > $o,X42: com] :
% 0.19/0.46 ( ( cond @ X31 @ X32 @ X33 )
% 0.19/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.distinct(19)
% 0.19/0.46 thf(fact_117_com_Odistinct_I5_J,axiom,
% 0.19/0.46 ! [X1: state > set_state,X41: state > $o,X42: com] :
% 0.19/0.46 ( ( do @ X1 )
% 0.19/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.distinct(5)
% 0.19/0.46 thf(fact_118_com_Odistinct_I13_J,axiom,
% 0.19/0.46 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 0.19/0.46 ( ( semi @ X21 @ X22 )
% 0.19/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % com.distinct(13)
% 0.19/0.46 thf(fact_119_execs__pres__termis,axiom,
% 0.19/0.46 ! [Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.19/0.46 => ( ( pHoare806997636termis @ Cs @ S )
% 0.19/0.46 => ( pHoare806997636termis @ Cs2 @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % execs_pres_termis
% 0.19/0.46 thf(fact_120_exec1p_OSemi,axiom,
% 0.19/0.46 ! [C1: com,C22: com,Cs: list_com,S: state] : ( pHoare202237534exec1p @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs ) @ S @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs ) ) @ S ) ).
% 0.19/0.46
% 0.19/0.46 % exec1p.Semi
% 0.19/0.46 thf(fact_121_exec1p_ODo,axiom,
% 0.19/0.46 ! [T: state,F2: state > set_state,S: state,Cs: list_com] :
% 0.19/0.46 ( ( member_state @ T @ ( F2 @ S ) )
% 0.19/0.46 => ( pHoare202237534exec1p @ ( cons_com @ ( do @ F2 ) @ Cs ) @ S @ Cs @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1p.Do
% 0.19/0.46 thf(fact_122_exec1p_OIfTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( pHoare202237534exec1p @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S @ ( cons_com @ C1 @ Cs ) @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1p.IfTrue
% 0.19/0.46 thf(fact_123_exec1p_OIfFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( pHoare202237534exec1p @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S @ ( cons_com @ C22 @ Cs ) @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1p.IfFalse
% 0.19/0.46 thf(fact_124_exec1p_OWhileTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( pHoare202237534exec1p @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S @ ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs ) ) @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1p.WhileTrue
% 0.19/0.46 thf(fact_125_renumber__aux,axiom,
% 0.19/0.46 ! [A: produc410756839_state,F2: nat > produc410756839_state,R: set_Pr2096893127_state,B: produc410756839_state] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F2 @ I2 ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 & ( member512523024_state @ ( produc2065881943_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 => ( ( B
% 0.19/0.46 = ( F2 @ zero_zero_nat ) )
% 0.19/0.46 => ? [F3: nat > produc410756839_state] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member512523024_state @ ( produc2065881943_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber_aux
% 0.19/0.46 thf(fact_126_renumber__aux,axiom,
% 0.19/0.46 ! [A: list_com,F2: nat > list_com,R: set_Pr602326075st_com,B: list_com] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ A @ ( F2 @ I2 ) ) @ ( transi436345274st_com @ R ) )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ A @ B ) @ ( transi436345274st_com @ R ) )
% 0.19/0.46 => ( ( B
% 0.19/0.46 = ( F2 @ zero_zero_nat ) )
% 0.19/0.46 => ? [F3: nat > list_com] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member32358020st_com @ ( produc1307105171st_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber_aux
% 0.19/0.46 thf(fact_127_renumber__aux,axiom,
% 0.19/0.46 ! [A: list_P1040014977_state,F2: nat > list_P1040014977_state,R: set_Pr1142642759_state,B: list_P1040014977_state] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ A @ ( F2 @ I2 ) ) @ ( transi339813252_state @ R ) )
% 0.19/0.46 & ( member1267359376_state @ ( produc1298457559_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ A @ B ) @ ( transi339813252_state @ R ) )
% 0.19/0.46 => ( ( B
% 0.19/0.46 = ( F2 @ zero_zero_nat ) )
% 0.19/0.46 => ? [F3: nat > list_P1040014977_state] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member1267359376_state @ ( produc1298457559_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber_aux
% 0.19/0.46 thf(fact_128_renumber__aux,axiom,
% 0.19/0.46 ! [A: com,F2: nat > com,R: set_Pr1822651163om_com,B: com] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ ( F2 @ I2 ) ) @ ( transi863150634cl_com @ R ) )
% 0.19/0.46 & ( member1333916004om_com @ ( product_Pair_com_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ ( transi863150634cl_com @ R ) )
% 0.19/0.46 => ( ( B
% 0.19/0.46 = ( F2 @ zero_zero_nat ) )
% 0.19/0.46 => ? [F3: nat > com] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member1333916004om_com @ ( product_Pair_com_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber_aux
% 0.19/0.46 thf(fact_129_renumber__aux,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,F2: nat > produc2041926651_state,R: set_Pr1165141447_state,B: produc2041926651_state] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ ( F2 @ I2 ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 & ( member1069318160_state @ ( produc1909270103_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( B
% 0.19/0.46 = ( F2 @ zero_zero_nat ) )
% 0.19/0.46 => ? [F3: nat > produc2041926651_state] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber_aux
% 0.19/0.46 thf(fact_130_renumber,axiom,
% 0.19/0.46 ! [A: produc410756839_state,F2: nat > produc410756839_state,R: set_Pr2096893127_state] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F2 @ I2 ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 & ( member512523024_state @ ( produc2065881943_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ? [F3: nat > produc410756839_state] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member512523024_state @ ( produc2065881943_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber
% 0.19/0.46 thf(fact_131_renumber,axiom,
% 0.19/0.46 ! [A: list_com,F2: nat > list_com,R: set_Pr602326075st_com] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ A @ ( F2 @ I2 ) ) @ ( transi436345274st_com @ R ) )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ? [F3: nat > list_com] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member32358020st_com @ ( produc1307105171st_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber
% 0.19/0.46 thf(fact_132_renumber,axiom,
% 0.19/0.46 ! [A: list_P1040014977_state,F2: nat > list_P1040014977_state,R: set_Pr1142642759_state] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ A @ ( F2 @ I2 ) ) @ ( transi339813252_state @ R ) )
% 0.19/0.46 & ( member1267359376_state @ ( produc1298457559_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ? [F3: nat > list_P1040014977_state] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member1267359376_state @ ( produc1298457559_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber
% 0.19/0.46 thf(fact_133_renumber,axiom,
% 0.19/0.46 ! [A: com,F2: nat > com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ ( F2 @ I2 ) ) @ ( transi863150634cl_com @ R ) )
% 0.19/0.46 & ( member1333916004om_com @ ( product_Pair_com_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ? [F3: nat > com] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member1333916004om_com @ ( product_Pair_com_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber
% 0.19/0.46 thf(fact_134_renumber,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,F2: nat > produc2041926651_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ! [I2: nat] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ ( F2 @ I2 ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 & ( member1069318160_state @ ( produc1909270103_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.19/0.46 => ? [F3: nat > produc2041926651_state] :
% 0.19/0.46 ( ( ( F3 @ zero_zero_nat )
% 0.19/0.46 = A )
% 0.19/0.46 & ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renumber
% 0.19/0.46 thf(fact_135_exec1p_OWhileFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( pHoare202237534exec1p @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S @ Cs @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1p.WhileFalse
% 0.19/0.46 thf(fact_136_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: com,Ay: com,Bx: com,By: com,R: set_Pr1675528647om_com,P: com > com > $o] :
% 0.19/0.46 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Ax @ Ay ) @ ( product_Pair_com_com @ Bx @ By ) ) @ ( transi1042416958om_com @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: com,B3: com,Aa: com,Ba: com] :
% 0.19/0.46 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ A3 @ B3 ) @ ( product_Pair_com_com @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Aa @ Ba ) @ ( product_Pair_com_com @ Bx @ By ) ) @ ( transi1042416958om_com @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_137_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.19/0.46 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.19/0.46 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A3 @ B3 ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Aa @ Ba ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_138_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.19/0.46 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: list_com,B3: list_com,Aa: list_com,Ba: list_com] :
% 0.19/0.46 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A3 @ B3 ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Aa @ Ba ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_139_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.19/0.46 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: list_list_com,B3: list_state,Aa: list_list_com,Ba: list_state] :
% 0.19/0.46 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A3 @ B3 ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Aa @ Ba ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_140_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.19/0.46 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: com > com > $o,B3: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.19/0.46 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A3 @ B3 ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Aa @ Ba ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_141_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: produc2041926651_state,B3: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_142_converse__rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ Bx @ By )
% 0.19/0.46 => ( ! [A3: list_com,B3: state,Aa: list_com,Ba: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A3 @ B3 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ Aa @ Ba )
% 0.19/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.19/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct2
% 0.19/0.46 thf(fact_143_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: com,Xb: com,Za: com,Zb: com,R: set_Pr1675528647om_com] :
% 0.19/0.46 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Xa @ Xb ) @ ( product_Pair_com_com @ Za @ Zb ) ) @ ( transi1042416958om_com @ R ) )
% 0.19/0.46 => ( ( ( product_Pair_com_com @ Xa @ Xb )
% 0.19/0.46 != ( product_Pair_com_com @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: com,B3: com] :
% 0.19/0.46 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Xa @ Xb ) @ ( product_Pair_com_com @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ A3 @ B3 ) @ ( product_Pair_com_com @ Za @ Zb ) ) @ ( transi1042416958om_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_144_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: list_P1040014977_state,Xb: list_P1040014977_state,Za: list_P1040014977_state,Zb: list_P1040014977_state,R: set_Pr1847866567_state] :
% 0.19/0.46 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) )
% 0.19/0.46 => ( ( ( produc1298457559_state @ Xa @ Xb )
% 0.19/0.46 != ( produc1298457559_state @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: list_P1040014977_state,B3: list_P1040014977_state] :
% 0.19/0.46 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A3 @ B3 ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_145_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: list_com,Xb: list_com,Za: list_com,Zb: list_com,R: set_Pr2083163591st_com] :
% 0.19/0.46 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) )
% 0.19/0.46 => ( ( ( produc1307105171st_com @ Xa @ Xb )
% 0.19/0.46 != ( produc1307105171st_com @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: list_com,B3: list_com] :
% 0.19/0.46 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A3 @ B3 ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_146_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: list_list_com,Xb: list_state,Za: list_list_com,Zb: list_state,R: set_Pr1419004359_state] :
% 0.19/0.46 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) )
% 0.19/0.46 => ( ( ( produc1742567891_state @ Xa @ Xb )
% 0.19/0.46 != ( produc1742567891_state @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: list_list_com,B3: list_state] :
% 0.19/0.46 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A3 @ B3 ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_147_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: com > com > $o,Xb: list_com,Za: com > com > $o,Zb: list_com,R: set_Pr135335153st_com] :
% 0.19/0.46 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) )
% 0.19/0.46 => ( ( ( produc1914379986st_com @ Xa @ Xb )
% 0.19/0.46 != ( produc1914379986st_com @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: com > com > $o,B3: list_com] :
% 0.19/0.46 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A3 @ B3 ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_148_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 => ( ( ( produc1909270103_state @ Xa @ Xb )
% 0.19/0.46 != ( produc1909270103_state @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_149_converse__rtranclE2,axiom,
% 0.19/0.46 ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( ( produc1204172211_state @ Xa @ Xb )
% 0.19/0.46 != ( produc1204172211_state @ Za @ Zb ) )
% 0.19/0.46 => ~ ! [A3: list_com,B3: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A3 @ B3 ) ) @ R )
% 0.19/0.46 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A3 @ B3 ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE2
% 0.19/0.46 thf(fact_150_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: com,Ay: com,Bx: com,By: com,R: set_Pr1675528647om_com,P: com > com > $o] :
% 0.19/0.46 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Ax @ Ay ) @ ( product_Pair_com_com @ Bx @ By ) ) @ ( transi1042416958om_com @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: com,B3: com,Aa: com,Ba: com] :
% 0.19/0.46 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Ax @ Ay ) @ ( product_Pair_com_com @ A3 @ B3 ) ) @ ( transi1042416958om_com @ R ) )
% 0.19/0.46 => ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ A3 @ B3 ) @ ( product_Pair_com_com @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_151_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.19/0.46 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.19/0.46 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ A3 @ B3 ) ) @ ( transi1428749162_state @ R ) )
% 0.19/0.46 => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A3 @ B3 ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_152_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.19/0.46 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: list_com,B3: list_com,Aa: list_com,Ba: list_com] :
% 0.19/0.46 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ A3 @ B3 ) ) @ ( transi1782245470st_com @ R ) )
% 0.19/0.46 => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A3 @ B3 ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_153_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.19/0.46 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: list_list_com,B3: list_state,Aa: list_list_com,Ba: list_state] :
% 0.19/0.46 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ A3 @ B3 ) ) @ ( transi89280670_state @ R ) )
% 0.19/0.46 => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A3 @ B3 ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_154_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.19/0.46 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: com > com > $o,B3: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.19/0.46 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ A3 @ B3 ) ) @ ( transi1592315797st_com @ R ) )
% 0.19/0.46 => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A3 @ B3 ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_155_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: produc2041926651_state,B3: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.19/0.46 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A3 @ B3 ) ) @ ( transi463013610_state @ R ) )
% 0.19/0.46 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_156_rtrancl__induct2,axiom,
% 0.19/0.46 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ Ax @ Ay )
% 0.19/0.46 => ( ! [A3: list_com,B3: state,Aa: list_com,Ba: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A3 @ B3 ) ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A3 @ B3 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.19/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct2
% 0.19/0.46 thf(fact_157_rtrancl__idemp,axiom,
% 0.19/0.46 ! [R: set_Pr2096893127_state] :
% 0.19/0.46 ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 0.19/0.46 = ( transi463013610_state @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_idemp
% 0.19/0.46 thf(fact_158_rtrancl__idemp,axiom,
% 0.19/0.46 ! [R: set_Pr602326075st_com] :
% 0.19/0.46 ( ( transi436345274st_com @ ( transi436345274st_com @ R ) )
% 0.19/0.46 = ( transi436345274st_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_idemp
% 0.19/0.46 thf(fact_159_rtrancl__idemp,axiom,
% 0.19/0.46 ! [R: set_Pr1142642759_state] :
% 0.19/0.46 ( ( transi339813252_state @ ( transi339813252_state @ R ) )
% 0.19/0.46 = ( transi339813252_state @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_idemp
% 0.19/0.46 thf(fact_160_rtrancl__idemp,axiom,
% 0.19/0.46 ! [R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( transi863150634cl_com @ ( transi863150634cl_com @ R ) )
% 0.19/0.46 = ( transi863150634cl_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_idemp
% 0.19/0.46 thf(fact_161_rtrancl__idemp,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 0.19/0.46 = ( transi1302705790_state @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_idemp
% 0.19/0.46 thf(fact_162_r__into__rtrancl,axiom,
% 0.19/0.46 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 0.19/0.46 ( ( member512523024_state @ P2 @ R )
% 0.19/0.46 => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % r_into_rtrancl
% 0.19/0.46 thf(fact_163_r__into__rtrancl,axiom,
% 0.19/0.46 ! [P2: produc258871771st_com,R: set_Pr602326075st_com] :
% 0.19/0.46 ( ( member32358020st_com @ P2 @ R )
% 0.19/0.46 => ( member32358020st_com @ P2 @ ( transi436345274st_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % r_into_rtrancl
% 0.19/0.46 thf(fact_164_r__into__rtrancl,axiom,
% 0.19/0.46 ! [P2: produc1225889383_state,R: set_Pr1142642759_state] :
% 0.19/0.46 ( ( member1267359376_state @ P2 @ R )
% 0.19/0.46 => ( member1267359376_state @ P2 @ ( transi339813252_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % r_into_rtrancl
% 0.19/0.46 thf(fact_165_r__into__rtrancl,axiom,
% 0.19/0.46 ! [P2: product_prod_com_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member1333916004om_com @ P2 @ R )
% 0.19/0.46 => ( member1333916004om_com @ P2 @ ( transi863150634cl_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % r_into_rtrancl
% 0.19/0.46 thf(fact_166_r__into__rtrancl,axiom,
% 0.19/0.46 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1069318160_state @ P2 @ R )
% 0.19/0.46 => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % r_into_rtrancl
% 0.19/0.46 thf(fact_167_exec__impl__execs,axiom,
% 0.19/0.46 ! [S: state,C: com,S2: state,Cs: list_com] :
% 0.19/0.46 ( ( exec @ S @ C @ S2 )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec_impl_execs
% 0.19/0.46 thf(fact_168_exec_OWhileTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C: com,T: state,U: state] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( ( exec @ S @ C @ T )
% 0.19/0.46 => ( ( exec @ T @ ( while @ B @ C ) @ U )
% 0.19/0.46 => ( exec @ S @ ( while @ B @ C ) @ U ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec.WhileTrue
% 0.19/0.46 thf(fact_169_exec_OWhileFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C: com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( exec @ S @ ( while @ B @ C ) @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec.WhileFalse
% 0.19/0.46 thf(fact_170_exec_OIfTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C1: com,T: state,C22: com] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( ( exec @ S @ C1 @ T )
% 0.19/0.46 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec.IfTrue
% 0.19/0.46 thf(fact_171_exec_OIfFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C22: com,T: state,C1: com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( ( exec @ S @ C22 @ T )
% 0.19/0.46 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec.IfFalse
% 0.19/0.46 thf(fact_172_exec_ODo,axiom,
% 0.19/0.46 ! [T: state,F2: state > set_state,S: state] :
% 0.19/0.46 ( ( member_state @ T @ ( F2 @ S ) )
% 0.19/0.46 => ( exec @ S @ ( do @ F2 ) @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec.Do
% 0.19/0.46 thf(fact_173_exec_OSemi,axiom,
% 0.19/0.46 ! [S0: state,C1: com,S1: state,C22: com,S22: state] :
% 0.19/0.46 ( ( exec @ S0 @ C1 @ S1 )
% 0.19/0.46 => ( ( exec @ S1 @ C22 @ S22 )
% 0.19/0.46 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec.Semi
% 0.19/0.46 thf(fact_174_converse__rtrancl__into__rtrancl,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_into_rtrancl
% 0.19/0.46 thf(fact_175_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl.rtrancl_into_rtrancl
% 0.19/0.46 thf(fact_176_converse__rtrancl__induct,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ B )
% 0.19/0.46 => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ Z )
% 0.19/0.46 => ( P @ Y3 ) ) ) )
% 0.19/0.46 => ( P @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtrancl_induct
% 0.19/0.46 thf(fact_177_rtrancl_Ortrancl__refl,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ ( transi1302705790_state @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl.rtrancl_refl
% 0.19/0.46 thf(fact_178_converse__rtranclE,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( X != Z2 )
% 0.19/0.46 => ~ ! [Y3: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % converse_rtranclE
% 0.19/0.46 thf(fact_179_rtrancl_Oinducts,axiom,
% 0.19/0.46 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ! [A3: produc2041926651_state] : ( P @ A3 @ A3 )
% 0.19/0.46 => ( ! [A3: produc2041926651_state,B3: produc2041926651_state,C2: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ A3 @ B3 )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ B3 @ C2 ) @ R )
% 0.19/0.46 => ( P @ A3 @ C2 ) ) ) )
% 0.19/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl.inducts
% 0.19/0.46 thf(fact_180_rtrancl__induct,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( P @ A )
% 0.19/0.46 => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.19/0.46 => ( ( P @ Y3 )
% 0.19/0.46 => ( P @ Z ) ) ) )
% 0.19/0.46 => ( P @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_induct
% 0.19/0.46 thf(fact_181_rtrancl__trans,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_trans
% 0.19/0.46 thf(fact_182_rtrancl_Osimps,axiom,
% 0.19/0.46 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 = ( ? [A5: produc2041926651_state] :
% 0.19/0.46 ( ( A1 = A5 )
% 0.19/0.46 & ( A22 = A5 ) )
% 0.19/0.46 | ? [A5: produc2041926651_state,B4: produc2041926651_state,C3: produc2041926651_state] :
% 0.19/0.46 ( ( A1 = A5 )
% 0.19/0.46 & ( A22 = C3 )
% 0.19/0.46 & ( member1069318160_state @ ( produc1909270103_state @ A5 @ B4 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 & ( member1069318160_state @ ( produc1909270103_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl.simps
% 0.19/0.46 thf(fact_183_rtrancl_Ocases,axiom,
% 0.19/0.46 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( A22 != A1 )
% 0.19/0.46 => ~ ! [B3: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B3 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ~ ( member1069318160_state @ ( produc1909270103_state @ B3 @ A22 ) @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl.cases
% 0.19/0.46 thf(fact_184_rtranclE,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( A != B )
% 0.19/0.46 => ~ ! [Y3: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ B ) @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtranclE
% 0.19/0.46 thf(fact_185_exec1s__impl__exec,axiom,
% 0.19/0.46 ! [C: com,S: state,T: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.19/0.46 => ( exec @ S @ C @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1s_impl_exec
% 0.19/0.46 thf(fact_186_app__execs,axiom,
% 0.19/0.46 ! [Cs: list_com,S: state,Cs2: list_com,S2: state,Cs22: list_com] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % app_execs
% 0.19/0.46 thf(fact_187_termis_Osimps_I2_J,axiom,
% 0.19/0.46 ! [C: com,Cs: list_com,S: state] :
% 0.19/0.46 ( ( pHoare806997636termis @ ( cons_com @ C @ Cs ) @ S )
% 0.19/0.46 = ( ( termi @ C @ S )
% 0.19/0.46 & ! [T2: state] :
% 0.19/0.46 ( ( exec @ S @ C @ T2 )
% 0.19/0.46 => ( pHoare806997636termis @ Cs @ T2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termis.simps(2)
% 0.19/0.46 thf(fact_188_execs_Ointros_I2_J,axiom,
% 0.19/0.46 ! [S: state,C: com,T: state,Cs: list_com,U: state] :
% 0.19/0.46 ( ( exec @ S @ C @ T )
% 0.19/0.46 => ( ( pHoare259243732_execs @ T @ Cs @ U )
% 0.19/0.46 => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs ) @ U ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % execs.intros(2)
% 0.19/0.46 thf(fact_189_same__fstI,axiom,
% 0.19/0.46 ! [P: list_com > $o,X: list_com,Y4: state,Y: state,R2: list_com > set_Pr795498619_state] :
% 0.19/0.46 ( ( P @ X )
% 0.19/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Y ) @ ( R2 @ X ) )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ X @ Y4 ) @ ( produc1204172211_state @ X @ Y ) ) @ ( same_f855297288_state @ P @ R2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % same_fstI
% 0.19/0.46 thf(fact_190_same__fstI,axiom,
% 0.19/0.46 ! [P: produc2041926651_state > $o,X: produc2041926651_state,Y4: produc2041926651_state,Y: produc2041926651_state,R2: produc2041926651_state > set_Pr1165141447_state] :
% 0.19/0.46 ( ( P @ X )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ Y4 @ Y ) @ ( R2 @ X ) )
% 0.19/0.46 => ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ X @ Y4 ) @ ( produc1909270103_state @ X @ Y ) ) @ ( same_f1258458156_state @ P @ R2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % same_fstI
% 0.19/0.46 thf(fact_191_same__append__eq,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ Ys )
% 0.19/0.46 = ( append_com @ Xs @ Zs ) )
% 0.19/0.46 = ( Ys = Zs ) ) ).
% 0.19/0.46
% 0.19/0.46 % same_append_eq
% 0.19/0.46 thf(fact_192_append__same__eq,axiom,
% 0.19/0.46 ! [Ys: list_com,Xs: list_com,Zs: list_com] :
% 0.19/0.46 ( ( ( append_com @ Ys @ Xs )
% 0.19/0.46 = ( append_com @ Zs @ Xs ) )
% 0.19/0.46 = ( Ys = Zs ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_same_eq
% 0.19/0.46 thf(fact_193_append__assoc,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ( append_com @ ( append_com @ Xs @ Ys ) @ Zs )
% 0.19/0.46 = ( append_com @ Xs @ ( append_com @ Ys @ Zs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_assoc
% 0.19/0.46 thf(fact_194_append_Oassoc,axiom,
% 0.19/0.46 ! [A: list_com,B: list_com,C: list_com] :
% 0.19/0.46 ( ( append_com @ ( append_com @ A @ B ) @ C )
% 0.19/0.46 = ( append_com @ A @ ( append_com @ B @ C ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append.assoc
% 0.19/0.46 thf(fact_195_append_Oright__neutral,axiom,
% 0.19/0.46 ! [A: list_com] :
% 0.19/0.46 ( ( append_com @ A @ nil_com )
% 0.19/0.46 = A ) ).
% 0.19/0.46
% 0.19/0.46 % append.right_neutral
% 0.19/0.46 thf(fact_196_append__is__Nil__conv,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ Ys )
% 0.19/0.46 = nil_com )
% 0.19/0.46 = ( ( Xs = nil_com )
% 0.19/0.46 & ( Ys = nil_com ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_is_Nil_conv
% 0.19/0.46 thf(fact_197_Nil__is__append__conv,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( nil_com
% 0.19/0.46 = ( append_com @ Xs @ Ys ) )
% 0.19/0.46 = ( ( Xs = nil_com )
% 0.19/0.46 & ( Ys = nil_com ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nil_is_append_conv
% 0.19/0.46 thf(fact_198_self__append__conv2,axiom,
% 0.19/0.46 ! [Ys: list_com,Xs: list_com] :
% 0.19/0.46 ( ( Ys
% 0.19/0.46 = ( append_com @ Xs @ Ys ) )
% 0.19/0.46 = ( Xs = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % self_append_conv2
% 0.19/0.46 thf(fact_199_append__self__conv2,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ Ys )
% 0.19/0.46 = Ys )
% 0.19/0.46 = ( Xs = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_self_conv2
% 0.19/0.46 thf(fact_200_self__append__conv,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( append_com @ Xs @ Ys ) )
% 0.19/0.46 = ( Ys = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % self_append_conv
% 0.19/0.46 thf(fact_201_append__self__conv,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ Ys )
% 0.19/0.46 = Xs )
% 0.19/0.46 = ( Ys = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_self_conv
% 0.19/0.46 thf(fact_202_append__Nil2,axiom,
% 0.19/0.46 ! [Xs: list_com] :
% 0.19/0.46 ( ( append_com @ Xs @ nil_com )
% 0.19/0.46 = Xs ) ).
% 0.19/0.46
% 0.19/0.46 % append_Nil2
% 0.19/0.46 thf(fact_203_append1__eq__conv,axiom,
% 0.19/0.46 ! [Xs: list_com,X: com,Ys: list_com,Y: com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ ( cons_com @ X @ nil_com ) )
% 0.19/0.46 = ( append_com @ Ys @ ( cons_com @ Y @ nil_com ) ) )
% 0.19/0.46 = ( ( Xs = Ys )
% 0.19/0.46 & ( X = Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append1_eq_conv
% 0.19/0.46 thf(fact_204_rev__nonempty__induct,axiom,
% 0.19/0.46 ! [Xs: list_com,P: list_com > $o] :
% 0.19/0.46 ( ( Xs != nil_com )
% 0.19/0.46 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com] :
% 0.19/0.46 ( ( Xs2 != nil_com )
% 0.19/0.46 => ( ( P @ Xs2 )
% 0.19/0.46 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 0.19/0.46 => ( P @ Xs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rev_nonempty_induct
% 0.19/0.46 thf(fact_205_append__eq__Cons__conv,axiom,
% 0.19/0.46 ! [Ys: list_com,Zs: list_com,X: com,Xs: list_com] :
% 0.19/0.46 ( ( ( append_com @ Ys @ Zs )
% 0.19/0.46 = ( cons_com @ X @ Xs ) )
% 0.19/0.46 = ( ( ( Ys = nil_com )
% 0.19/0.46 & ( Zs
% 0.19/0.46 = ( cons_com @ X @ Xs ) ) )
% 0.19/0.46 | ? [Ys2: list_com] :
% 0.19/0.46 ( ( Ys
% 0.19/0.46 = ( cons_com @ X @ Ys2 ) )
% 0.19/0.46 & ( ( append_com @ Ys2 @ Zs )
% 0.19/0.46 = Xs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_eq_Cons_conv
% 0.19/0.46 thf(fact_206_Cons__eq__append__conv,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ( ( cons_com @ X @ Xs )
% 0.19/0.46 = ( append_com @ Ys @ Zs ) )
% 0.19/0.46 = ( ( ( Ys = nil_com )
% 0.19/0.46 & ( ( cons_com @ X @ Xs )
% 0.19/0.46 = Zs ) )
% 0.19/0.46 | ? [Ys2: list_com] :
% 0.19/0.46 ( ( ( cons_com @ X @ Ys2 )
% 0.19/0.46 = Ys )
% 0.19/0.46 & ( Xs
% 0.19/0.46 = ( append_com @ Ys2 @ Zs ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_eq_append_conv
% 0.19/0.46 thf(fact_207_rev__exhaust,axiom,
% 0.19/0.46 ! [Xs: list_com] :
% 0.19/0.46 ( ( Xs != nil_com )
% 0.19/0.46 => ~ ! [Ys3: list_com,Y3: com] :
% 0.19/0.46 ( Xs
% 0.19/0.46 != ( append_com @ Ys3 @ ( cons_com @ Y3 @ nil_com ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rev_exhaust
% 0.19/0.46 thf(fact_208_rev__induct,axiom,
% 0.19/0.46 ! [P: list_com > $o,Xs: list_com] :
% 0.19/0.46 ( ( P @ nil_com )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com] :
% 0.19/0.46 ( ( P @ Xs2 )
% 0.19/0.46 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) )
% 0.19/0.46 => ( P @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rev_induct
% 0.19/0.46 thf(fact_209_transpose_Ocases,axiom,
% 0.19/0.46 ! [X: list_list_com] :
% 0.19/0.46 ( ( X != nil_list_com )
% 0.19/0.46 => ( ! [Xss: list_list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_list_com @ nil_com @ Xss ) )
% 0.19/0.46 => ~ ! [X3: com,Xs2: list_com,Xss: list_list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_list_com @ ( cons_com @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transpose.cases
% 0.19/0.46 thf(fact_210_execs_Ointros_I1_J,axiom,
% 0.19/0.46 ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 0.19/0.46
% 0.19/0.46 % execs.intros(1)
% 0.19/0.46 thf(fact_211_append__eq__append__conv2,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,Zs: list_com,Ts: list_com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ Ys )
% 0.19/0.46 = ( append_com @ Zs @ Ts ) )
% 0.19/0.46 = ( ? [Us: list_com] :
% 0.19/0.46 ( ( ( Xs
% 0.19/0.46 = ( append_com @ Zs @ Us ) )
% 0.19/0.46 & ( ( append_com @ Us @ Ys )
% 0.19/0.46 = Ts ) )
% 0.19/0.46 | ( ( ( append_com @ Xs @ Us )
% 0.19/0.46 = Zs )
% 0.19/0.46 & ( Ys
% 0.19/0.46 = ( append_com @ Us @ Ts ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_eq_append_conv2
% 0.19/0.46 thf(fact_212_append_Oleft__neutral,axiom,
% 0.19/0.46 ! [A: list_com] :
% 0.19/0.46 ( ( append_com @ nil_com @ A )
% 0.19/0.46 = A ) ).
% 0.19/0.46
% 0.19/0.46 % append.left_neutral
% 0.19/0.46 thf(fact_213_append__eq__appendI,axiom,
% 0.19/0.46 ! [Xs: list_com,Xs1: list_com,Zs: list_com,Ys: list_com,Us2: list_com] :
% 0.19/0.46 ( ( ( append_com @ Xs @ Xs1 )
% 0.19/0.46 = Zs )
% 0.19/0.46 => ( ( Ys
% 0.19/0.46 = ( append_com @ Xs1 @ Us2 ) )
% 0.19/0.46 => ( ( append_com @ Xs @ Ys )
% 0.19/0.46 = ( append_com @ Zs @ Us2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_eq_appendI
% 0.19/0.46 thf(fact_214_append__Nil,axiom,
% 0.19/0.46 ! [Ys: list_com] :
% 0.19/0.46 ( ( append_com @ nil_com @ Ys )
% 0.19/0.46 = Ys ) ).
% 0.19/0.46
% 0.19/0.46 % append_Nil
% 0.19/0.46 thf(fact_215_eq__Nil__appendI,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( Xs = Ys )
% 0.19/0.46 => ( Xs
% 0.19/0.46 = ( append_com @ nil_com @ Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_Nil_appendI
% 0.19/0.46 thf(fact_216_append__Cons,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( append_com @ ( cons_com @ X @ Xs ) @ Ys )
% 0.19/0.46 = ( cons_com @ X @ ( append_com @ Xs @ Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_Cons
% 0.19/0.46 thf(fact_217_Cons__eq__appendI,axiom,
% 0.19/0.46 ! [X: com,Xs1: list_com,Ys: list_com,Xs: list_com,Zs: list_com] :
% 0.19/0.46 ( ( ( cons_com @ X @ Xs1 )
% 0.19/0.46 = Ys )
% 0.19/0.46 => ( ( Xs
% 0.19/0.46 = ( append_com @ Xs1 @ Zs ) )
% 0.19/0.46 => ( ( cons_com @ X @ Xs )
% 0.19/0.46 = ( append_com @ Ys @ Zs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_eq_appendI
% 0.19/0.46 thf(fact_218_splice_Ocases,axiom,
% 0.19/0.46 ! [X: produc258871771st_com] :
% 0.19/0.46 ( ! [Ys3: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 0.19/0.46 => ~ ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % splice.cases
% 0.19/0.46 thf(fact_219_shuffles_Ocases,axiom,
% 0.19/0.46 ! [X: produc258871771st_com] :
% 0.19/0.46 ( ! [Ys3: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 0.19/0.46 => ( ! [Xs2: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1307105171st_com @ Xs2 @ nil_com ) )
% 0.19/0.46 => ~ ! [X3: com,Xs2: list_com,Y3: com,Ys3: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % shuffles.cases
% 0.19/0.46 thf(fact_220_sorted__wrt_Ocases,axiom,
% 0.19/0.46 ! [X: produc2058209240st_com] :
% 0.19/0.46 ( ! [P3: com > com > $o] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.19/0.46 => ~ ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % sorted_wrt.cases
% 0.19/0.46 thf(fact_221_successively_Ocases,axiom,
% 0.19/0.46 ! [X: produc2058209240st_com] :
% 0.19/0.46 ( ! [P3: com > com > $o] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.19/0.46 => ( ! [P3: com > com > $o,X3: com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 0.19/0.46 => ~ ! [P3: com > com > $o,X3: com,Y3: com,Xs2: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % successively.cases
% 0.19/0.46 thf(fact_222_map__tailrec__rev_Oinduct,axiom,
% 0.19/0.46 ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 0.19/0.46 ( ! [F3: com > com,X_1: list_com] : ( P @ F3 @ nil_com @ X_1 )
% 0.19/0.46 => ( ! [F3: com > com,A3: com,As: list_com,Bs: list_com] :
% 0.19/0.46 ( ( P @ F3 @ As @ ( cons_com @ ( F3 @ A3 ) @ Bs ) )
% 0.19/0.46 => ( P @ F3 @ ( cons_com @ A3 @ As ) @ Bs ) )
% 0.19/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % map_tailrec_rev.induct
% 0.19/0.46 thf(fact_223_list__nonempty__induct,axiom,
% 0.19/0.46 ! [Xs: list_com,P: list_com > $o] :
% 0.19/0.46 ( ( Xs != nil_com )
% 0.19/0.46 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com] :
% 0.19/0.46 ( ( Xs2 != nil_com )
% 0.19/0.46 => ( ( P @ Xs2 )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ Xs2 ) ) ) )
% 0.19/0.46 => ( P @ Xs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list_nonempty_induct
% 0.19/0.46 thf(fact_224_successively_Oinduct,axiom,
% 0.19/0.46 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.19/0.46 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.19/0.46 => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 0.19/0.46 => ( ! [P3: com > com > $o,X3: com,Y3: com,Xs2: list_com] :
% 0.19/0.46 ( ( P @ P3 @ ( cons_com @ Y3 @ Xs2 ) )
% 0.19/0.46 => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % successively.induct
% 0.19/0.46 thf(fact_225_remdups__adj_Oinduct,axiom,
% 0.19/0.46 ! [P: list_com > $o,A0: list_com] :
% 0.19/0.46 ( ( P @ nil_com )
% 0.19/0.46 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.19/0.46 => ( ! [X3: com,Y3: com,Xs2: list_com] :
% 0.19/0.46 ( ( ( X3 = Y3 )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ Xs2 ) ) )
% 0.19/0.46 => ( ( ( X3 != Y3 )
% 0.19/0.46 => ( P @ ( cons_com @ Y3 @ Xs2 ) ) )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) ) )
% 0.19/0.46 => ( P @ A0 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % remdups_adj.induct
% 0.19/0.46 thf(fact_226_sorted__wrt_Oinduct,axiom,
% 0.19/0.46 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.19/0.46 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.19/0.46 => ( ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 0.19/0.46 ( ( P @ P3 @ Ys3 )
% 0.19/0.46 => ( P @ P3 @ ( cons_com @ X3 @ Ys3 ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % sorted_wrt.induct
% 0.19/0.46 thf(fact_227_remdups__adj_Ocases,axiom,
% 0.19/0.46 ! [X: list_com] :
% 0.19/0.46 ( ( X != nil_com )
% 0.19/0.46 => ( ! [X3: com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_com @ X3 @ nil_com ) )
% 0.19/0.46 => ~ ! [X3: com,Y3: com,Xs2: list_com] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % remdups_adj.cases
% 0.19/0.46 thf(fact_228_shuffles_Oinduct,axiom,
% 0.19/0.46 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.19/0.46 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.19/0.46 => ( ! [Xs2: list_com] : ( P @ Xs2 @ nil_com )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com,Y3: com,Ys3: list_com] :
% 0.19/0.46 ( ( P @ Xs2 @ ( cons_com @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % shuffles.induct
% 0.19/0.46 thf(fact_229_induct__list012,axiom,
% 0.19/0.46 ! [P: list_com > $o,Xs: list_com] :
% 0.19/0.46 ( ( P @ nil_com )
% 0.19/0.46 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.19/0.46 => ( ! [X3: com,Y3: com,Zs2: list_com] :
% 0.19/0.46 ( ( P @ Zs2 )
% 0.19/0.46 => ( ( P @ ( cons_com @ Y3 @ Zs2 ) )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Zs2 ) ) ) ) )
% 0.19/0.46 => ( P @ Xs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % induct_list012
% 0.19/0.46 thf(fact_230_splice_Oinduct,axiom,
% 0.19/0.46 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.19/0.46 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 0.19/0.46 ( ( P @ Ys3 @ Xs2 )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % splice.induct
% 0.19/0.46 thf(fact_231_list__induct2_H,axiom,
% 0.19/0.46 ! [P: list_com > list_com > $o,Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( P @ nil_com @ nil_com )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com] : ( P @ ( cons_com @ X3 @ Xs2 ) @ nil_com )
% 0.19/0.46 => ( ! [Y3: com,Ys3: list_com] : ( P @ nil_com @ ( cons_com @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ! [X3: com,Xs2: list_com,Y3: com,Ys3: list_com] :
% 0.19/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) )
% 0.19/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list_induct2'
% 0.19/0.46 thf(fact_232_neq__Nil__conv,axiom,
% 0.19/0.46 ! [Xs: list_com] :
% 0.19/0.46 ( ( Xs != nil_com )
% 0.19/0.46 = ( ? [Y5: com,Ys4: list_com] :
% 0.19/0.46 ( Xs
% 0.19/0.46 = ( cons_com @ Y5 @ Ys4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % neq_Nil_conv
% 0.19/0.46 thf(fact_233_list_Oinducts,axiom,
% 0.19/0.46 ! [P: list_com > $o,List: list_com] :
% 0.19/0.46 ( ( P @ nil_com )
% 0.19/0.46 => ( ! [X12: com,X23: list_com] :
% 0.19/0.46 ( ( P @ X23 )
% 0.19/0.46 => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 0.19/0.46 => ( P @ List ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inducts
% 0.19/0.46 thf(fact_234_list_Oexhaust,axiom,
% 0.19/0.46 ! [Y: list_com] :
% 0.19/0.46 ( ( Y != nil_com )
% 0.19/0.46 => ~ ! [X212: com,X222: list_com] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( cons_com @ X212 @ X222 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.exhaust
% 0.19/0.46 thf(fact_235_list_OdiscI,axiom,
% 0.19/0.46 ! [List: list_com,X21: com,X22: list_com] :
% 0.19/0.46 ( ( List
% 0.19/0.46 = ( cons_com @ X21 @ X22 ) )
% 0.19/0.46 => ( List != nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.discI
% 0.19/0.46 thf(fact_236_list_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X21: com,X22: list_com] :
% 0.19/0.46 ( nil_com
% 0.19/0.46 != ( cons_com @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.distinct(1)
% 0.19/0.46 thf(fact_237_execs_Ocases,axiom,
% 0.19/0.46 ! [A1: state,A22: list_com,A32: state] :
% 0.19/0.46 ( ( pHoare259243732_execs @ A1 @ A22 @ A32 )
% 0.19/0.46 => ( ( ( A22 = nil_com )
% 0.19/0.46 => ( A32 != A1 ) )
% 0.19/0.46 => ~ ! [C2: com,T3: state,Cs4: list_com] :
% 0.19/0.46 ( ( A22
% 0.19/0.46 = ( cons_com @ C2 @ Cs4 ) )
% 0.19/0.46 => ( ( exec @ A1 @ C2 @ T3 )
% 0.19/0.46 => ~ ( pHoare259243732_execs @ T3 @ Cs4 @ A32 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % execs.cases
% 0.19/0.46 thf(fact_238_execs_Osimps,axiom,
% 0.19/0.46 ( pHoare259243732_execs
% 0.19/0.46 = ( ^ [A12: state,A23: list_com,A33: state] :
% 0.19/0.46 ( ? [S3: state] :
% 0.19/0.46 ( ( A12 = S3 )
% 0.19/0.46 & ( A23 = nil_com )
% 0.19/0.46 & ( A33 = S3 ) )
% 0.19/0.46 | ? [S3: state,C3: com,T2: state,Cs3: list_com,U2: state] :
% 0.19/0.46 ( ( A12 = S3 )
% 0.19/0.46 & ( A23
% 0.19/0.46 = ( cons_com @ C3 @ Cs3 ) )
% 0.19/0.46 & ( A33 = U2 )
% 0.19/0.46 & ( exec @ S3 @ C3 @ T2 )
% 0.19/0.46 & ( pHoare259243732_execs @ T2 @ Cs3 @ U2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % execs.simps
% 0.19/0.46 thf(fact_239_execs_Oinducts,axiom,
% 0.19/0.46 ! [X1: state,X2: list_com,X34: state,P: state > list_com > state > $o] :
% 0.19/0.46 ( ( pHoare259243732_execs @ X1 @ X2 @ X34 )
% 0.19/0.46 => ( ! [S4: state] : ( P @ S4 @ nil_com @ S4 )
% 0.19/0.46 => ( ! [S4: state,C2: com,T3: state,Cs4: list_com,U3: state] :
% 0.19/0.46 ( ( exec @ S4 @ C2 @ T3 )
% 0.19/0.46 => ( ( pHoare259243732_execs @ T3 @ Cs4 @ U3 )
% 0.19/0.46 => ( ( P @ T3 @ Cs4 @ U3 )
% 0.19/0.46 => ( P @ S4 @ ( cons_com @ C2 @ Cs4 ) @ U3 ) ) ) )
% 0.19/0.46 => ( P @ X1 @ X2 @ X34 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % execs.inducts
% 0.19/0.46 thf(fact_240_while__termiE,axiom,
% 0.19/0.46 ! [B: state > $o,C: com,S: state] :
% 0.19/0.46 ( ( termi @ ( while @ B @ C ) @ S )
% 0.19/0.46 => ( ( B @ S )
% 0.19/0.46 => ( termi @ C @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % while_termiE
% 0.19/0.46 thf(fact_241_termis_Osimps_I1_J,axiom,
% 0.19/0.46 ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 0.19/0.46
% 0.19/0.46 % termis.simps(1)
% 0.19/0.46 thf(fact_242_gen__length__code_I1_J,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( ( gen_length_com @ N @ nil_com )
% 0.19/0.46 = N ) ).
% 0.19/0.46
% 0.19/0.46 % gen_length_code(1)
% 0.19/0.46 thf(fact_243_while__termiE2,axiom,
% 0.19/0.46 ! [B: state > $o,C: com,S: state,T: state] :
% 0.19/0.46 ( ( termi @ ( while @ B @ C ) @ S )
% 0.19/0.46 => ( ( B @ S )
% 0.19/0.46 => ( ( exec @ S @ C @ T )
% 0.19/0.46 => ( termi @ ( while @ B @ C ) @ T ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % while_termiE2
% 0.19/0.46 thf(fact_244_exec1s__impl__execs,axiom,
% 0.19/0.46 ! [Cs: list_com,S: state,T: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.19/0.46 => ( pHoare259243732_execs @ S @ Cs @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % exec1s_impl_execs
% 0.19/0.46 thf(fact_245_execs__pres__termi,axiom,
% 0.19/0.46 ! [C: com,S: state,C4: com,Cs2: list_com,S2: state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C4 @ Cs2 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.19/0.46 => ( ( termi @ C @ S )
% 0.19/0.46 => ( termi @ C4 @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % execs_pres_termi
% 0.19/0.46 thf(fact_246_app__exec,axiom,
% 0.19/0.46 ! [Cs: list_com,S: state,Cs2: list_com,S2: state,Cs22: list_com] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.19/0.46 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % app_exec
% 0.19/0.46 thf(fact_247_exec1E_I1_J,axiom,
% 0.19/0.46 ! [S: state,Cs2: list_com,S2: state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ nil_com @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 ) ).
% 0.19/0.46
% 0.19/0.46 % exec1E(1)
% 0.19/0.46 thf(fact_248_termi__while,axiom,
% 0.19/0.46 ! [B: state > $o,C: com,F2: nat > state,K: nat] :
% 0.19/0.46 ( ( termi @ ( while @ B @ C ) @ ( F2 @ K ) )
% 0.19/0.46 => ( ! [I2: nat] : ( exec @ ( F2 @ I2 ) @ C @ ( F2 @ ( suc @ I2 ) ) )
% 0.19/0.46 => ? [I2: nat] :
% 0.19/0.46 ~ ( B @ ( F2 @ I2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi_while
% 0.19/0.46 thf(fact_249_termi__while__lemma,axiom,
% 0.19/0.46 ! [W: com,Fk: state,F2: nat > state,K: nat,B: state > $o,C: com] :
% 0.19/0.46 ( ( termi @ W @ Fk )
% 0.19/0.46 => ( ( ( Fk
% 0.19/0.46 = ( F2 @ K ) )
% 0.19/0.46 & ( W
% 0.19/0.46 = ( while @ B @ C ) )
% 0.19/0.46 & ! [I2: nat] : ( exec @ ( F2 @ I2 ) @ C @ ( F2 @ ( suc @ I2 ) ) ) )
% 0.19/0.46 => ? [I2: nat] :
% 0.19/0.46 ~ ( B @ ( F2 @ I2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi_while_lemma
% 0.19/0.46 thf(fact_250_termi_OSemi,axiom,
% 0.19/0.46 ! [C1: com,S0: state,C22: com] :
% 0.19/0.46 ( ( termi @ C1 @ S0 )
% 0.19/0.46 => ( ! [S12: state] :
% 0.19/0.46 ( ( exec @ S0 @ C1 @ S12 )
% 0.19/0.46 => ( termi @ C22 @ S12 ) )
% 0.19/0.46 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi.Semi
% 0.19/0.46 thf(fact_251_termi_OWhileTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C: com] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( ( termi @ C @ S )
% 0.19/0.46 => ( ! [T3: state] :
% 0.19/0.46 ( ( exec @ S @ C @ T3 )
% 0.19/0.46 => ( termi @ ( while @ B @ C ) @ T3 ) )
% 0.19/0.46 => ( termi @ ( while @ B @ C ) @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi.WhileTrue
% 0.19/0.46 thf(fact_252_termi_OIfFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C22: com,C1: com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( ( termi @ C22 @ S )
% 0.19/0.46 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi.IfFalse
% 0.19/0.46 thf(fact_253_termi_OWhileFalse,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C: com] :
% 0.19/0.46 ( ~ ( B @ S )
% 0.19/0.46 => ( termi @ ( while @ B @ C ) @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi.WhileFalse
% 0.19/0.46 thf(fact_254_termi_OIfTrue,axiom,
% 0.19/0.46 ! [B: state > $o,S: state,C1: com,C22: com] :
% 0.19/0.46 ( ( B @ S )
% 0.19/0.46 => ( ( termi @ C1 @ S )
% 0.19/0.46 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % termi.IfTrue
% 0.19/0.46 thf(fact_255_n__lists__Nil,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( ( ( N = zero_zero_nat )
% 0.19/0.46 => ( ( n_lists_com @ N @ nil_com )
% 0.19/0.46 = ( cons_list_com @ nil_com @ nil_list_com ) ) )
% 0.19/0.46 & ( ( N != zero_zero_nat )
% 0.19/0.46 => ( ( n_lists_com @ N @ nil_com )
% 0.19/0.46 = nil_list_com ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % n_lists_Nil
% 0.19/0.46 thf(fact_256_n__lists_Osimps_I1_J,axiom,
% 0.19/0.46 ! [Xs: list_com] :
% 0.19/0.46 ( ( n_lists_com @ zero_zero_nat @ Xs )
% 0.19/0.46 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % n_lists.simps(1)
% 0.19/0.46 thf(fact_257_product__lists_Osimps_I1_J,axiom,
% 0.19/0.46 ( ( product_lists_com @ nil_list_com )
% 0.19/0.46 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % product_lists.simps(1)
% 0.19/0.46 thf(fact_258_bind__simps_I2_J,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com,F2: com > list_com] :
% 0.19/0.46 ( ( bind_com_com @ ( cons_com @ X @ Xs ) @ F2 )
% 0.19/0.46 = ( append_com @ ( F2 @ X ) @ ( bind_com_com @ Xs @ F2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % bind_simps(2)
% 0.19/0.46 thf(fact_259_subseqs_Osimps_I1_J,axiom,
% 0.19/0.46 ( ( subseqs_com @ nil_com )
% 0.19/0.46 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % subseqs.simps(1)
% 0.19/0.46 thf(fact_260_snoc__listrel1__snoc__iff,axiom,
% 0.19/0.46 ! [Xs: list_com,X: com,Ys: list_com,Y: com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 0.19/0.46 = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.19/0.46 & ( X = Y ) )
% 0.19/0.46 | ( ( Xs = Ys )
% 0.19/0.46 & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % snoc_listrel1_snoc_iff
% 0.19/0.46 thf(fact_261_snoc__listrel1__snoc__iff,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,X: produc2041926651_state,Ys: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 & ( X = Y ) )
% 0.19/0.46 | ( ( Xs = Ys )
% 0.19/0.46 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % snoc_listrel1_snoc_iff
% 0.19/0.46 thf(fact_262_bind__simps_I1_J,axiom,
% 0.19/0.46 ! [F2: com > list_com] :
% 0.19/0.46 ( ( bind_com_com @ nil_com @ F2 )
% 0.19/0.46 = nil_com ) ).
% 0.19/0.46
% 0.19/0.46 % bind_simps(1)
% 0.19/0.46 thf(fact_263_Cons__listrel1__Cons,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( listrel1_com @ R ) )
% 0.19/0.46 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.19/0.46 & ( Xs = Ys ) )
% 0.19/0.46 | ( ( X = Y )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_listrel1_Cons
% 0.19/0.46 thf(fact_264_Cons__listrel1__Cons,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.19/0.46 & ( Xs = Ys ) )
% 0.19/0.46 | ( ( X = Y )
% 0.19/0.46 & ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_listrel1_Cons
% 0.19/0.46 thf(fact_265_rtrancl__listrel1__ConsI1,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_listrel1_ConsI1
% 0.19/0.46 thf(fact_266_listrel1I2,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1I2
% 0.19/0.46 thf(fact_267_not__Nil__listrel1,axiom,
% 0.19/0.46 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel1_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_Nil_listrel1
% 0.19/0.46 thf(fact_268_not__listrel1__Nil,axiom,
% 0.19/0.46 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_listrel1_Nil
% 0.19/0.46 thf(fact_269_append__listrel1I,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com,Us2: list_com,Vs: list_com] :
% 0.19/0.46 ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.19/0.46 & ( Us2 = Vs ) )
% 0.19/0.46 | ( ( Xs = Ys )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ Us2 @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Us2 ) @ ( append_com @ Ys @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_listrel1I
% 0.19/0.46 thf(fact_270_listrel1I1,axiom,
% 0.19/0.46 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Xs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1I1
% 0.19/0.46 thf(fact_271_listrel1I1,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Xs ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1I1
% 0.19/0.46 thf(fact_272_Cons__listrel1E1,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ Ys ) @ ( listrel1_com @ R ) )
% 0.19/0.46 => ( ! [Y3: com] :
% 0.19/0.46 ( ( Ys
% 0.19/0.46 = ( cons_com @ Y3 @ Xs ) )
% 0.19/0.46 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y3 ) @ R ) )
% 0.19/0.46 => ~ ! [Zs2: list_com] :
% 0.19/0.46 ( ( Ys
% 0.19/0.46 = ( cons_com @ X @ Zs2 ) )
% 0.19/0.46 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Zs2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_listrel1E1
% 0.19/0.46 thf(fact_273_Cons__listrel1E1,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 => ( ! [Y3: produc2041926651_state] :
% 0.19/0.46 ( ( Ys
% 0.19/0.46 = ( cons_P465369265_state @ Y3 @ Xs ) )
% 0.19/0.46 => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R ) )
% 0.19/0.46 => ~ ! [Zs2: list_P1040014977_state] :
% 0.19/0.46 ( ( Ys
% 0.19/0.46 = ( cons_P465369265_state @ X @ Zs2 ) )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_listrel1E1
% 0.19/0.46 thf(fact_274_Cons__listrel1E2,axiom,
% 0.19/0.46 ! [Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys ) ) @ ( listrel1_com @ R ) )
% 0.19/0.46 => ( ! [X3: com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_com @ X3 @ Ys ) )
% 0.19/0.46 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 0.19/0.46 => ~ ! [Zs2: list_com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_com @ Y @ Zs2 ) )
% 0.19/0.46 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs2 @ Ys ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_listrel1E2
% 0.19/0.46 thf(fact_275_Cons__listrel1E2,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 => ( ! [X3: produc2041926651_state] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_P465369265_state @ X3 @ Ys ) )
% 0.19/0.46 => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 0.19/0.46 => ~ ! [Zs2: list_P1040014977_state] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_P465369265_state @ Y @ Zs2 ) )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs2 @ Ys ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_listrel1E2
% 0.19/0.46 thf(fact_276_listrel1I,axiom,
% 0.19/0.46 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Us2: list_com,Vs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.19/0.46 => ( ( Xs
% 0.19/0.46 = ( append_com @ Us2 @ ( cons_com @ X @ Vs ) ) )
% 0.19/0.46 => ( ( Ys
% 0.19/0.46 = ( append_com @ Us2 @ ( cons_com @ Y @ Vs ) ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1I
% 0.19/0.46 thf(fact_277_listrel1I,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Us2: list_P1040014977_state,Vs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.19/0.46 => ( ( Xs
% 0.19/0.46 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ X @ Vs ) ) )
% 0.19/0.46 => ( ( Ys
% 0.19/0.46 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1I
% 0.19/0.46 thf(fact_278_listrel1E,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.19/0.46 => ~ ! [X3: com,Y3: com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ! [Us3: list_com,Vs2: list_com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 0.19/0.46 => ( Ys
% 0.19/0.46 != ( append_com @ Us3 @ ( cons_com @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1E
% 0.19/0.46 thf(fact_279_listrel1E,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 0.19/0.46 => ( Ys
% 0.19/0.46 != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel1E
% 0.19/0.46 thf(fact_280_rtrancl__listrel1__ConsI2,axiom,
% 0.19/0.46 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_listrel1_ConsI2
% 0.19/0.46 thf(fact_281_rtrancl__listrel1__ConsI2,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rtrancl_listrel1_ConsI2
% 0.19/0.46 thf(fact_282_maps__simps_I1_J,axiom,
% 0.19/0.46 ! [F2: com > list_com,X: com,Xs: list_com] :
% 0.19/0.46 ( ( maps_com_com @ F2 @ ( cons_com @ X @ Xs ) )
% 0.19/0.46 = ( append_com @ ( F2 @ X ) @ ( maps_com_com @ F2 @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % maps_simps(1)
% 0.19/0.46 thf(fact_283_insert__Nil,axiom,
% 0.19/0.46 ! [X: com] :
% 0.19/0.46 ( ( insert_com @ X @ nil_com )
% 0.19/0.46 = ( cons_com @ X @ nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % insert_Nil
% 0.19/0.46 thf(fact_284_concat__eq__append__conv,axiom,
% 0.19/0.46 ! [Xss2: list_list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ( ( concat_com @ Xss2 )
% 0.19/0.46 = ( append_com @ Ys @ Zs ) )
% 0.19/0.46 = ( ( ( Xss2 = nil_list_com )
% 0.19/0.46 => ( ( Ys = nil_com )
% 0.19/0.46 & ( Zs = nil_com ) ) )
% 0.19/0.46 & ( ( Xss2 != nil_list_com )
% 0.19/0.46 => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 0.19/0.46 ( ( Xss2
% 0.19/0.46 = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.19/0.46 & ( Ys
% 0.19/0.46 = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 0.19/0.46 & ( Zs
% 0.19/0.46 = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % concat_eq_append_conv
% 0.19/0.46 thf(fact_285_concat__append,axiom,
% 0.19/0.46 ! [Xs: list_list_com,Ys: list_list_com] :
% 0.19/0.46 ( ( concat_com @ ( append_list_com @ Xs @ Ys ) )
% 0.19/0.46 = ( append_com @ ( concat_com @ Xs ) @ ( concat_com @ Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % concat_append
% 0.19/0.46 thf(fact_286_concat_Osimps_I1_J,axiom,
% 0.19/0.46 ( ( concat_com @ nil_list_com )
% 0.19/0.46 = nil_com ) ).
% 0.19/0.46
% 0.19/0.46 % concat.simps(1)
% 0.19/0.46 thf(fact_287_concat_Osimps_I2_J,axiom,
% 0.19/0.46 ! [X: list_com,Xs: list_list_com] :
% 0.19/0.46 ( ( concat_com @ ( cons_list_com @ X @ Xs ) )
% 0.19/0.46 = ( append_com @ X @ ( concat_com @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % concat.simps(2)
% 0.19/0.46 thf(fact_288_maps__simps_I2_J,axiom,
% 0.19/0.46 ! [F2: com > list_com] :
% 0.19/0.46 ( ( maps_com_com @ F2 @ nil_com )
% 0.19/0.46 = nil_com ) ).
% 0.19/0.46
% 0.19/0.46 % maps_simps(2)
% 0.19/0.46 thf(fact_289_concat__eq__appendD,axiom,
% 0.19/0.46 ! [Xss2: list_list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ( ( concat_com @ Xss2 )
% 0.19/0.46 = ( append_com @ Ys @ Zs ) )
% 0.19/0.46 => ( ( Xss2 != nil_list_com )
% 0.19/0.46 => ? [Xss12: list_list_com,Xs2: list_com,Xs5: list_com,Xss23: list_list_com] :
% 0.19/0.46 ( ( Xss2
% 0.19/0.46 = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.19/0.46 & ( Ys
% 0.19/0.46 = ( append_com @ ( concat_com @ Xss12 ) @ Xs2 ) )
% 0.19/0.46 & ( Zs
% 0.19/0.46 = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % concat_eq_appendD
% 0.19/0.46 thf(fact_290_nths__singleton,axiom,
% 0.19/0.46 ! [A4: set_nat,X: com] :
% 0.19/0.46 ( ( ( member_nat @ zero_zero_nat @ A4 )
% 0.19/0.46 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 0.19/0.46 = ( cons_com @ X @ nil_com ) ) )
% 0.19/0.46 & ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.19/0.46 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 0.19/0.46 = nil_com ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nths_singleton
% 0.19/0.46 thf(fact_291_lexord__append__left__rightI,axiom,
% 0.19/0.46 ! [A: com,B: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A @ X ) ) @ ( append_com @ U @ ( cons_com @ B @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_append_left_rightI
% 0.19/0.46 thf(fact_292_lexord__append__left__rightI,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_append_left_rightI
% 0.19/0.46 thf(fact_293_nths__nil,axiom,
% 0.19/0.46 ! [A4: set_nat] :
% 0.19/0.46 ( ( nths_com @ nil_com @ A4 )
% 0.19/0.46 = nil_com ) ).
% 0.19/0.46
% 0.19/0.46 % nths_nil
% 0.19/0.46 thf(fact_294_lexord__cons__cons,axiom,
% 0.19/0.46 ! [A: com,X: list_com,B: com,Y: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A @ X ) @ ( cons_com @ B @ Y ) ) @ ( lexord_com @ R ) )
% 0.19/0.46 = ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 0.19/0.46 | ( ( A = B )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_cons_cons
% 0.19/0.46 thf(fact_295_lexord__cons__cons,axiom,
% 0.19/0.46 ! [A: produc2041926651_state,X: list_P1040014977_state,B: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A @ X ) @ ( cons_P465369265_state @ B @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 0.19/0.46 = ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.19/0.46 | ( ( A = B )
% 0.19/0.46 & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_cons_cons
% 0.19/0.46 thf(fact_296_lexord__Nil__left,axiom,
% 0.19/0.46 ! [Y: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 0.19/0.46 = ( ? [A5: com,X4: list_com] :
% 0.19/0.46 ( Y
% 0.19/0.46 = ( cons_com @ A5 @ X4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_Nil_left
% 0.19/0.46 thf(fact_297_lexord__linear,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.19/0.46 ( ! [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ R )
% 0.19/0.46 | ( A3 = B3 )
% 0.19/0.46 | ( member1069318160_state @ ( produc1909270103_state @ B3 @ A3 ) @ R ) )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 0.19/0.46 | ( X = Y )
% 0.19/0.46 | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_linear
% 0.19/0.46 thf(fact_298_lexord__irreflexive,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.19/0.46 ( ! [X3: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_irreflexive
% 0.19/0.46 thf(fact_299_lexord__Nil__right,axiom,
% 0.19/0.46 ! [X: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_Nil_right
% 0.19/0.46 thf(fact_300_lexord__append__leftI,axiom,
% 0.19/0.46 ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_append_leftI
% 0.19/0.46 thf(fact_301_lexord__append__leftD,axiom,
% 0.19/0.46 ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 0.19/0.46 => ( ! [A3: com] :
% 0.19/0.46 ~ ( member1333916004om_com @ ( product_Pair_com_com @ A3 @ A3 ) @ R )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_append_leftD
% 0.19/0.46 thf(fact_302_lexord__append__leftD,axiom,
% 0.19/0.46 ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 0.19/0.46 => ( ! [A3: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ A3 @ A3 ) @ R )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_append_leftD
% 0.19/0.46 thf(fact_303_lexord__append__rightI,axiom,
% 0.19/0.46 ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ? [B5: com,Z3: list_com] :
% 0.19/0.46 ( Y
% 0.19/0.46 = ( cons_com @ B5 @ Z3 ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_append_rightI
% 0.19/0.46 thf(fact_304_lexord__same__pref__if__irrefl,axiom,
% 0.19/0.46 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ( irrefl_com @ R )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lexord_com @ R ) )
% 0.19/0.46 = ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lexord_com @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lexord_same_pref_if_irrefl
% 0.19/0.46 thf(fact_305_listrel_Ocases,axiom,
% 0.19/0.46 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ( ( ( A1 = nil_com )
% 0.19/0.46 => ( A22 != nil_com ) )
% 0.19/0.46 => ~ ! [X3: com,Y3: com,Xs2: list_com] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons_com @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Ys3: list_com] :
% 0.19/0.46 ( ( A22
% 0.19/0.46 = ( cons_com @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.cases
% 0.19/0.46 thf(fact_306_listrel_Ocases,axiom,
% 0.19/0.46 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.19/0.46 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 => ( ( ( A1 = nil_list_com )
% 0.19/0.46 => ( A22 != nil_state ) )
% 0.19/0.46 => ~ ! [X3: list_com,Y3: state,Xs2: list_list_com] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons_list_com @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Ys3: list_state] :
% 0.19/0.46 ( ( A22
% 0.19/0.46 = ( cons_state @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.cases
% 0.19/0.46 thf(fact_307_listrel_Ocases,axiom,
% 0.19/0.46 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 => ( ( ( A1 = nil_Pr1844458753_state )
% 0.19/0.46 => ( A22 != nil_Pr1844458753_state ) )
% 0.19/0.46 => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs2: list_P1040014977_state] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Ys3: list_P1040014977_state] :
% 0.19/0.46 ( ( A22
% 0.19/0.46 = ( cons_P465369265_state @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.cases
% 0.19/0.46 thf(fact_308_listrel__rtrancl__refl,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_rtrancl_refl
% 0.19/0.46 thf(fact_309_listrel_ONil,axiom,
% 0.19/0.46 ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.Nil
% 0.19/0.46 thf(fact_310_listrel__Nil1,axiom,
% 0.19/0.46 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ( Xs = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Nil1
% 0.19/0.46 thf(fact_311_listrel__Nil2,axiom,
% 0.19/0.46 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ( Xs = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Nil2
% 0.19/0.46 thf(fact_312_listrel__rtrancl__trans,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state,Zs: list_P1040014977_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ Ys @ Zs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_rtrancl_trans
% 0.19/0.46 thf(fact_313_listrel__Cons2,axiom,
% 0.19/0.46 ! [Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys ) ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ~ ! [X3: com,Xs2: list_com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_com @ X3 @ Xs2 ) )
% 0.19/0.46 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 0.19/0.46 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Cons2
% 0.19/0.46 thf(fact_314_listrel__Cons2,axiom,
% 0.19/0.46 ! [Xs: list_list_com,Y: state,Ys: list_state,R: set_Pr849496667_state] :
% 0.19/0.46 ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ ( cons_state @ Y @ Ys ) ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 => ~ ! [X3: list_com,Xs2: list_list_com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_list_com @ X3 @ Xs2 ) )
% 0.19/0.46 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 0.19/0.46 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Cons2
% 0.19/0.46 thf(fact_315_listrel__Cons2,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 => ~ ! [X3: produc2041926651_state,Xs2: list_P1040014977_state] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Cons2
% 0.19/0.46 thf(fact_316_listrel__Cons1,axiom,
% 0.19/0.46 ! [Y: com,Ys: list_com,Xs: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys ) @ Xs ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ~ ! [Y3: com,Ys3: list_com] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_com @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Cons1
% 0.19/0.46 thf(fact_317_listrel__Cons1,axiom,
% 0.19/0.46 ! [Y: list_com,Ys: list_list_com,Xs: list_state,R: set_Pr849496667_state] :
% 0.19/0.46 ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys ) @ Xs ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 => ~ ! [Y3: state,Ys3: list_state] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_state @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Cons1
% 0.19/0.46 thf(fact_318_listrel__Cons1,axiom,
% 0.19/0.46 ! [Y: produc2041926651_state,Ys: list_P1040014977_state,Xs: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys ) @ Xs ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 => ~ ! [Y3: produc2041926651_state,Ys3: list_P1040014977_state] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 = ( cons_P465369265_state @ Y3 @ Ys3 ) )
% 0.19/0.46 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y3 ) @ R )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_Cons1
% 0.19/0.46 thf(fact_319_listrel_OCons,axiom,
% 0.19/0.46 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.Cons
% 0.19/0.46 thf(fact_320_listrel_OCons,axiom,
% 0.19/0.46 ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs: list_list_com,Ys: list_state] :
% 0.19/0.46 ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 0.19/0.46 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs ) @ ( cons_state @ Y @ Ys ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.Cons
% 0.19/0.46 thf(fact_321_listrel_OCons,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.Cons
% 0.19/0.46 thf(fact_322_listrel__reflcl__if__listrel1,axiom,
% 0.19/0.46 ! [Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_reflcl_if_listrel1
% 0.19/0.46 thf(fact_323_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 0.19/0.46 = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel_rtrancl_eq_rtrancl_listrel1
% 0.19/0.46 thf(fact_324_listrel_Oinducts,axiom,
% 0.19/0.46 ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ( ( P @ nil_com @ nil_com )
% 0.19/0.46 => ( ! [X3: com,Y3: com,Xs2: list_com,Ys3: list_com] :
% 0.19/0.46 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.19/0.46 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) ) ) )
% 0.19/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.inducts
% 0.19/0.46 thf(fact_325_listrel_Oinducts,axiom,
% 0.19/0.46 ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 0.19/0.46 ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 => ( ( P @ nil_list_com @ nil_state )
% 0.19/0.46 => ( ! [X3: list_com,Y3: state,Xs2: list_list_com,Ys3: list_state] :
% 0.19/0.46 ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.19/0.46 => ( P @ ( cons_list_com @ X3 @ Xs2 ) @ ( cons_state @ Y3 @ Ys3 ) ) ) ) )
% 0.19/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.inducts
% 0.19/0.46 thf(fact_326_listrel_Oinducts,axiom,
% 0.19/0.46 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 0.19/0.46 => ( ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs2: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 0.19/0.46 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.19/0.46 => ( P @ ( cons_P465369265_state @ X3 @ Xs2 ) @ ( cons_P465369265_state @ Y3 @ Ys3 ) ) ) ) )
% 0.19/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.inducts
% 0.19/0.46 thf(fact_327_listrel_Osimps,axiom,
% 0.19/0.46 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.19/0.46 = ( ( ( A1 = nil_com )
% 0.19/0.46 & ( A22 = nil_com ) )
% 0.19/0.46 | ? [X4: com,Y5: com,Xs3: list_com,Ys4: list_com] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons_com @ X4 @ Xs3 ) )
% 0.19/0.46 & ( A22
% 0.19/0.46 = ( cons_com @ Y5 @ Ys4 ) )
% 0.19/0.46 & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y5 ) @ R )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys4 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.simps
% 0.19/0.46 thf(fact_328_listrel_Osimps,axiom,
% 0.19/0.46 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.19/0.46 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.19/0.46 = ( ( ( A1 = nil_list_com )
% 0.19/0.46 & ( A22 = nil_state ) )
% 0.19/0.46 | ? [X4: list_com,Y5: state,Xs3: list_list_com,Ys4: list_state] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons_list_com @ X4 @ Xs3 ) )
% 0.19/0.46 & ( A22
% 0.19/0.46 = ( cons_state @ Y5 @ Ys4 ) )
% 0.19/0.46 & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y5 ) @ R )
% 0.19/0.46 & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys4 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.simps
% 0.19/0.46 thf(fact_329_listrel_Osimps,axiom,
% 0.19/0.46 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.19/0.46 = ( ( ( A1 = nil_Pr1844458753_state )
% 0.19/0.46 & ( A22 = nil_Pr1844458753_state ) )
% 0.19/0.46 | ? [X4: produc2041926651_state,Y5: produc2041926651_state,Xs3: list_P1040014977_state,Ys4: list_P1040014977_state] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 0.19/0.46 & ( A22
% 0.19/0.46 = ( cons_P465369265_state @ Y5 @ Ys4 ) )
% 0.19/0.46 & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y5 ) @ R )
% 0.19/0.46 & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys4 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % listrel.simps
% 0.19/0.46 thf(fact_330_irreflI,axiom,
% 0.19/0.46 ! [R2: set_Pr1165141447_state] :
% 0.19/0.46 ( ! [A3: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ A3 @ A3 ) @ R2 )
% 0.19/0.46 => ( irrefl654089520_state @ R2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % irreflI
% 0.19/0.46 thf(fact_331_irrefl__def,axiom,
% 0.19/0.46 ( irrefl654089520_state
% 0.19/0.46 = ( ^ [R3: set_Pr1165141447_state] :
% 0.19/0.46 ! [A5: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % irrefl_def
% 0.19/0.46 thf(fact_332_lenlex__append2,axiom,
% 0.19/0.46 ! [R2: set_Pr1822651163om_com,Us2: list_com,Xs: list_com,Ys: list_com] :
% 0.19/0.46 ( ( irrefl_com @ R2 )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us2 @ Xs ) @ ( append_com @ Us2 @ Ys ) ) @ ( lenlex_com @ R2 ) )
% 0.19/0.46 = ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lenlex_append2
% 0.19/0.46 thf(fact_333_Nil__lenlex__iff1,axiom,
% 0.19/0.46 ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ns ) @ ( lenlex_com @ R ) )
% 0.19/0.46 = ( Ns != nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nil_lenlex_iff1
% 0.19/0.46 thf(fact_334_Nil__notin__lex,axiom,
% 0.19/0.46 ! [Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ys ) @ ( lex_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nil_notin_lex
% 0.19/0.46 thf(fact_335_Nil2__notin__lex,axiom,
% 0.19/0.46 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( lex_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nil2_notin_lex
% 0.19/0.46 thf(fact_336_lex__append__leftI,axiom,
% 0.19/0.46 ! [Ys: list_com,Zs: list_com,R: set_Pr1822651163om_com,Xs: list_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lex_com @ R ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lex_com @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lex_append_leftI
% 0.19/0.46 thf(fact_337_lenlex__irreflexive,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.19/0.46 ( ! [X3: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.19/0.46 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( lenlex295247238_state @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lenlex_irreflexive
% 0.19/0.46 thf(fact_338_Nil__lenlex__iff2,axiom,
% 0.19/0.46 ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ~ ( member32358020st_com @ ( produc1307105171st_com @ Ns @ nil_com ) @ ( lenlex_com @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nil_lenlex_iff2
% 0.19/0.46 thf(fact_339_lex__append__leftD,axiom,
% 0.19/0.46 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ! [X3: com] :
% 0.19/0.46 ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lex_com @ R ) )
% 0.19/0.46 => ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lex_com @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lex_append_leftD
% 0.19/0.46 thf(fact_340_lex__append__leftD,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state,Zs: list_P1040014977_state] :
% 0.19/0.46 ( ! [X3: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ Ys ) @ ( append982487830_state @ Xs @ Zs ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.19/0.46 => ( member1267359376_state @ ( produc1298457559_state @ Ys @ Zs ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lex_append_leftD
% 0.19/0.46 thf(fact_341_lex__append__left__iff,axiom,
% 0.19/0.46 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.19/0.46 ( ! [X3: com] :
% 0.19/0.46 ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.19/0.46 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lex_com @ R ) )
% 0.19/0.46 = ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lex_com @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lex_append_left_iff
% 0.19/0.46 thf(fact_342_lex__append__left__iff,axiom,
% 0.19/0.46 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state,Zs: list_P1040014977_state] :
% 0.19/0.46 ( ! [X3: produc2041926651_state] :
% 0.19/0.46 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.19/0.46 => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ Ys ) @ ( append982487830_state @ Xs @ Zs ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.19/0.46 = ( member1267359376_state @ ( produc1298457559_state @ Ys @ Zs ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lex_append_left_iff
% 0.19/0.46 thf(fact_343_Cons__in__lex,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.19/0.46 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( lex_com @ R ) )
% 0.19/0.46 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.19/0.46 & ( ( size_size_list_com @ Xs )
% 0.19/0.46 = ( size_size_list_com @ Ys ) ) )
% 0.19/0.46 | ( ( X = Y )
% 0.19/0.46 & ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( lex_com @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_in_lex
% 0.19/0.46 thf(fact_344_Cons__in__lex,axiom,
% 0.19/0.46 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.19/0.46 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.19/0.46 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.19/0.46 & ( ( size_s213202669_state @ Xs )
% 0.19/0.46 = ( size_s213202669_state @ Ys ) ) )
% 0.19/0.46 | ( ( X = Y )
% 0.19/0.46 & ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( lex_Pr570247525_state @ R ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Cons_in_lex
% 0.19/0.46 thf(fact_345_rotate1_Osimps_I2_J,axiom,
% 0.19/0.46 ! [X: com,Xs: list_com] :
% 0.19/0.46 ( ( rotate1_com @ ( cons_com @ X @ Xs ) )
% 0.19/0.46 = ( append_com @ Xs @ ( cons_com @ X @ nil_com ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rotate1.simps(2)
% 0.19/0.46 thf(fact_346_append__eq__append__conv,axiom,
% 0.19/0.46 ! [Xs: list_com,Ys: list_com,Us2: list_com,Vs: list_com] :
% 0.19/0.46 ( ( ( ( size_size_list_com @ Xs )
% 0.19/0.46 = ( size_size_list_com @ Ys ) )
% 0.19/0.46 | ( ( size_size_list_com @ Us2 )
% 0.19/0.46 = ( size_size_list_com @ Vs ) ) )
% 0.19/0.46 => ( ( ( append_com @ Xs @ Us2 )
% 0.19/0.46 = ( append_com @ Ys @ Vs ) )
% 0.19/0.46 = ( ( Xs = Ys )
% 0.19/0.46 & ( Us2 = Vs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % append_eq_append_conv
% 0.19/0.46 thf(fact_347_rotate1__is__Nil__conv,axiom,
% 0.19/0.46 ! [Xs: list_com] :
% 0.19/0.46 ( ( ( rotate1_com @ Xs )
% 0.19/0.46 = nil_com )
% 0.19/0.46 = ( Xs = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % rotate1_is_Nil_conv
% 0.19/0.46 thf(fact_348_length__0__conv,axiom,
% 0.19/0.46 ! [Xs: list_com] :
% 0.19/0.46 ( ( ( size_size_list_com @ Xs )
% 0.19/0.46 = zero_zero_nat )
% 0.19/0.46 = ( Xs = nil_com ) ) ).
% 0.19/0.46
% 0.19/0.46 % length_0_conv
% 0.19/0.46
% 0.19/0.46 % Conjectures (5)
% 0.19/0.46 thf(conj_0,hypothesis,
% 0.19/0.46 ( ( f @ zero_zero_nat )
% 0.19/0.46 = ( produc1204172211_state @ ( cons_com @ ( while @ b @ c ) @ cs ) @ s ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(conj_1,hypothesis,
% 0.19/0.46 ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ I3 ) @ ( f @ ( suc @ I3 ) ) ) @ pHoare259243666_exec1 ) ).
% 0.19/0.46
% 0.19/0.46 thf(conj_2,hypothesis,
% 0.19/0.46 member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ zero_zero_nat ) ) ) @ pHoare259243666_exec1 ).
% 0.19/0.46
% 0.19/0.46 thf(conj_3,hypothesis,
% 0.19/0.46 ( ( f @ ( suc @ zero_zero_nat ) )
% 0.19/0.46 = ( produc1204172211_state @ a @ ba ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(conj_4,conjecture,
% 0.19/0.46 ( ~ ( b @ s )
% 0.19/0.46 | ? [F4: nat > produc2041926651_state] :
% 0.19/0.46 ( ( ( F4 @ zero_zero_nat )
% 0.19/0.47 = ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s ) )
% 0.19/0.47 & ! [I2: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F4 @ I2 ) @ ( F4 @ ( suc @ I2 ) ) ) @ pHoare259243666_exec1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 0.31/1.80 ---- Embedded in THF ---
% 0.31/1.80 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.80 %%% Generated on Tue Feb 24 08:27:45 EST 2026
% 0.31/1.80 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.80 %%% Logic specification used:
% 0.31/1.80 %%% thf(spec, logic, $$dhol).
% 0.31/1.80
% 0.31/1.80 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2DTF15884.p
% See solution above
% 0.31/1.81 ------------------------
% 0.31/1.88 ---- Cleaned THF ---
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J_J,type,
% 0.31/1.88 set_Pr1847866567_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/1.88 produc1519776487_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/1.88 set_Pr2096893127_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/1.88 produc186437863_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J_J,type,
% 0.31/1.88 set_Pr1419004359_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J_J,type,
% 0.31/1.88 set_Pr135335153st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.31/1.88 produc392316135_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/1.88 produc1440412305st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/1.88 set_Pr1142642759_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J_J,type,
% 0.31/1.88 set_Pr2083163591st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/1.88 produc1225889383_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/1.88 produc1762014951st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/1.88 set_Pr1165141447_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/1.88 produc410756839_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_Mt__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J_J,type,
% 0.31/1.88 set_Pr1675528647om_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_Mt__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J,type,
% 0.31/1.88 produc1065433319om_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.31/1.88 set_Pr391631483_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.31/1.88 produc1393453339_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/1.88 produc2058209240st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/1.88 set_Pr602326075st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/1.88 list_P1040014977_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/1.88 set_Pr849496667_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/1.88 produc258871771st_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 0.31/1.88 set_Pr795498619_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/1.88 produc2041926651_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J,type,
% 0.31/1.88 set_Pr1822651163om_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/1.88 produc1115495963_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.31/1.88 product_prod_com_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/1.88 list_list_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__List__Olist_It__PLang__Ostate_J,type,
% 0.31/1.88 list_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__PLang__Ostate_J,type,
% 0.31/1.88 set_state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/1.88 list_com: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/1.88 set_nat: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__PLang__Ostate,type,
% 0.31/1.88 state: $tType ).
% 0.31/1.88
% 0.31/1.88 thf(ty_n_t__PLang__Ocom,type,
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% 0.31/1.89 transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/1.89 transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/1.89 transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.31/1.89 transi1042416958om_com: set_Pr1675528647om_com > set_Pr1675528647om_com ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/1.89 transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_Wfrec_Osame__fst_001t__List__Olist_It__PLang__Ocom_J_001t__PLang__Ostate,type,
% 0.31/1.89 same_f855297288_state: ( list_com > $o ) > ( list_com > set_Pr795498619_state ) > set_Pr1165141447_state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_Wfrec_Osame__fst_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/1.89 same_f1258458156_state: ( produc2041926651_state > $o ) > ( produc2041926651_state > set_Pr1165141447_state ) > set_Pr2096893127_state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Nat__Onat,type,
% 0.31/1.89 member_nat: nat > set_nat > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__PLang__Ostate,type,
% 0.31/1.89 member_state: state > set_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.31/1.89 member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/1.89 member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/1.89 member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/1.89 member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.31/1.89 member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/1.89 member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/1.89 member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.31/1.89 member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/1.89 member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/1.89 member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/1.89 member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_Mt__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J,type,
% 0.31/1.89 member2105207824om_com: produc1065433319om_com > set_Pr1675528647om_com > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/1.89 member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_a,type,
% 0.31/1.89 a: list_com ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_b,type,
% 0.31/1.89 b: state > $o ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_ba,type,
% 0.31/1.89 ba: state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_c,type,
% 0.31/1.89 c: com ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_cs,type,
% 0.31/1.89 cs: list_com ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_f,type,
% 0.31/1.89 f: nat > produc2041926651_state ).
% 0.31/1.89
% 0.31/1.89 thf(sy_v_s,type,
% 0.31/1.89 s: state ).
% 0.31/1.89
% 0.31/1.89 thf(fact_0_exec1E_I5_J,axiom,
% 0.31/1.89 ! [B: state > $o,C: com,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/1.89 => ( ( ( Cs2 = Cs )
% 0.31/1.89 => ( ( S2 = S )
% 0.31/1.89 => ( B @ S ) ) )
% 0.31/1.89 => ~ ( ( Cs2
% 0.31/1.89 = ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs ) ) )
% 0.31/1.89 => ( ( S2 = S )
% 0.31/1.89 => ~ ( B @ S ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_1_exec1_OWhileTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_2_exec1_OWhileFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_3_inf__def,axiom,
% 0.31/1.89 ( pHoare2126160787le_inf
% 0.31/1.89 = ( ^ [Cs3: list_com,S3: state] :
% 0.31/1.89 ? [F: nat > produc2041926651_state] :
% 0.31/1.89 ( ( ( F @ zero_zero_nat )
% 0.31/1.89 = ( produc1204172211_state @ Cs3 @ S3 ) )
% 0.31/1.89 & ! [I: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ pHoare259243666_exec1 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_4_com_Oinject_I4_J,axiom,
% 0.31/1.89 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.31/1.89 ( ( ( while @ X41 @ X42 )
% 0.31/1.89 = ( while @ Y41 @ Y42 ) )
% 0.31/1.89 = ( ( X41 = Y41 )
% 0.31/1.89 & ( X42 = Y42 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_5_nat_Oinject,axiom,
% 0.31/1.89 ! [X2: nat,Y2: nat] :
% 0.31/1.89 ( ( ( suc @ X2 )
% 0.31/1.89 = ( suc @ Y2 ) )
% 0.31/1.89 = ( X2 = Y2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_6_old_Onat_Oinject,axiom,
% 0.31/1.89 ! [Nat: nat,Nat2: nat] :
% 0.31/1.89 ( ( ( suc @ Nat )
% 0.31/1.89 = ( suc @ Nat2 ) )
% 0.31/1.89 = ( Nat = Nat2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_7_list_Oinject,axiom,
% 0.31/1.89 ! [X21: list_com,X22: list_list_com,Y21: list_com,Y22: list_list_com] :
% 0.31/1.89 ( ( ( cons_list_com @ X21 @ X22 )
% 0.31/1.89 = ( cons_list_com @ Y21 @ Y22 ) )
% 0.31/1.89 = ( ( X21 = Y21 )
% 0.31/1.89 & ( X22 = Y22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_8_list_Oinject,axiom,
% 0.31/1.89 ! [X21: produc2041926651_state,X22: list_P1040014977_state,Y21: produc2041926651_state,Y22: list_P1040014977_state] :
% 0.31/1.89 ( ( ( cons_P465369265_state @ X21 @ X22 )
% 0.31/1.89 = ( cons_P465369265_state @ Y21 @ Y22 ) )
% 0.31/1.89 = ( ( X21 = Y21 )
% 0.31/1.89 & ( X22 = Y22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_9_list_Oinject,axiom,
% 0.31/1.89 ! [X21: state,X22: list_state,Y21: state,Y22: list_state] :
% 0.31/1.89 ( ( ( cons_state @ X21 @ X22 )
% 0.31/1.89 = ( cons_state @ Y21 @ Y22 ) )
% 0.31/1.89 = ( ( X21 = Y21 )
% 0.31/1.89 & ( X22 = Y22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_10_list_Oinject,axiom,
% 0.31/1.89 ! [X21: com,X22: list_com,Y21: com,Y22: list_com] :
% 0.31/1.89 ( ( ( cons_com @ X21 @ X22 )
% 0.31/1.89 = ( cons_com @ Y21 @ Y22 ) )
% 0.31/1.89 = ( ( X21 = Y21 )
% 0.31/1.89 & ( X22 = Y22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_11_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: com,X2: com,Y1: com,Y2: com] :
% 0.31/1.89 ( ( ( product_Pair_com_com @ X1 @ X2 )
% 0.31/1.89 = ( product_Pair_com_com @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_12_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,Y1: list_P1040014977_state,Y2: list_P1040014977_state] :
% 0.31/1.89 ( ( ( produc1298457559_state @ X1 @ X2 )
% 0.31/1.89 = ( produc1298457559_state @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_13_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: list_com,X2: list_com,Y1: list_com,Y2: list_com] :
% 0.31/1.89 ( ( ( produc1307105171st_com @ X1 @ X2 )
% 0.31/1.89 = ( produc1307105171st_com @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_14_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: list_list_com,X2: list_state,Y1: list_list_com,Y2: list_state] :
% 0.31/1.89 ( ( ( produc1742567891_state @ X1 @ X2 )
% 0.31/1.89 = ( produc1742567891_state @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_15_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: com > com > $o,X2: list_com,Y1: com > com > $o,Y2: list_com] :
% 0.31/1.89 ( ( ( produc1914379986st_com @ X1 @ X2 )
% 0.31/1.89 = ( produc1914379986st_com @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_16_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: list_com,X2: state,Y1: list_com,Y2: state] :
% 0.31/1.89 ( ( ( produc1204172211_state @ X1 @ X2 )
% 0.31/1.89 = ( produc1204172211_state @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_17_prod_Oinject,axiom,
% 0.31/1.89 ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y2: produc2041926651_state] :
% 0.31/1.89 ( ( ( produc1909270103_state @ X1 @ X2 )
% 0.31/1.89 = ( produc1909270103_state @ Y1 @ Y2 ) )
% 0.31/1.89 = ( ( X1 = Y1 )
% 0.31/1.89 & ( X2 = Y2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_18_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: com,B: com,A2: com,B2: com] :
% 0.31/1.89 ( ( ( product_Pair_com_com @ A @ B )
% 0.31/1.89 = ( product_Pair_com_com @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_19_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: list_P1040014977_state,B: list_P1040014977_state,A2: list_P1040014977_state,B2: list_P1040014977_state] :
% 0.31/1.89 ( ( ( produc1298457559_state @ A @ B )
% 0.31/1.89 = ( produc1298457559_state @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_20_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: list_com,B: list_com,A2: list_com,B2: list_com] :
% 0.31/1.89 ( ( ( produc1307105171st_com @ A @ B )
% 0.31/1.89 = ( produc1307105171st_com @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_21_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: list_list_com,B: list_state,A2: list_list_com,B2: list_state] :
% 0.31/1.89 ( ( ( produc1742567891_state @ A @ B )
% 0.31/1.89 = ( produc1742567891_state @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_22_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: com > com > $o,B: list_com,A2: com > com > $o,B2: list_com] :
% 0.31/1.89 ( ( ( produc1914379986st_com @ A @ B )
% 0.31/1.89 = ( produc1914379986st_com @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_23_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: list_com,B: state,A2: list_com,B2: state] :
% 0.31/1.89 ( ( ( produc1204172211_state @ A @ B )
% 0.31/1.89 = ( produc1204172211_state @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_24_old_Oprod_Oinject,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.31/1.89 ( ( ( produc1909270103_state @ A @ B )
% 0.31/1.89 = ( produc1909270103_state @ A2 @ B2 ) )
% 0.31/1.89 = ( ( A = A2 )
% 0.31/1.89 & ( B = B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_25_exec1__pres__termis,axiom,
% 0.31/1.89 ! [Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/1.89 => ( ( pHoare806997636termis @ Cs @ S )
% 0.31/1.89 => ( pHoare806997636termis @ Cs2 @ S2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_26_prod__cases3,axiom,
% 0.31/1.89 ! [Y: produc410756839_state] :
% 0.31/1.89 ~ ! [A3: produc2041926651_state,B3: list_com,C2: state] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1909270103_state @ A3 @ ( produc1204172211_state @ B3 @ C2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_27_zero__reorient,axiom,
% 0.31/1.89 ! [X: nat] :
% 0.31/1.89 ( ( zero_zero_nat = X )
% 0.31/1.89 = ( X = zero_zero_nat ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_28_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: product_prod_com_com > $o,Prod: product_prod_com_com] :
% 0.31/1.89 ( ! [A3: com,B3: com] : ( P @ ( product_Pair_com_com @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_29_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: produc1225889383_state > $o,Prod: produc1225889383_state] :
% 0.31/1.89 ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state] : ( P @ ( produc1298457559_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_30_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: produc258871771st_com > $o,Prod: produc258871771st_com] :
% 0.31/1.89 ( ! [A3: list_com,B3: list_com] : ( P @ ( produc1307105171st_com @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_31_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: produc1393453339_state > $o,Prod: produc1393453339_state] :
% 0.31/1.89 ( ! [A3: list_list_com,B3: list_state] : ( P @ ( produc1742567891_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_32_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: produc2058209240st_com > $o,Prod: produc2058209240st_com] :
% 0.31/1.89 ( ! [A3: com > com > $o,B3: list_com] : ( P @ ( produc1914379986st_com @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_33_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 0.31/1.89 ( ! [A3: list_com,B3: state] : ( P @ ( produc1204172211_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_34_old_Oprod_Oinducts,axiom,
% 0.31/1.89 ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 0.31/1.89 ( ! [A3: produc2041926651_state,B3: produc2041926651_state] : ( P @ ( produc1909270103_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ Prod ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_35_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: product_prod_com_com] :
% 0.31/1.89 ~ ! [A3: com,B3: com] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( product_Pair_com_com @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_36_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: produc1225889383_state] :
% 0.31/1.89 ~ ! [A3: list_P1040014977_state,B3: list_P1040014977_state] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1298457559_state @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_37_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: produc258871771st_com] :
% 0.31/1.89 ~ ! [A3: list_com,B3: list_com] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1307105171st_com @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_38_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: produc1393453339_state] :
% 0.31/1.89 ~ ! [A3: list_list_com,B3: list_state] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1742567891_state @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_39_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: produc2058209240st_com] :
% 0.31/1.89 ~ ! [A3: com > com > $o,B3: list_com] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1914379986st_com @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_40_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: produc2041926651_state] :
% 0.31/1.89 ~ ! [A3: list_com,B3: state] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1204172211_state @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_41_old_Oprod_Oexhaust,axiom,
% 0.31/1.89 ! [Y: produc410756839_state] :
% 0.31/1.89 ~ ! [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( produc1909270103_state @ A3 @ B3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_42_Pair__inject,axiom,
% 0.31/1.89 ! [A: com,B: com,A2: com,B2: com] :
% 0.31/1.89 ( ( ( product_Pair_com_com @ A @ B )
% 0.31/1.89 = ( product_Pair_com_com @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_43_Pair__inject,axiom,
% 0.31/1.89 ! [A: list_P1040014977_state,B: list_P1040014977_state,A2: list_P1040014977_state,B2: list_P1040014977_state] :
% 0.31/1.89 ( ( ( produc1298457559_state @ A @ B )
% 0.31/1.89 = ( produc1298457559_state @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_44_Pair__inject,axiom,
% 0.31/1.89 ! [A: list_com,B: list_com,A2: list_com,B2: list_com] :
% 0.31/1.89 ( ( ( produc1307105171st_com @ A @ B )
% 0.31/1.89 = ( produc1307105171st_com @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_45_Pair__inject,axiom,
% 0.31/1.89 ! [A: list_list_com,B: list_state,A2: list_list_com,B2: list_state] :
% 0.31/1.89 ( ( ( produc1742567891_state @ A @ B )
% 0.31/1.89 = ( produc1742567891_state @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_46_Pair__inject,axiom,
% 0.31/1.89 ! [A: com > com > $o,B: list_com,A2: com > com > $o,B2: list_com] :
% 0.31/1.89 ( ( ( produc1914379986st_com @ A @ B )
% 0.31/1.89 = ( produc1914379986st_com @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_47_Pair__inject,axiom,
% 0.31/1.89 ! [A: list_com,B: state,A2: list_com,B2: state] :
% 0.31/1.89 ( ( ( produc1204172211_state @ A @ B )
% 0.31/1.89 = ( produc1204172211_state @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_48_Pair__inject,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.31/1.89 ( ( ( produc1909270103_state @ A @ B )
% 0.31/1.89 = ( produc1909270103_state @ A2 @ B2 ) )
% 0.31/1.89 => ~ ( ( A = A2 )
% 0.31/1.89 => ( B != B2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_49_prod__cases,axiom,
% 0.31/1.89 ! [P: product_prod_com_com > $o,P2: product_prod_com_com] :
% 0.31/1.89 ( ! [A3: com,B3: com] : ( P @ ( product_Pair_com_com @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_50_prod__cases,axiom,
% 0.31/1.89 ! [P: produc1225889383_state > $o,P2: produc1225889383_state] :
% 0.31/1.89 ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state] : ( P @ ( produc1298457559_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_51_prod__cases,axiom,
% 0.31/1.89 ! [P: produc258871771st_com > $o,P2: produc258871771st_com] :
% 0.31/1.89 ( ! [A3: list_com,B3: list_com] : ( P @ ( produc1307105171st_com @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_52_prod__cases,axiom,
% 0.31/1.89 ! [P: produc1393453339_state > $o,P2: produc1393453339_state] :
% 0.31/1.89 ( ! [A3: list_list_com,B3: list_state] : ( P @ ( produc1742567891_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_53_prod__cases,axiom,
% 0.31/1.89 ! [P: produc2058209240st_com > $o,P2: produc2058209240st_com] :
% 0.31/1.89 ( ! [A3: com > com > $o,B3: list_com] : ( P @ ( produc1914379986st_com @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_54_prod__cases,axiom,
% 0.31/1.89 ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 0.31/1.89 ( ! [A3: list_com,B3: state] : ( P @ ( produc1204172211_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_55_prod__cases,axiom,
% 0.31/1.89 ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 0.31/1.89 ( ! [A3: produc2041926651_state,B3: produc2041926651_state] : ( P @ ( produc1909270103_state @ A3 @ B3 ) )
% 0.31/1.89 => ( P @ P2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_56_surj__pair,axiom,
% 0.31/1.89 ! [P2: product_prod_com_com] :
% 0.31/1.89 ? [X3: com,Y3: com] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( product_Pair_com_com @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_57_surj__pair,axiom,
% 0.31/1.89 ! [P2: produc1225889383_state] :
% 0.31/1.89 ? [X3: list_P1040014977_state,Y3: list_P1040014977_state] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( produc1298457559_state @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_58_surj__pair,axiom,
% 0.31/1.89 ! [P2: produc258871771st_com] :
% 0.31/1.89 ? [X3: list_com,Y3: list_com] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( produc1307105171st_com @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_59_surj__pair,axiom,
% 0.31/1.89 ! [P2: produc1393453339_state] :
% 0.31/1.89 ? [X3: list_list_com,Y3: list_state] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( produc1742567891_state @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_60_surj__pair,axiom,
% 0.31/1.89 ! [P2: produc2058209240st_com] :
% 0.31/1.89 ? [X3: com > com > $o,Y3: list_com] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( produc1914379986st_com @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_61_surj__pair,axiom,
% 0.31/1.89 ! [P2: produc2041926651_state] :
% 0.31/1.89 ? [X3: list_com,Y3: state] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( produc1204172211_state @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_62_surj__pair,axiom,
% 0.31/1.89 ! [P2: produc410756839_state] :
% 0.31/1.89 ? [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.31/1.89 ( P2
% 0.31/1.89 = ( produc1909270103_state @ X3 @ Y3 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_63_not__Cons__self2,axiom,
% 0.31/1.89 ! [X: list_com,Xs: list_list_com] :
% 0.31/1.89 ( ( cons_list_com @ X @ Xs )
% 0.31/1.89 != Xs ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_64_not__Cons__self2,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.31/1.89 ( ( cons_P465369265_state @ X @ Xs )
% 0.31/1.89 != Xs ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_65_not__Cons__self2,axiom,
% 0.31/1.89 ! [X: state,Xs: list_state] :
% 0.31/1.89 ( ( cons_state @ X @ Xs )
% 0.31/1.89 != Xs ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_66_not__Cons__self2,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com] :
% 0.31/1.89 ( ( cons_com @ X @ Xs )
% 0.31/1.89 != Xs ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_67_n__not__Suc__n,axiom,
% 0.31/1.89 ! [N: nat] :
% 0.31/1.89 ( N
% 0.31/1.89 != ( suc @ N ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_68_Suc__inject,axiom,
% 0.31/1.89 ! [X: nat,Y: nat] :
% 0.31/1.89 ( ( ( suc @ X )
% 0.31/1.89 = ( suc @ Y ) )
% 0.31/1.89 => ( X = Y ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_69_not0__implies__Suc,axiom,
% 0.31/1.89 ! [N: nat] :
% 0.31/1.89 ( ( N != zero_zero_nat )
% 0.31/1.89 => ? [M: nat] :
% 0.31/1.89 ( N
% 0.31/1.89 = ( suc @ M ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_70_old_Onat_Oinducts,axiom,
% 0.31/1.89 ! [P: nat > $o,Nat: nat] :
% 0.31/1.89 ( ( P @ zero_zero_nat )
% 0.31/1.89 => ( ! [Nat3: nat] :
% 0.31/1.89 ( ( P @ Nat3 )
% 0.31/1.89 => ( P @ ( suc @ Nat3 ) ) )
% 0.31/1.89 => ( P @ Nat ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_71_old_Onat_Oexhaust,axiom,
% 0.31/1.89 ! [Y: nat] :
% 0.31/1.89 ( ( Y != zero_zero_nat )
% 0.31/1.89 => ~ ! [Nat3: nat] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( suc @ Nat3 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_72_Zero__not__Suc,axiom,
% 0.31/1.89 ! [M2: nat] :
% 0.31/1.89 ( zero_zero_nat
% 0.31/1.89 != ( suc @ M2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_73_Zero__neq__Suc,axiom,
% 0.31/1.89 ! [M2: nat] :
% 0.31/1.89 ( zero_zero_nat
% 0.31/1.89 != ( suc @ M2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_74_Suc__neq__Zero,axiom,
% 0.31/1.89 ! [M2: nat] :
% 0.31/1.89 ( ( suc @ M2 )
% 0.31/1.89 != zero_zero_nat ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_75_zero__induct,axiom,
% 0.31/1.89 ! [P: nat > $o,K: nat] :
% 0.31/1.89 ( ( P @ K )
% 0.31/1.89 => ( ! [N2: nat] :
% 0.31/1.89 ( ( P @ ( suc @ N2 ) )
% 0.31/1.89 => ( P @ N2 ) )
% 0.31/1.89 => ( P @ zero_zero_nat ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_76_diff__induct,axiom,
% 0.31/1.89 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 0.31/1.89 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.31/1.89 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.31/1.89 => ( ! [X3: nat,Y3: nat] :
% 0.31/1.89 ( ( P @ X3 @ Y3 )
% 0.31/1.89 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.31/1.89 => ( P @ M2 @ N ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_77_nat__induct,axiom,
% 0.31/1.89 ! [P: nat > $o,N: nat] :
% 0.31/1.89 ( ( P @ zero_zero_nat )
% 0.31/1.89 => ( ! [N2: nat] :
% 0.31/1.89 ( ( P @ N2 )
% 0.31/1.89 => ( P @ ( suc @ N2 ) ) )
% 0.31/1.89 => ( P @ N ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_78_nat_OdiscI,axiom,
% 0.31/1.89 ! [Nat: nat,X2: nat] :
% 0.31/1.89 ( ( Nat
% 0.31/1.89 = ( suc @ X2 ) )
% 0.31/1.89 => ( Nat != zero_zero_nat ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_79_old_Onat_Odistinct_I1_J,axiom,
% 0.31/1.89 ! [Nat2: nat] :
% 0.31/1.89 ( zero_zero_nat
% 0.31/1.89 != ( suc @ Nat2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_80_old_Onat_Odistinct_I2_J,axiom,
% 0.31/1.89 ! [Nat2: nat] :
% 0.31/1.89 ( ( suc @ Nat2 )
% 0.31/1.89 != zero_zero_nat ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_81_nat_Odistinct_I1_J,axiom,
% 0.31/1.89 ! [X2: nat] :
% 0.31/1.89 ( zero_zero_nat
% 0.31/1.89 != ( suc @ X2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_82_prod__induct3,axiom,
% 0.31/1.89 ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 0.31/1.89 ( ! [A3: produc2041926651_state,B3: list_com,C2: state] : ( P @ ( produc1909270103_state @ A3 @ ( produc1204172211_state @ B3 @ C2 ) ) )
% 0.31/1.89 => ( P @ X ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_83_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: produc1225889383_state,P: produc1225889383_state > $o] :
% 0.31/1.89 ( ( member1267359376_state @ A @ ( collec183560402_state @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_84_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,P: produc2041926651_state > $o] :
% 0.31/1.89 ( ( member64234660_state @ A @ ( collec1409185766_state @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_85_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: produc258871771st_com,P: produc258871771st_com > $o] :
% 0.31/1.89 ( ( member32358020st_com @ A @ ( collec328862150st_com @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_86_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: produc1393453339_state,P: produc1393453339_state > $o] :
% 0.31/1.89 ( ( member1442949316_state @ A @ ( collec924674566_state @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_87_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: nat,P: nat > $o] :
% 0.31/1.89 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_88_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: produc410756839_state,P: produc410756839_state > $o] :
% 0.31/1.89 ( ( member1069318160_state @ A @ ( collec300063826_state @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_89_mem__Collect__eq,axiom,
% 0.31/1.89 ! [A: state,P: state > $o] :
% 0.31/1.89 ( ( member_state @ A @ ( collect_state @ P ) )
% 0.31/1.89 = ( P @ A ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_90_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_Pr1142642759_state] :
% 0.31/1.89 ( ( collec183560402_state
% 0.31/1.89 @ ^ [X4: produc1225889383_state] : ( member1267359376_state @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_91_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_Pr849496667_state] :
% 0.31/1.89 ( ( collec1409185766_state
% 0.31/1.89 @ ^ [X4: produc2041926651_state] : ( member64234660_state @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_92_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_Pr602326075st_com] :
% 0.31/1.89 ( ( collec328862150st_com
% 0.31/1.89 @ ^ [X4: produc258871771st_com] : ( member32358020st_com @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_93_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_Pr391631483_state] :
% 0.31/1.89 ( ( collec924674566_state
% 0.31/1.89 @ ^ [X4: produc1393453339_state] : ( member1442949316_state @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_94_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_nat] :
% 0.31/1.89 ( ( collect_nat
% 0.31/1.89 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_95_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_Pr1165141447_state] :
% 0.31/1.89 ( ( collec300063826_state
% 0.31/1.89 @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_96_Collect__mem__eq,axiom,
% 0.31/1.89 ! [A4: set_state] :
% 0.31/1.89 ( ( collect_state
% 0.31/1.89 @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 0.31/1.89 = A4 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_97_Collect__cong,axiom,
% 0.31/1.89 ! [P: state > $o,Q: state > $o] :
% 0.31/1.89 ( ! [X3: state] :
% 0.31/1.89 ( ( P @ X3 )
% 0.31/1.89 = ( Q @ X3 ) )
% 0.31/1.89 => ( ( collect_state @ P )
% 0.31/1.89 = ( collect_state @ Q ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_98_Collect__cong,axiom,
% 0.31/1.89 ! [P: produc410756839_state > $o,Q: produc410756839_state > $o] :
% 0.31/1.89 ( ! [X3: produc410756839_state] :
% 0.31/1.89 ( ( P @ X3 )
% 0.31/1.89 = ( Q @ X3 ) )
% 0.31/1.89 => ( ( collec300063826_state @ P )
% 0.31/1.89 = ( collec300063826_state @ Q ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_99_exec1_OSemi,axiom,
% 0.31/1.89 ! [C1: com,C22: com,Cs: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_100_exec1E_I3_J,axiom,
% 0.31/1.89 ! [C1: com,C22: com,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/1.89 => ~ ( ( Cs2
% 0.31/1.89 = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs ) ) )
% 0.31/1.89 => ( S2 != S ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_101_exec1_ODo,axiom,
% 0.31/1.89 ! [T: state,F2: state > set_state,S: state,Cs: list_com] :
% 0.31/1.89 ( ( member_state @ T @ ( F2 @ S ) )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs @ T ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_102_exec1E_I2_J,axiom,
% 0.31/1.89 ! [F2: state > set_state,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/1.89 => ~ ( ( Cs2 = Cs )
% 0.31/1.89 => ~ ( member_state @ S2 @ ( F2 @ S ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_103_exec1_OIfFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_104_exec1_OIfTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_105_exec1E_I4_J,axiom,
% 0.31/1.89 ! [B: state > $o,C1: com,C22: com,Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/1.89 => ( ( ( Cs2
% 0.31/1.89 = ( cons_com @ C1 @ Cs ) )
% 0.31/1.89 => ( ( S2 = S )
% 0.31/1.89 => ~ ( B @ S ) ) )
% 0.31/1.89 => ~ ( ( Cs2
% 0.31/1.89 = ( cons_com @ C22 @ Cs ) )
% 0.31/1.89 => ( ( S2 = S )
% 0.31/1.89 => ( B @ S ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_106_gen__length__code_I2_J,axiom,
% 0.31/1.89 ! [N: nat,X: list_com,Xs: list_list_com] :
% 0.31/1.89 ( ( gen_length_list_com @ N @ ( cons_list_com @ X @ Xs ) )
% 0.31/1.89 = ( gen_length_list_com @ ( suc @ N ) @ Xs ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_107_gen__length__code_I2_J,axiom,
% 0.31/1.89 ! [N: nat,X: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.31/1.89 ( ( gen_le1266608782_state @ N @ ( cons_P465369265_state @ X @ Xs ) )
% 0.31/1.89 = ( gen_le1266608782_state @ ( suc @ N ) @ Xs ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_108_gen__length__code_I2_J,axiom,
% 0.31/1.89 ! [N: nat,X: state,Xs: list_state] :
% 0.31/1.89 ( ( gen_length_state @ N @ ( cons_state @ X @ Xs ) )
% 0.31/1.89 = ( gen_length_state @ ( suc @ N ) @ Xs ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_109_gen__length__code_I2_J,axiom,
% 0.31/1.89 ! [N: nat,X: com,Xs: list_com] :
% 0.31/1.89 ( ( gen_length_com @ N @ ( cons_com @ X @ Xs ) )
% 0.31/1.89 = ( gen_length_com @ ( suc @ N ) @ Xs ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_110_com_Oinject_I3_J,axiom,
% 0.31/1.89 ! [X31: state > $o,X32: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 0.31/1.89 ( ( ( cond @ X31 @ X32 @ X33 )
% 0.31/1.89 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 0.31/1.89 = ( ( X31 = Y31 )
% 0.31/1.89 & ( X32 = Y32 )
% 0.31/1.89 & ( X33 = Y33 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_111_com_Oinject_I1_J,axiom,
% 0.31/1.89 ! [X1: state > set_state,Y1: state > set_state] :
% 0.31/1.89 ( ( ( do @ X1 )
% 0.31/1.89 = ( do @ Y1 ) )
% 0.31/1.89 = ( X1 = Y1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_112_com_Oinject_I2_J,axiom,
% 0.31/1.89 ! [X21: com,X22: com,Y21: com,Y22: com] :
% 0.31/1.89 ( ( ( semi @ X21 @ X22 )
% 0.31/1.89 = ( semi @ Y21 @ Y22 ) )
% 0.31/1.89 = ( ( X21 = Y21 )
% 0.31/1.89 & ( X22 = Y22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_113_com_Odistinct_I11_J,axiom,
% 0.31/1.89 ! [X21: com,X22: com,X31: state > $o,X32: com,X33: com] :
% 0.31/1.89 ( ( semi @ X21 @ X22 )
% 0.31/1.89 != ( cond @ X31 @ X32 @ X33 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_114_com_Odistinct_I3_J,axiom,
% 0.31/1.89 ! [X1: state > set_state,X31: state > $o,X32: com,X33: com] :
% 0.31/1.89 ( ( do @ X1 )
% 0.31/1.89 != ( cond @ X31 @ X32 @ X33 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_115_com_Odistinct_I1_J,axiom,
% 0.31/1.89 ! [X1: state > set_state,X21: com,X22: com] :
% 0.31/1.89 ( ( do @ X1 )
% 0.31/1.89 != ( semi @ X21 @ X22 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_116_com_Odistinct_I19_J,axiom,
% 0.31/1.89 ! [X31: state > $o,X32: com,X33: com,X41: state > $o,X42: com] :
% 0.31/1.89 ( ( cond @ X31 @ X32 @ X33 )
% 0.31/1.89 != ( while @ X41 @ X42 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_117_com_Odistinct_I5_J,axiom,
% 0.31/1.89 ! [X1: state > set_state,X41: state > $o,X42: com] :
% 0.31/1.89 ( ( do @ X1 )
% 0.31/1.89 != ( while @ X41 @ X42 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_118_com_Odistinct_I13_J,axiom,
% 0.31/1.89 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 0.31/1.89 ( ( semi @ X21 @ X22 )
% 0.31/1.89 != ( while @ X41 @ X42 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_119_execs__pres__termis,axiom,
% 0.31/1.89 ! [Cs: list_com,S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/1.89 => ( ( pHoare806997636termis @ Cs @ S )
% 0.31/1.89 => ( pHoare806997636termis @ Cs2 @ S2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_120_exec1p_OSemi,axiom,
% 0.31/1.89 ! [C1: com,C22: com,Cs: list_com,S: state] : ( pHoare202237534exec1p @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs ) @ S @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs ) ) @ S ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_121_exec1p_ODo,axiom,
% 0.31/1.89 ! [T: state,F2: state > set_state,S: state,Cs: list_com] :
% 0.31/1.89 ( ( member_state @ T @ ( F2 @ S ) )
% 0.31/1.89 => ( pHoare202237534exec1p @ ( cons_com @ ( do @ F2 ) @ Cs ) @ S @ Cs @ T ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_122_exec1p_OIfTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( pHoare202237534exec1p @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S @ ( cons_com @ C1 @ Cs ) @ S ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_123_exec1p_OIfFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C1: com,C22: com,Cs: list_com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( pHoare202237534exec1p @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs ) @ S @ ( cons_com @ C22 @ Cs ) @ S ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_124_exec1p_OWhileTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( pHoare202237534exec1p @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S @ ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs ) ) @ S ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_125_renumber__aux,axiom,
% 0.31/1.89 ! [A: produc410756839_state,F2: nat > produc410756839_state,R: set_Pr2096893127_state,B: produc410756839_state] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F2 @ I2 ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 & ( member512523024_state @ ( produc2065881943_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 => ( ( B
% 0.31/1.89 = ( F2 @ zero_zero_nat ) )
% 0.31/1.89 => ? [F3: nat > produc410756839_state] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member512523024_state @ ( produc2065881943_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_126_renumber__aux,axiom,
% 0.31/1.89 ! [A: list_com,F2: nat > list_com,R: set_Pr602326075st_com,B: list_com] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ A @ ( F2 @ I2 ) ) @ ( transi436345274st_com @ R ) )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ A @ B ) @ ( transi436345274st_com @ R ) )
% 0.31/1.89 => ( ( B
% 0.31/1.89 = ( F2 @ zero_zero_nat ) )
% 0.31/1.89 => ? [F3: nat > list_com] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member32358020st_com @ ( produc1307105171st_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_127_renumber__aux,axiom,
% 0.31/1.89 ! [A: list_P1040014977_state,F2: nat > list_P1040014977_state,R: set_Pr1142642759_state,B: list_P1040014977_state] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ A @ ( F2 @ I2 ) ) @ ( transi339813252_state @ R ) )
% 0.31/1.89 & ( member1267359376_state @ ( produc1298457559_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ A @ B ) @ ( transi339813252_state @ R ) )
% 0.31/1.89 => ( ( B
% 0.31/1.89 = ( F2 @ zero_zero_nat ) )
% 0.31/1.89 => ? [F3: nat > list_P1040014977_state] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member1267359376_state @ ( produc1298457559_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_128_renumber__aux,axiom,
% 0.31/1.89 ! [A: com,F2: nat > com,R: set_Pr1822651163om_com,B: com] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ ( F2 @ I2 ) ) @ ( transi863150634cl_com @ R ) )
% 0.31/1.89 & ( member1333916004om_com @ ( product_Pair_com_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ ( transi863150634cl_com @ R ) )
% 0.31/1.89 => ( ( B
% 0.31/1.89 = ( F2 @ zero_zero_nat ) )
% 0.31/1.89 => ? [F3: nat > com] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member1333916004om_com @ ( product_Pair_com_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_129_renumber__aux,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,F2: nat > produc2041926651_state,R: set_Pr1165141447_state,B: produc2041926651_state] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ ( F2 @ I2 ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 & ( member1069318160_state @ ( produc1909270103_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( B
% 0.31/1.89 = ( F2 @ zero_zero_nat ) )
% 0.31/1.89 => ? [F3: nat > produc2041926651_state] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_130_renumber,axiom,
% 0.31/1.89 ! [A: produc410756839_state,F2: nat > produc410756839_state,R: set_Pr2096893127_state] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F2 @ I2 ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 & ( member512523024_state @ ( produc2065881943_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ? [F3: nat > produc410756839_state] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member512523024_state @ ( produc2065881943_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_131_renumber,axiom,
% 0.31/1.89 ! [A: list_com,F2: nat > list_com,R: set_Pr602326075st_com] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ A @ ( F2 @ I2 ) ) @ ( transi436345274st_com @ R ) )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ? [F3: nat > list_com] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member32358020st_com @ ( produc1307105171st_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_132_renumber,axiom,
% 0.31/1.89 ! [A: list_P1040014977_state,F2: nat > list_P1040014977_state,R: set_Pr1142642759_state] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ A @ ( F2 @ I2 ) ) @ ( transi339813252_state @ R ) )
% 0.31/1.89 & ( member1267359376_state @ ( produc1298457559_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ? [F3: nat > list_P1040014977_state] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member1267359376_state @ ( produc1298457559_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_133_renumber,axiom,
% 0.31/1.89 ! [A: com,F2: nat > com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ ( F2 @ I2 ) ) @ ( transi863150634cl_com @ R ) )
% 0.31/1.89 & ( member1333916004om_com @ ( product_Pair_com_com @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ? [F3: nat > com] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member1333916004om_com @ ( product_Pair_com_com @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_134_renumber,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,F2: nat > produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ! [I2: nat] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ ( F2 @ I2 ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 & ( member1069318160_state @ ( produc1909270103_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) )
% 0.31/1.89 => ? [F3: nat > produc2041926651_state] :
% 0.31/1.89 ( ( ( F3 @ zero_zero_nat )
% 0.31/1.89 = A )
% 0.31/1.89 & ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_135_exec1p_OWhileFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com,Cs: list_com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( pHoare202237534exec1p @ ( cons_com @ ( while @ B @ C ) @ Cs ) @ S @ Cs @ S ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_136_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: com,Ay: com,Bx: com,By: com,R: set_Pr1675528647om_com,P: com > com > $o] :
% 0.31/1.89 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Ax @ Ay ) @ ( product_Pair_com_com @ Bx @ By ) ) @ ( transi1042416958om_com @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: com,B3: com,Aa: com,Ba: com] :
% 0.31/1.89 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ A3 @ B3 ) @ ( product_Pair_com_com @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Aa @ Ba ) @ ( product_Pair_com_com @ Bx @ By ) ) @ ( transi1042416958om_com @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_137_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.31/1.89 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.31/1.89 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A3 @ B3 ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Aa @ Ba ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_138_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.31/1.89 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: list_com,B3: list_com,Aa: list_com,Ba: list_com] :
% 0.31/1.89 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A3 @ B3 ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Aa @ Ba ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_139_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.31/1.89 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: list_list_com,B3: list_state,Aa: list_list_com,Ba: list_state] :
% 0.31/1.89 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A3 @ B3 ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Aa @ Ba ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_140_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.31/1.89 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: com > com > $o,B3: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.31/1.89 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A3 @ B3 ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Aa @ Ba ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_141_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: produc2041926651_state,B3: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_142_converse__rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ Bx @ By )
% 0.31/1.89 => ( ! [A3: list_com,B3: state,Aa: list_com,Ba: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A3 @ B3 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ Aa @ Ba )
% 0.31/1.89 => ( P @ A3 @ B3 ) ) ) )
% 0.31/1.89 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_143_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: com,Xb: com,Za: com,Zb: com,R: set_Pr1675528647om_com] :
% 0.31/1.89 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Xa @ Xb ) @ ( product_Pair_com_com @ Za @ Zb ) ) @ ( transi1042416958om_com @ R ) )
% 0.31/1.89 => ( ( ( product_Pair_com_com @ Xa @ Xb )
% 0.31/1.89 != ( product_Pair_com_com @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: com,B3: com] :
% 0.31/1.89 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Xa @ Xb ) @ ( product_Pair_com_com @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ A3 @ B3 ) @ ( product_Pair_com_com @ Za @ Zb ) ) @ ( transi1042416958om_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_144_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: list_P1040014977_state,Xb: list_P1040014977_state,Za: list_P1040014977_state,Zb: list_P1040014977_state,R: set_Pr1847866567_state] :
% 0.31/1.89 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) )
% 0.31/1.89 => ( ( ( produc1298457559_state @ Xa @ Xb )
% 0.31/1.89 != ( produc1298457559_state @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: list_P1040014977_state,B3: list_P1040014977_state] :
% 0.31/1.89 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A3 @ B3 ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_145_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: list_com,Xb: list_com,Za: list_com,Zb: list_com,R: set_Pr2083163591st_com] :
% 0.31/1.89 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/1.89 => ( ( ( produc1307105171st_com @ Xa @ Xb )
% 0.31/1.89 != ( produc1307105171st_com @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: list_com,B3: list_com] :
% 0.31/1.89 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A3 @ B3 ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_146_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: list_list_com,Xb: list_state,Za: list_list_com,Zb: list_state,R: set_Pr1419004359_state] :
% 0.31/1.89 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) )
% 0.31/1.89 => ( ( ( produc1742567891_state @ Xa @ Xb )
% 0.31/1.89 != ( produc1742567891_state @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: list_list_com,B3: list_state] :
% 0.31/1.89 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A3 @ B3 ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_147_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: com > com > $o,Xb: list_com,Za: com > com > $o,Zb: list_com,R: set_Pr135335153st_com] :
% 0.31/1.89 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/1.89 => ( ( ( produc1914379986st_com @ Xa @ Xb )
% 0.31/1.89 != ( produc1914379986st_com @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: com > com > $o,B3: list_com] :
% 0.31/1.89 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A3 @ B3 ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_148_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 => ( ( ( produc1909270103_state @ Xa @ Xb )
% 0.31/1.89 != ( produc1909270103_state @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_149_converse__rtranclE2,axiom,
% 0.31/1.89 ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( ( produc1204172211_state @ Xa @ Xb )
% 0.31/1.89 != ( produc1204172211_state @ Za @ Zb ) )
% 0.31/1.89 => ~ ! [A3: list_com,B3: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A3 @ B3 ) ) @ R )
% 0.31/1.89 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A3 @ B3 ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_150_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: com,Ay: com,Bx: com,By: com,R: set_Pr1675528647om_com,P: com > com > $o] :
% 0.31/1.89 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Ax @ Ay ) @ ( product_Pair_com_com @ Bx @ By ) ) @ ( transi1042416958om_com @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: com,B3: com,Aa: com,Ba: com] :
% 0.31/1.89 ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ Ax @ Ay ) @ ( product_Pair_com_com @ A3 @ B3 ) ) @ ( transi1042416958om_com @ R ) )
% 0.31/1.89 => ( ( member2105207824om_com @ ( produc1140939351om_com @ ( product_Pair_com_com @ A3 @ B3 ) @ ( product_Pair_com_com @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_151_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.31/1.89 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: list_P1040014977_state,B3: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.31/1.89 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ A3 @ B3 ) ) @ ( transi1428749162_state @ R ) )
% 0.31/1.89 => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A3 @ B3 ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_152_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.31/1.89 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: list_com,B3: list_com,Aa: list_com,Ba: list_com] :
% 0.31/1.89 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ A3 @ B3 ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/1.89 => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A3 @ B3 ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_153_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.31/1.89 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: list_list_com,B3: list_state,Aa: list_list_com,Ba: list_state] :
% 0.31/1.89 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ A3 @ B3 ) ) @ ( transi89280670_state @ R ) )
% 0.31/1.89 => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A3 @ B3 ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_154_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.31/1.89 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: com > com > $o,B3: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.31/1.89 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ A3 @ B3 ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/1.89 => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A3 @ B3 ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_155_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: produc2041926651_state,B3: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.31/1.89 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A3 @ B3 ) ) @ ( transi463013610_state @ R ) )
% 0.31/1.89 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_156_rtrancl__induct2,axiom,
% 0.31/1.89 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ Ax @ Ay )
% 0.31/1.89 => ( ! [A3: list_com,B3: state,Aa: list_com,Ba: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A3 @ B3 ) ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A3 @ B3 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( P @ Aa @ Ba ) ) ) )
% 0.31/1.89 => ( P @ Bx @ By ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_157_rtrancl__idemp,axiom,
% 0.31/1.89 ! [R: set_Pr2096893127_state] :
% 0.31/1.89 ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 0.31/1.89 = ( transi463013610_state @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_158_rtrancl__idemp,axiom,
% 0.31/1.89 ! [R: set_Pr602326075st_com] :
% 0.31/1.89 ( ( transi436345274st_com @ ( transi436345274st_com @ R ) )
% 0.31/1.89 = ( transi436345274st_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_159_rtrancl__idemp,axiom,
% 0.31/1.89 ! [R: set_Pr1142642759_state] :
% 0.31/1.89 ( ( transi339813252_state @ ( transi339813252_state @ R ) )
% 0.31/1.89 = ( transi339813252_state @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_160_rtrancl__idemp,axiom,
% 0.31/1.89 ! [R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( transi863150634cl_com @ ( transi863150634cl_com @ R ) )
% 0.31/1.89 = ( transi863150634cl_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_161_rtrancl__idemp,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 0.31/1.89 = ( transi1302705790_state @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_162_r__into__rtrancl,axiom,
% 0.31/1.89 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 0.31/1.89 ( ( member512523024_state @ P2 @ R )
% 0.31/1.89 => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_163_r__into__rtrancl,axiom,
% 0.31/1.89 ! [P2: produc258871771st_com,R: set_Pr602326075st_com] :
% 0.31/1.89 ( ( member32358020st_com @ P2 @ R )
% 0.31/1.89 => ( member32358020st_com @ P2 @ ( transi436345274st_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_164_r__into__rtrancl,axiom,
% 0.31/1.89 ! [P2: produc1225889383_state,R: set_Pr1142642759_state] :
% 0.31/1.89 ( ( member1267359376_state @ P2 @ R )
% 0.31/1.89 => ( member1267359376_state @ P2 @ ( transi339813252_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_165_r__into__rtrancl,axiom,
% 0.31/1.89 ! [P2: product_prod_com_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member1333916004om_com @ P2 @ R )
% 0.31/1.89 => ( member1333916004om_com @ P2 @ ( transi863150634cl_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_166_r__into__rtrancl,axiom,
% 0.31/1.89 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1069318160_state @ P2 @ R )
% 0.31/1.89 => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_167_exec__impl__execs,axiom,
% 0.31/1.89 ! [S: state,C: com,S2: state,Cs: list_com] :
% 0.31/1.89 ( ( exec @ S @ C @ S2 )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_168_exec_OWhileTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com,T: state,U: state] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( ( exec @ S @ C @ T )
% 0.31/1.89 => ( ( exec @ T @ ( while @ B @ C ) @ U )
% 0.31/1.89 => ( exec @ S @ ( while @ B @ C ) @ U ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_169_exec_OWhileFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( exec @ S @ ( while @ B @ C ) @ S ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_170_exec_OIfTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C1: com,T: state,C22: com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( ( exec @ S @ C1 @ T )
% 0.31/1.89 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_171_exec_OIfFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C22: com,T: state,C1: com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( ( exec @ S @ C22 @ T )
% 0.31/1.89 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_172_exec_ODo,axiom,
% 0.31/1.89 ! [T: state,F2: state > set_state,S: state] :
% 0.31/1.89 ( ( member_state @ T @ ( F2 @ S ) )
% 0.31/1.89 => ( exec @ S @ ( do @ F2 ) @ T ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_173_exec_OSemi,axiom,
% 0.31/1.89 ! [S0: state,C1: com,S1: state,C22: com,S22: state] :
% 0.31/1.89 ( ( exec @ S0 @ C1 @ S1 )
% 0.31/1.89 => ( ( exec @ S1 @ C22 @ S22 )
% 0.31/1.89 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_174_converse__rtrancl__into__rtrancl,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_175_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_176_converse__rtrancl__induct,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ B )
% 0.31/1.89 => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ Z )
% 0.31/1.89 => ( P @ Y3 ) ) ) )
% 0.31/1.89 => ( P @ A ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_177_rtrancl_Ortrancl__refl,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ ( transi1302705790_state @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_178_converse__rtranclE,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( X != Z2 )
% 0.31/1.89 => ~ ! [Y3: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_179_rtrancl_Oinducts,axiom,
% 0.31/1.89 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ! [A3: produc2041926651_state] : ( P @ A3 @ A3 )
% 0.31/1.89 => ( ! [A3: produc2041926651_state,B3: produc2041926651_state,C2: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ A3 @ B3 )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ B3 @ C2 ) @ R )
% 0.31/1.89 => ( P @ A3 @ C2 ) ) ) )
% 0.31/1.89 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_180_rtrancl__induct,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( P @ A )
% 0.31/1.89 => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.31/1.89 => ( ( P @ Y3 )
% 0.31/1.89 => ( P @ Z ) ) ) )
% 0.31/1.89 => ( P @ B ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_181_rtrancl__trans,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_182_rtrancl_Osimps,axiom,
% 0.31/1.89 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 = ( ? [A5: produc2041926651_state] :
% 0.31/1.89 ( ( A1 = A5 )
% 0.31/1.89 & ( A22 = A5 ) )
% 0.31/1.89 | ? [A5: produc2041926651_state,B4: produc2041926651_state,C3: produc2041926651_state] :
% 0.31/1.89 ( ( A1 = A5 )
% 0.31/1.89 & ( A22 = C3 )
% 0.31/1.89 & ( member1069318160_state @ ( produc1909270103_state @ A5 @ B4 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 & ( member1069318160_state @ ( produc1909270103_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_183_rtrancl_Ocases,axiom,
% 0.31/1.89 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( A22 != A1 )
% 0.31/1.89 => ~ ! [B3: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B3 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ~ ( member1069318160_state @ ( produc1909270103_state @ B3 @ A22 ) @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_184_rtranclE,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( A != B )
% 0.31/1.89 => ~ ! [Y3: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ B ) @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_185_exec1s__impl__exec,axiom,
% 0.31/1.89 ! [C: com,S: state,T: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/1.89 => ( exec @ S @ C @ T ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_186_app__execs,axiom,
% 0.31/1.89 ! [Cs: list_com,S: state,Cs2: list_com,S2: state,Cs22: list_com] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_187_termis_Osimps_I2_J,axiom,
% 0.31/1.89 ! [C: com,Cs: list_com,S: state] :
% 0.31/1.89 ( ( pHoare806997636termis @ ( cons_com @ C @ Cs ) @ S )
% 0.31/1.89 = ( ( termi @ C @ S )
% 0.31/1.89 & ! [T2: state] :
% 0.31/1.89 ( ( exec @ S @ C @ T2 )
% 0.31/1.89 => ( pHoare806997636termis @ Cs @ T2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_188_execs_Ointros_I2_J,axiom,
% 0.31/1.89 ! [S: state,C: com,T: state,Cs: list_com,U: state] :
% 0.31/1.89 ( ( exec @ S @ C @ T )
% 0.31/1.89 => ( ( pHoare259243732_execs @ T @ Cs @ U )
% 0.31/1.89 => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs ) @ U ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_189_same__fstI,axiom,
% 0.31/1.89 ! [P: list_com > $o,X: list_com,Y4: state,Y: state,R2: list_com > set_Pr795498619_state] :
% 0.31/1.89 ( ( P @ X )
% 0.31/1.89 => ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Y ) @ ( R2 @ X ) )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ X @ Y4 ) @ ( produc1204172211_state @ X @ Y ) ) @ ( same_f855297288_state @ P @ R2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_190_same__fstI,axiom,
% 0.31/1.89 ! [P: produc2041926651_state > $o,X: produc2041926651_state,Y4: produc2041926651_state,Y: produc2041926651_state,R2: produc2041926651_state > set_Pr1165141447_state] :
% 0.31/1.89 ( ( P @ X )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ Y4 @ Y ) @ ( R2 @ X ) )
% 0.31/1.89 => ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ X @ Y4 ) @ ( produc1909270103_state @ X @ Y ) ) @ ( same_f1258458156_state @ P @ R2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_191_same__append__eq,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ Ys )
% 0.31/1.89 = ( append_com @ Xs @ Zs ) )
% 0.31/1.89 = ( Ys = Zs ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_192_append__same__eq,axiom,
% 0.31/1.89 ! [Ys: list_com,Xs: list_com,Zs: list_com] :
% 0.31/1.89 ( ( ( append_com @ Ys @ Xs )
% 0.31/1.89 = ( append_com @ Zs @ Xs ) )
% 0.31/1.89 = ( Ys = Zs ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_193_append__assoc,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ( append_com @ ( append_com @ Xs @ Ys ) @ Zs )
% 0.31/1.89 = ( append_com @ Xs @ ( append_com @ Ys @ Zs ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_194_append_Oassoc,axiom,
% 0.31/1.89 ! [A: list_com,B: list_com,C: list_com] :
% 0.31/1.89 ( ( append_com @ ( append_com @ A @ B ) @ C )
% 0.31/1.89 = ( append_com @ A @ ( append_com @ B @ C ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_195_append_Oright__neutral,axiom,
% 0.31/1.89 ! [A: list_com] :
% 0.31/1.89 ( ( append_com @ A @ nil_com )
% 0.31/1.89 = A ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_196_append__is__Nil__conv,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ Ys )
% 0.31/1.89 = nil_com )
% 0.31/1.89 = ( ( Xs = nil_com )
% 0.31/1.89 & ( Ys = nil_com ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_197_Nil__is__append__conv,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( nil_com
% 0.31/1.89 = ( append_com @ Xs @ Ys ) )
% 0.31/1.89 = ( ( Xs = nil_com )
% 0.31/1.89 & ( Ys = nil_com ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_198_self__append__conv2,axiom,
% 0.31/1.89 ! [Ys: list_com,Xs: list_com] :
% 0.31/1.89 ( ( Ys
% 0.31/1.89 = ( append_com @ Xs @ Ys ) )
% 0.31/1.89 = ( Xs = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_199_append__self__conv2,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ Ys )
% 0.31/1.89 = Ys )
% 0.31/1.89 = ( Xs = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_200_self__append__conv,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( append_com @ Xs @ Ys ) )
% 0.31/1.89 = ( Ys = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_201_append__self__conv,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ Ys )
% 0.31/1.89 = Xs )
% 0.31/1.89 = ( Ys = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_202_append__Nil2,axiom,
% 0.31/1.89 ! [Xs: list_com] :
% 0.31/1.89 ( ( append_com @ Xs @ nil_com )
% 0.31/1.89 = Xs ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_203_append1__eq__conv,axiom,
% 0.31/1.89 ! [Xs: list_com,X: com,Ys: list_com,Y: com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ ( cons_com @ X @ nil_com ) )
% 0.31/1.89 = ( append_com @ Ys @ ( cons_com @ Y @ nil_com ) ) )
% 0.31/1.89 = ( ( Xs = Ys )
% 0.31/1.89 & ( X = Y ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_204_rev__nonempty__induct,axiom,
% 0.31/1.89 ! [Xs: list_com,P: list_com > $o] :
% 0.31/1.89 ( ( Xs != nil_com )
% 0.31/1.89 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com] :
% 0.31/1.89 ( ( Xs2 != nil_com )
% 0.31/1.89 => ( ( P @ Xs2 )
% 0.31/1.89 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 0.31/1.89 => ( P @ Xs ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_205_append__eq__Cons__conv,axiom,
% 0.31/1.89 ! [Ys: list_com,Zs: list_com,X: com,Xs: list_com] :
% 0.31/1.89 ( ( ( append_com @ Ys @ Zs )
% 0.31/1.89 = ( cons_com @ X @ Xs ) )
% 0.31/1.89 = ( ( ( Ys = nil_com )
% 0.31/1.89 & ( Zs
% 0.31/1.89 = ( cons_com @ X @ Xs ) ) )
% 0.31/1.89 | ? [Ys2: list_com] :
% 0.31/1.89 ( ( Ys
% 0.31/1.89 = ( cons_com @ X @ Ys2 ) )
% 0.31/1.89 & ( ( append_com @ Ys2 @ Zs )
% 0.31/1.89 = Xs ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_206_Cons__eq__append__conv,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ( ( cons_com @ X @ Xs )
% 0.31/1.89 = ( append_com @ Ys @ Zs ) )
% 0.31/1.89 = ( ( ( Ys = nil_com )
% 0.31/1.89 & ( ( cons_com @ X @ Xs )
% 0.31/1.89 = Zs ) )
% 0.31/1.89 | ? [Ys2: list_com] :
% 0.31/1.89 ( ( ( cons_com @ X @ Ys2 )
% 0.31/1.89 = Ys )
% 0.31/1.89 & ( Xs
% 0.31/1.89 = ( append_com @ Ys2 @ Zs ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_207_rev__exhaust,axiom,
% 0.31/1.89 ! [Xs: list_com] :
% 0.31/1.89 ( ( Xs != nil_com )
% 0.31/1.89 => ~ ! [Ys3: list_com,Y3: com] :
% 0.31/1.89 ( Xs
% 0.31/1.89 != ( append_com @ Ys3 @ ( cons_com @ Y3 @ nil_com ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_208_rev__induct,axiom,
% 0.31/1.89 ! [P: list_com > $o,Xs: list_com] :
% 0.31/1.89 ( ( P @ nil_com )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com] :
% 0.31/1.89 ( ( P @ Xs2 )
% 0.31/1.89 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) )
% 0.31/1.89 => ( P @ Xs ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_209_transpose_Ocases,axiom,
% 0.31/1.89 ! [X: list_list_com] :
% 0.31/1.89 ( ( X != nil_list_com )
% 0.31/1.89 => ( ! [Xss: list_list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( cons_list_com @ nil_com @ Xss ) )
% 0.31/1.89 => ~ ! [X3: com,Xs2: list_com,Xss: list_list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( cons_list_com @ ( cons_com @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_210_execs_Ointros_I1_J,axiom,
% 0.31/1.89 ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_211_append__eq__append__conv2,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,Zs: list_com,Ts: list_com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ Ys )
% 0.31/1.89 = ( append_com @ Zs @ Ts ) )
% 0.31/1.89 = ( ? [Us: list_com] :
% 0.31/1.89 ( ( ( Xs
% 0.31/1.89 = ( append_com @ Zs @ Us ) )
% 0.31/1.89 & ( ( append_com @ Us @ Ys )
% 0.31/1.89 = Ts ) )
% 0.31/1.89 | ( ( ( append_com @ Xs @ Us )
% 0.31/1.89 = Zs )
% 0.31/1.89 & ( Ys
% 0.31/1.89 = ( append_com @ Us @ Ts ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_212_append_Oleft__neutral,axiom,
% 0.31/1.89 ! [A: list_com] :
% 0.31/1.89 ( ( append_com @ nil_com @ A )
% 0.31/1.89 = A ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_213_append__eq__appendI,axiom,
% 0.31/1.89 ! [Xs: list_com,Xs1: list_com,Zs: list_com,Ys: list_com,Us2: list_com] :
% 0.31/1.89 ( ( ( append_com @ Xs @ Xs1 )
% 0.31/1.89 = Zs )
% 0.31/1.89 => ( ( Ys
% 0.31/1.89 = ( append_com @ Xs1 @ Us2 ) )
% 0.31/1.89 => ( ( append_com @ Xs @ Ys )
% 0.31/1.89 = ( append_com @ Zs @ Us2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_214_append__Nil,axiom,
% 0.31/1.89 ! [Ys: list_com] :
% 0.31/1.89 ( ( append_com @ nil_com @ Ys )
% 0.31/1.89 = Ys ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_215_eq__Nil__appendI,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( Xs = Ys )
% 0.31/1.89 => ( Xs
% 0.31/1.89 = ( append_com @ nil_com @ Ys ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_216_append__Cons,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( append_com @ ( cons_com @ X @ Xs ) @ Ys )
% 0.31/1.89 = ( cons_com @ X @ ( append_com @ Xs @ Ys ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_217_Cons__eq__appendI,axiom,
% 0.31/1.89 ! [X: com,Xs1: list_com,Ys: list_com,Xs: list_com,Zs: list_com] :
% 0.31/1.89 ( ( ( cons_com @ X @ Xs1 )
% 0.31/1.89 = Ys )
% 0.31/1.89 => ( ( Xs
% 0.31/1.89 = ( append_com @ Xs1 @ Zs ) )
% 0.31/1.89 => ( ( cons_com @ X @ Xs )
% 0.31/1.89 = ( append_com @ Ys @ Zs ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_218_splice_Ocases,axiom,
% 0.31/1.89 ! [X: produc258871771st_com] :
% 0.31/1.89 ( ! [Ys3: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 0.31/1.89 => ~ ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_219_shuffles_Ocases,axiom,
% 0.31/1.89 ! [X: produc258871771st_com] :
% 0.31/1.89 ( ! [Ys3: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 0.31/1.89 => ( ! [Xs2: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1307105171st_com @ Xs2 @ nil_com ) )
% 0.31/1.89 => ~ ! [X3: com,Xs2: list_com,Y3: com,Ys3: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_220_sorted__wrt_Ocases,axiom,
% 0.31/1.89 ! [X: produc2058209240st_com] :
% 0.31/1.89 ( ! [P3: com > com > $o] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.31/1.89 => ~ ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys3 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_221_successively_Ocases,axiom,
% 0.31/1.89 ! [X: produc2058209240st_com] :
% 0.31/1.89 ( ! [P3: com > com > $o] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.31/1.89 => ( ! [P3: com > com > $o,X3: com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 0.31/1.89 => ~ ! [P3: com > com > $o,X3: com,Y3: com,Xs2: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_222_map__tailrec__rev_Oinduct,axiom,
% 0.31/1.89 ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 0.31/1.89 ( ! [F3: com > com,X_1: list_com] : ( P @ F3 @ nil_com @ X_1 )
% 0.31/1.89 => ( ! [F3: com > com,A3: com,As: list_com,Bs: list_com] :
% 0.31/1.89 ( ( P @ F3 @ As @ ( cons_com @ ( F3 @ A3 ) @ Bs ) )
% 0.31/1.89 => ( P @ F3 @ ( cons_com @ A3 @ As ) @ Bs ) )
% 0.31/1.89 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_223_list__nonempty__induct,axiom,
% 0.31/1.89 ! [Xs: list_com,P: list_com > $o] :
% 0.31/1.89 ( ( Xs != nil_com )
% 0.31/1.89 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com] :
% 0.31/1.89 ( ( Xs2 != nil_com )
% 0.31/1.89 => ( ( P @ Xs2 )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ Xs2 ) ) ) )
% 0.31/1.89 => ( P @ Xs ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_224_successively_Oinduct,axiom,
% 0.31/1.89 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.31/1.89 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.31/1.89 => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 0.31/1.89 => ( ! [P3: com > com > $o,X3: com,Y3: com,Xs2: list_com] :
% 0.31/1.89 ( ( P @ P3 @ ( cons_com @ Y3 @ Xs2 ) )
% 0.31/1.89 => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) )
% 0.31/1.89 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_225_remdups__adj_Oinduct,axiom,
% 0.31/1.89 ! [P: list_com > $o,A0: list_com] :
% 0.31/1.89 ( ( P @ nil_com )
% 0.31/1.89 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/1.89 => ( ! [X3: com,Y3: com,Xs2: list_com] :
% 0.31/1.89 ( ( ( X3 = Y3 )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ Xs2 ) ) )
% 0.31/1.89 => ( ( ( X3 != Y3 )
% 0.31/1.89 => ( P @ ( cons_com @ Y3 @ Xs2 ) ) )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) ) )
% 0.31/1.89 => ( P @ A0 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_226_sorted__wrt_Oinduct,axiom,
% 0.31/1.89 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.31/1.89 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.31/1.89 => ( ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 0.31/1.89 ( ( P @ P3 @ Ys3 )
% 0.31/1.89 => ( P @ P3 @ ( cons_com @ X3 @ Ys3 ) ) )
% 0.31/1.89 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_227_remdups__adj_Ocases,axiom,
% 0.31/1.89 ! [X: list_com] :
% 0.31/1.89 ( ( X != nil_com )
% 0.31/1.89 => ( ! [X3: com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( cons_com @ X3 @ nil_com ) )
% 0.31/1.89 => ~ ! [X3: com,Y3: com,Xs2: list_com] :
% 0.31/1.89 ( X
% 0.31/1.89 != ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_228_shuffles_Oinduct,axiom,
% 0.31/1.89 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.31/1.89 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.31/1.89 => ( ! [Xs2: list_com] : ( P @ Xs2 @ nil_com )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com,Y3: com,Ys3: list_com] :
% 0.31/1.89 ( ( P @ Xs2 @ ( cons_com @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) ) )
% 0.31/1.89 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_229_induct__list012,axiom,
% 0.31/1.89 ! [P: list_com > $o,Xs: list_com] :
% 0.31/1.89 ( ( P @ nil_com )
% 0.31/1.89 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/1.89 => ( ! [X3: com,Y3: com,Zs2: list_com] :
% 0.31/1.89 ( ( P @ Zs2 )
% 0.31/1.89 => ( ( P @ ( cons_com @ Y3 @ Zs2 ) )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Zs2 ) ) ) ) )
% 0.31/1.89 => ( P @ Xs ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_230_splice_Oinduct,axiom,
% 0.31/1.89 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.31/1.89 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 0.31/1.89 ( ( P @ Ys3 @ Xs2 )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) )
% 0.31/1.89 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_231_list__induct2_H,axiom,
% 0.31/1.89 ! [P: list_com > list_com > $o,Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( P @ nil_com @ nil_com )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com] : ( P @ ( cons_com @ X3 @ Xs2 ) @ nil_com )
% 0.31/1.89 => ( ! [Y3: com,Ys3: list_com] : ( P @ nil_com @ ( cons_com @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ! [X3: com,Xs2: list_com,Y3: com,Ys3: list_com] :
% 0.31/1.89 ( ( P @ Xs2 @ Ys3 )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) )
% 0.31/1.89 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_232_neq__Nil__conv,axiom,
% 0.31/1.89 ! [Xs: list_com] :
% 0.31/1.89 ( ( Xs != nil_com )
% 0.31/1.89 = ( ? [Y5: com,Ys4: list_com] :
% 0.31/1.89 ( Xs
% 0.31/1.89 = ( cons_com @ Y5 @ Ys4 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_233_list_Oinducts,axiom,
% 0.31/1.89 ! [P: list_com > $o,List: list_com] :
% 0.31/1.89 ( ( P @ nil_com )
% 0.31/1.89 => ( ! [X12: com,X23: list_com] :
% 0.31/1.89 ( ( P @ X23 )
% 0.31/1.89 => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 0.31/1.89 => ( P @ List ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_234_list_Oexhaust,axiom,
% 0.31/1.89 ! [Y: list_com] :
% 0.31/1.89 ( ( Y != nil_com )
% 0.31/1.89 => ~ ! [X212: com,X222: list_com] :
% 0.31/1.89 ( Y
% 0.31/1.89 != ( cons_com @ X212 @ X222 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_235_list_OdiscI,axiom,
% 0.31/1.89 ! [List: list_com,X21: com,X22: list_com] :
% 0.31/1.89 ( ( List
% 0.31/1.89 = ( cons_com @ X21 @ X22 ) )
% 0.31/1.89 => ( List != nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_236_list_Odistinct_I1_J,axiom,
% 0.31/1.89 ! [X21: com,X22: list_com] :
% 0.31/1.89 ( nil_com
% 0.31/1.89 != ( cons_com @ X21 @ X22 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_237_execs_Ocases,axiom,
% 0.31/1.89 ! [A1: state,A22: list_com,A32: state] :
% 0.31/1.89 ( ( pHoare259243732_execs @ A1 @ A22 @ A32 )
% 0.31/1.89 => ( ( ( A22 = nil_com )
% 0.31/1.89 => ( A32 != A1 ) )
% 0.31/1.89 => ~ ! [C2: com,T3: state,Cs4: list_com] :
% 0.31/1.89 ( ( A22
% 0.31/1.89 = ( cons_com @ C2 @ Cs4 ) )
% 0.31/1.89 => ( ( exec @ A1 @ C2 @ T3 )
% 0.31/1.89 => ~ ( pHoare259243732_execs @ T3 @ Cs4 @ A32 ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_238_execs_Osimps,axiom,
% 0.31/1.89 ( pHoare259243732_execs
% 0.31/1.89 = ( ^ [A12: state,A23: list_com,A33: state] :
% 0.31/1.89 ( ? [S3: state] :
% 0.31/1.89 ( ( A12 = S3 )
% 0.31/1.89 & ( A23 = nil_com )
% 0.31/1.89 & ( A33 = S3 ) )
% 0.31/1.89 | ? [S3: state,C3: com,T2: state,Cs3: list_com,U2: state] :
% 0.31/1.89 ( ( A12 = S3 )
% 0.31/1.89 & ( A23
% 0.31/1.89 = ( cons_com @ C3 @ Cs3 ) )
% 0.31/1.89 & ( A33 = U2 )
% 0.31/1.89 & ( exec @ S3 @ C3 @ T2 )
% 0.31/1.89 & ( pHoare259243732_execs @ T2 @ Cs3 @ U2 ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_239_execs_Oinducts,axiom,
% 0.31/1.89 ! [X1: state,X2: list_com,X34: state,P: state > list_com > state > $o] :
% 0.31/1.89 ( ( pHoare259243732_execs @ X1 @ X2 @ X34 )
% 0.31/1.89 => ( ! [S4: state] : ( P @ S4 @ nil_com @ S4 )
% 0.31/1.89 => ( ! [S4: state,C2: com,T3: state,Cs4: list_com,U3: state] :
% 0.31/1.89 ( ( exec @ S4 @ C2 @ T3 )
% 0.31/1.89 => ( ( pHoare259243732_execs @ T3 @ Cs4 @ U3 )
% 0.31/1.89 => ( ( P @ T3 @ Cs4 @ U3 )
% 0.31/1.89 => ( P @ S4 @ ( cons_com @ C2 @ Cs4 ) @ U3 ) ) ) )
% 0.31/1.89 => ( P @ X1 @ X2 @ X34 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_240_while__termiE,axiom,
% 0.31/1.89 ! [B: state > $o,C: com,S: state] :
% 0.31/1.89 ( ( termi @ ( while @ B @ C ) @ S )
% 0.31/1.89 => ( ( B @ S )
% 0.31/1.89 => ( termi @ C @ S ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_241_termis_Osimps_I1_J,axiom,
% 0.31/1.89 ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_242_gen__length__code_I1_J,axiom,
% 0.31/1.89 ! [N: nat] :
% 0.31/1.89 ( ( gen_length_com @ N @ nil_com )
% 0.31/1.89 = N ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_243_while__termiE2,axiom,
% 0.31/1.89 ! [B: state > $o,C: com,S: state,T: state] :
% 0.31/1.89 ( ( termi @ ( while @ B @ C ) @ S )
% 0.31/1.89 => ( ( B @ S )
% 0.31/1.89 => ( ( exec @ S @ C @ T )
% 0.31/1.89 => ( termi @ ( while @ B @ C ) @ T ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_244_exec1s__impl__execs,axiom,
% 0.31/1.89 ! [Cs: list_com,S: state,T: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/1.89 => ( pHoare259243732_execs @ S @ Cs @ T ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_245_execs__pres__termi,axiom,
% 0.31/1.89 ! [C: com,S: state,C4: com,Cs2: list_com,S2: state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C4 @ Cs2 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/1.89 => ( ( termi @ C @ S )
% 0.31/1.89 => ( termi @ C4 @ S2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_246_app__exec,axiom,
% 0.31/1.89 ! [Cs: list_com,S: state,Cs2: list_com,S2: state,Cs22: list_com] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/1.89 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_247_exec1E_I1_J,axiom,
% 0.31/1.89 ! [S: state,Cs2: list_com,S2: state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ nil_com @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ pHoare259243666_exec1 ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_248_termi__while,axiom,
% 0.31/1.89 ! [B: state > $o,C: com,F2: nat > state,K: nat] :
% 0.31/1.89 ( ( termi @ ( while @ B @ C ) @ ( F2 @ K ) )
% 0.31/1.89 => ( ! [I2: nat] : ( exec @ ( F2 @ I2 ) @ C @ ( F2 @ ( suc @ I2 ) ) )
% 0.31/1.89 => ? [I2: nat] :
% 0.31/1.89 ~ ( B @ ( F2 @ I2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_249_termi__while__lemma,axiom,
% 0.31/1.89 ! [W: com,Fk: state,F2: nat > state,K: nat,B: state > $o,C: com] :
% 0.31/1.89 ( ( termi @ W @ Fk )
% 0.31/1.89 => ( ( ( Fk
% 0.31/1.89 = ( F2 @ K ) )
% 0.31/1.89 & ( W
% 0.31/1.89 = ( while @ B @ C ) )
% 0.31/1.89 & ! [I2: nat] : ( exec @ ( F2 @ I2 ) @ C @ ( F2 @ ( suc @ I2 ) ) ) )
% 0.31/1.89 => ? [I2: nat] :
% 0.31/1.89 ~ ( B @ ( F2 @ I2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_250_termi_OSemi,axiom,
% 0.31/1.89 ! [C1: com,S0: state,C22: com] :
% 0.31/1.89 ( ( termi @ C1 @ S0 )
% 0.31/1.89 => ( ! [S12: state] :
% 0.31/1.89 ( ( exec @ S0 @ C1 @ S12 )
% 0.31/1.89 => ( termi @ C22 @ S12 ) )
% 0.31/1.89 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_251_termi_OWhileTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( ( termi @ C @ S )
% 0.31/1.89 => ( ! [T3: state] :
% 0.31/1.89 ( ( exec @ S @ C @ T3 )
% 0.31/1.89 => ( termi @ ( while @ B @ C ) @ T3 ) )
% 0.31/1.89 => ( termi @ ( while @ B @ C ) @ S ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_252_termi_OIfFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C22: com,C1: com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( ( termi @ C22 @ S )
% 0.31/1.89 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_253_termi_OWhileFalse,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C: com] :
% 0.31/1.89 ( ~ ( B @ S )
% 0.31/1.89 => ( termi @ ( while @ B @ C ) @ S ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_254_termi_OIfTrue,axiom,
% 0.31/1.89 ! [B: state > $o,S: state,C1: com,C22: com] :
% 0.31/1.89 ( ( B @ S )
% 0.31/1.89 => ( ( termi @ C1 @ S )
% 0.31/1.89 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_255_n__lists__Nil,axiom,
% 0.31/1.89 ! [N: nat] :
% 0.31/1.89 ( ( ( N = zero_zero_nat )
% 0.31/1.89 => ( ( n_lists_com @ N @ nil_com )
% 0.31/1.89 = ( cons_list_com @ nil_com @ nil_list_com ) ) )
% 0.31/1.89 & ( ( N != zero_zero_nat )
% 0.31/1.89 => ( ( n_lists_com @ N @ nil_com )
% 0.31/1.89 = nil_list_com ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_256_n__lists_Osimps_I1_J,axiom,
% 0.31/1.89 ! [Xs: list_com] :
% 0.31/1.89 ( ( n_lists_com @ zero_zero_nat @ Xs )
% 0.31/1.89 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_257_product__lists_Osimps_I1_J,axiom,
% 0.31/1.89 ( ( product_lists_com @ nil_list_com )
% 0.31/1.89 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_258_bind__simps_I2_J,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com,F2: com > list_com] :
% 0.31/1.89 ( ( bind_com_com @ ( cons_com @ X @ Xs ) @ F2 )
% 0.31/1.89 = ( append_com @ ( F2 @ X ) @ ( bind_com_com @ Xs @ F2 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_259_subseqs_Osimps_I1_J,axiom,
% 0.31/1.89 ( ( subseqs_com @ nil_com )
% 0.31/1.89 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_260_snoc__listrel1__snoc__iff,axiom,
% 0.31/1.89 ! [Xs: list_com,X: com,Ys: list_com,Y: com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 0.31/1.89 = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.31/1.89 & ( X = Y ) )
% 0.31/1.89 | ( ( Xs = Ys )
% 0.31/1.89 & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_261_snoc__listrel1__snoc__iff,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,X: produc2041926651_state,Ys: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 & ( X = Y ) )
% 0.31/1.89 | ( ( Xs = Ys )
% 0.31/1.89 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_262_bind__simps_I1_J,axiom,
% 0.31/1.89 ! [F2: com > list_com] :
% 0.31/1.89 ( ( bind_com_com @ nil_com @ F2 )
% 0.31/1.89 = nil_com ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_263_Cons__listrel1__Cons,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( listrel1_com @ R ) )
% 0.31/1.89 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/1.89 & ( Xs = Ys ) )
% 0.31/1.89 | ( ( X = Y )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_264_Cons__listrel1__Cons,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/1.89 & ( Xs = Ys ) )
% 0.31/1.89 | ( ( X = Y )
% 0.31/1.89 & ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_265_rtrancl__listrel1__ConsI1,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_266_listrel1I2,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_267_not__Nil__listrel1,axiom,
% 0.31/1.89 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel1_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_268_not__listrel1__Nil,axiom,
% 0.31/1.89 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_269_append__listrel1I,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com,Us2: list_com,Vs: list_com] :
% 0.31/1.89 ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.31/1.89 & ( Us2 = Vs ) )
% 0.31/1.89 | ( ( Xs = Ys )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ Us2 @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Us2 ) @ ( append_com @ Ys @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_270_listrel1I1,axiom,
% 0.31/1.89 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Xs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_271_listrel1I1,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Xs ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_272_Cons__listrel1E1,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ Ys ) @ ( listrel1_com @ R ) )
% 0.31/1.89 => ( ! [Y3: com] :
% 0.31/1.89 ( ( Ys
% 0.31/1.89 = ( cons_com @ Y3 @ Xs ) )
% 0.31/1.89 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y3 ) @ R ) )
% 0.31/1.89 => ~ ! [Zs2: list_com] :
% 0.31/1.89 ( ( Ys
% 0.31/1.89 = ( cons_com @ X @ Zs2 ) )
% 0.31/1.89 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Zs2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_273_Cons__listrel1E1,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 => ( ! [Y3: produc2041926651_state] :
% 0.31/1.89 ( ( Ys
% 0.31/1.89 = ( cons_P465369265_state @ Y3 @ Xs ) )
% 0.31/1.89 => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R ) )
% 0.31/1.89 => ~ ! [Zs2: list_P1040014977_state] :
% 0.31/1.89 ( ( Ys
% 0.31/1.89 = ( cons_P465369265_state @ X @ Zs2 ) )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_274_Cons__listrel1E2,axiom,
% 0.31/1.89 ! [Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys ) ) @ ( listrel1_com @ R ) )
% 0.31/1.89 => ( ! [X3: com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_com @ X3 @ Ys ) )
% 0.31/1.89 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 0.31/1.89 => ~ ! [Zs2: list_com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_com @ Y @ Zs2 ) )
% 0.31/1.89 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs2 @ Ys ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_275_Cons__listrel1E2,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 => ( ! [X3: produc2041926651_state] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_P465369265_state @ X3 @ Ys ) )
% 0.31/1.89 => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 0.31/1.89 => ~ ! [Zs2: list_P1040014977_state] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_P465369265_state @ Y @ Zs2 ) )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs2 @ Ys ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_276_listrel1I,axiom,
% 0.31/1.89 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Us2: list_com,Vs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/1.89 => ( ( Xs
% 0.31/1.89 = ( append_com @ Us2 @ ( cons_com @ X @ Vs ) ) )
% 0.31/1.89 => ( ( Ys
% 0.31/1.89 = ( append_com @ Us2 @ ( cons_com @ Y @ Vs ) ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_277_listrel1I,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Us2: list_P1040014977_state,Vs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/1.89 => ( ( Xs
% 0.31/1.89 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ X @ Vs ) ) )
% 0.31/1.89 => ( ( Ys
% 0.31/1.89 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_278_listrel1E,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel1_com @ R ) )
% 0.31/1.89 => ~ ! [X3: com,Y3: com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ! [Us3: list_com,Vs2: list_com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 0.31/1.89 => ( Ys
% 0.31/1.89 != ( append_com @ Us3 @ ( cons_com @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_279_listrel1E,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 0.31/1.89 => ( Ys
% 0.31/1.89 != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_280_rtrancl__listrel1__ConsI2,axiom,
% 0.31/1.89 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_281_rtrancl__listrel1__ConsI2,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_282_maps__simps_I1_J,axiom,
% 0.31/1.89 ! [F2: com > list_com,X: com,Xs: list_com] :
% 0.31/1.89 ( ( maps_com_com @ F2 @ ( cons_com @ X @ Xs ) )
% 0.31/1.89 = ( append_com @ ( F2 @ X ) @ ( maps_com_com @ F2 @ Xs ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_283_insert__Nil,axiom,
% 0.31/1.89 ! [X: com] :
% 0.31/1.89 ( ( insert_com @ X @ nil_com )
% 0.31/1.89 = ( cons_com @ X @ nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_284_concat__eq__append__conv,axiom,
% 0.31/1.89 ! [Xss2: list_list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ( ( concat_com @ Xss2 )
% 0.31/1.89 = ( append_com @ Ys @ Zs ) )
% 0.31/1.89 = ( ( ( Xss2 = nil_list_com )
% 0.31/1.89 => ( ( Ys = nil_com )
% 0.31/1.89 & ( Zs = nil_com ) ) )
% 0.31/1.89 & ( ( Xss2 != nil_list_com )
% 0.31/1.89 => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 0.31/1.89 ( ( Xss2
% 0.31/1.89 = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.31/1.89 & ( Ys
% 0.31/1.89 = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 0.31/1.89 & ( Zs
% 0.31/1.89 = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_285_concat__append,axiom,
% 0.31/1.89 ! [Xs: list_list_com,Ys: list_list_com] :
% 0.31/1.89 ( ( concat_com @ ( append_list_com @ Xs @ Ys ) )
% 0.31/1.89 = ( append_com @ ( concat_com @ Xs ) @ ( concat_com @ Ys ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_286_concat_Osimps_I1_J,axiom,
% 0.31/1.89 ( ( concat_com @ nil_list_com )
% 0.31/1.89 = nil_com ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_287_concat_Osimps_I2_J,axiom,
% 0.31/1.89 ! [X: list_com,Xs: list_list_com] :
% 0.31/1.89 ( ( concat_com @ ( cons_list_com @ X @ Xs ) )
% 0.31/1.89 = ( append_com @ X @ ( concat_com @ Xs ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_288_maps__simps_I2_J,axiom,
% 0.31/1.89 ! [F2: com > list_com] :
% 0.31/1.89 ( ( maps_com_com @ F2 @ nil_com )
% 0.31/1.89 = nil_com ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_289_concat__eq__appendD,axiom,
% 0.31/1.89 ! [Xss2: list_list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ( ( concat_com @ Xss2 )
% 0.31/1.89 = ( append_com @ Ys @ Zs ) )
% 0.31/1.89 => ( ( Xss2 != nil_list_com )
% 0.31/1.89 => ? [Xss12: list_list_com,Xs2: list_com,Xs5: list_com,Xss23: list_list_com] :
% 0.31/1.89 ( ( Xss2
% 0.31/1.89 = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.31/1.89 & ( Ys
% 0.31/1.89 = ( append_com @ ( concat_com @ Xss12 ) @ Xs2 ) )
% 0.31/1.89 & ( Zs
% 0.31/1.89 = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_290_nths__singleton,axiom,
% 0.31/1.89 ! [A4: set_nat,X: com] :
% 0.31/1.89 ( ( ( member_nat @ zero_zero_nat @ A4 )
% 0.31/1.89 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 0.31/1.89 = ( cons_com @ X @ nil_com ) ) )
% 0.31/1.89 & ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.31/1.89 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 0.31/1.89 = nil_com ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_291_lexord__append__left__rightI,axiom,
% 0.31/1.89 ! [A: com,B: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A @ X ) ) @ ( append_com @ U @ ( cons_com @ B @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_292_lexord__append__left__rightI,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_293_nths__nil,axiom,
% 0.31/1.89 ! [A4: set_nat] :
% 0.31/1.89 ( ( nths_com @ nil_com @ A4 )
% 0.31/1.89 = nil_com ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_294_lexord__cons__cons,axiom,
% 0.31/1.89 ! [A: com,X: list_com,B: com,Y: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A @ X ) @ ( cons_com @ B @ Y ) ) @ ( lexord_com @ R ) )
% 0.31/1.89 = ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 0.31/1.89 | ( ( A = B )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_295_lexord__cons__cons,axiom,
% 0.31/1.89 ! [A: produc2041926651_state,X: list_P1040014977_state,B: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A @ X ) @ ( cons_P465369265_state @ B @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 0.31/1.89 = ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.31/1.89 | ( ( A = B )
% 0.31/1.89 & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_296_lexord__Nil__left,axiom,
% 0.31/1.89 ! [Y: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 0.31/1.89 = ( ? [A5: com,X4: list_com] :
% 0.31/1.89 ( Y
% 0.31/1.89 = ( cons_com @ A5 @ X4 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_297_lexord__linear,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.31/1.89 ( ! [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ R )
% 0.31/1.89 | ( A3 = B3 )
% 0.31/1.89 | ( member1069318160_state @ ( produc1909270103_state @ B3 @ A3 ) @ R ) )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 0.31/1.89 | ( X = Y )
% 0.31/1.89 | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_298_lexord__irreflexive,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.31/1.89 ( ! [X3: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_299_lexord__Nil__right,axiom,
% 0.31/1.89 ! [X: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_300_lexord__append__leftI,axiom,
% 0.31/1.89 ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_301_lexord__append__leftD,axiom,
% 0.31/1.89 ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 0.31/1.89 => ( ! [A3: com] :
% 0.31/1.89 ~ ( member1333916004om_com @ ( product_Pair_com_com @ A3 @ A3 ) @ R )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_302_lexord__append__leftD,axiom,
% 0.31/1.89 ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 0.31/1.89 => ( ! [A3: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ A3 @ A3 ) @ R )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_303_lexord__append__rightI,axiom,
% 0.31/1.89 ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ? [B5: com,Z3: list_com] :
% 0.31/1.89 ( Y
% 0.31/1.89 = ( cons_com @ B5 @ Z3 ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_304_lexord__same__pref__if__irrefl,axiom,
% 0.31/1.89 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ( irrefl_com @ R )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lexord_com @ R ) )
% 0.31/1.89 = ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lexord_com @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_305_listrel_Ocases,axiom,
% 0.31/1.89 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ( ( ( A1 = nil_com )
% 0.31/1.89 => ( A22 != nil_com ) )
% 0.31/1.89 => ~ ! [X3: com,Y3: com,Xs2: list_com] :
% 0.31/1.89 ( ( A1
% 0.31/1.89 = ( cons_com @ X3 @ Xs2 ) )
% 0.31/1.89 => ! [Ys3: list_com] :
% 0.31/1.89 ( ( A22
% 0.31/1.89 = ( cons_com @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_306_listrel_Ocases,axiom,
% 0.31/1.89 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.31/1.89 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 => ( ( ( A1 = nil_list_com )
% 0.31/1.89 => ( A22 != nil_state ) )
% 0.31/1.89 => ~ ! [X3: list_com,Y3: state,Xs2: list_list_com] :
% 0.31/1.89 ( ( A1
% 0.31/1.89 = ( cons_list_com @ X3 @ Xs2 ) )
% 0.31/1.89 => ! [Ys3: list_state] :
% 0.31/1.89 ( ( A22
% 0.31/1.89 = ( cons_state @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_307_listrel_Ocases,axiom,
% 0.31/1.89 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 => ( ( ( A1 = nil_Pr1844458753_state )
% 0.31/1.89 => ( A22 != nil_Pr1844458753_state ) )
% 0.31/1.89 => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs2: list_P1040014977_state] :
% 0.31/1.89 ( ( A1
% 0.31/1.89 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 0.31/1.89 => ! [Ys3: list_P1040014977_state] :
% 0.31/1.89 ( ( A22
% 0.31/1.89 = ( cons_P465369265_state @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_308_listrel__rtrancl__refl,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_309_listrel_ONil,axiom,
% 0.31/1.89 ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_310_listrel__Nil1,axiom,
% 0.31/1.89 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ( Xs = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_311_listrel__Nil2,axiom,
% 0.31/1.89 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ( Xs = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_312_listrel__rtrancl__trans,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state,Zs: list_P1040014977_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ Ys @ Zs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_313_listrel__Cons2,axiom,
% 0.31/1.89 ! [Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys ) ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ~ ! [X3: com,Xs2: list_com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_com @ X3 @ Xs2 ) )
% 0.31/1.89 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 0.31/1.89 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_314_listrel__Cons2,axiom,
% 0.31/1.89 ! [Xs: list_list_com,Y: state,Ys: list_state,R: set_Pr849496667_state] :
% 0.31/1.89 ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ ( cons_state @ Y @ Ys ) ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 => ~ ! [X3: list_com,Xs2: list_list_com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_list_com @ X3 @ Xs2 ) )
% 0.31/1.89 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 0.31/1.89 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_315_listrel__Cons2,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 => ~ ! [X3: produc2041926651_state,Xs2: list_P1040014977_state] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_316_listrel__Cons1,axiom,
% 0.31/1.89 ! [Y: com,Ys: list_com,Xs: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys ) @ Xs ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ~ ! [Y3: com,Ys3: list_com] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_com @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_317_listrel__Cons1,axiom,
% 0.31/1.89 ! [Y: list_com,Ys: list_list_com,Xs: list_state,R: set_Pr849496667_state] :
% 0.31/1.89 ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys ) @ Xs ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 => ~ ! [Y3: state,Ys3: list_state] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_state @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_318_listrel__Cons1,axiom,
% 0.31/1.89 ! [Y: produc2041926651_state,Ys: list_P1040014977_state,Xs: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys ) @ Xs ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 => ~ ! [Y3: produc2041926651_state,Ys3: list_P1040014977_state] :
% 0.31/1.89 ( ( Xs
% 0.31/1.89 = ( cons_P465369265_state @ Y3 @ Ys3 ) )
% 0.31/1.89 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y3 ) @ R )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_319_listrel_OCons,axiom,
% 0.31/1.89 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_320_listrel_OCons,axiom,
% 0.31/1.89 ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs: list_list_com,Ys: list_state] :
% 0.31/1.89 ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 0.31/1.89 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs ) @ ( cons_state @ Y @ Ys ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_321_listrel_OCons,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_322_listrel__reflcl__if__listrel1,axiom,
% 0.31/1.89 ! [Xs: list_P1040014977_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre1738592858_state @ R ) )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_323_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 0.31/1.89 = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_324_listrel_Oinducts,axiom,
% 0.31/1.89 ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ( ( P @ nil_com @ nil_com )
% 0.31/1.89 => ( ! [X3: com,Y3: com,Xs2: list_com,Ys3: list_com] :
% 0.31/1.89 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 => ( ( P @ Xs2 @ Ys3 )
% 0.31/1.89 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y3 @ Ys3 ) ) ) ) )
% 0.31/1.89 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_325_listrel_Oinducts,axiom,
% 0.31/1.89 ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 0.31/1.89 ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 => ( ( P @ nil_list_com @ nil_state )
% 0.31/1.89 => ( ! [X3: list_com,Y3: state,Xs2: list_list_com,Ys3: list_state] :
% 0.31/1.89 ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 => ( ( P @ Xs2 @ Ys3 )
% 0.31/1.89 => ( P @ ( cons_list_com @ X3 @ Xs2 ) @ ( cons_state @ Y3 @ Ys3 ) ) ) ) )
% 0.31/1.89 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_326_listrel_Oinducts,axiom,
% 0.31/1.89 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 0.31/1.89 => ( ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs2: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 0.31/1.89 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 => ( ( P @ Xs2 @ Ys3 )
% 0.31/1.89 => ( P @ ( cons_P465369265_state @ X3 @ Xs2 ) @ ( cons_P465369265_state @ Y3 @ Ys3 ) ) ) ) )
% 0.31/1.89 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_327_listrel_Osimps,axiom,
% 0.31/1.89 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.31/1.89 = ( ( ( A1 = nil_com )
% 0.31/1.89 & ( A22 = nil_com ) )
% 0.31/1.89 | ? [X4: com,Y5: com,Xs3: list_com,Ys4: list_com] :
% 0.31/1.89 ( ( A1
% 0.31/1.89 = ( cons_com @ X4 @ Xs3 ) )
% 0.31/1.89 & ( A22
% 0.31/1.89 = ( cons_com @ Y5 @ Ys4 ) )
% 0.31/1.89 & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y5 ) @ R )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys4 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_328_listrel_Osimps,axiom,
% 0.31/1.89 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.31/1.89 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.31/1.89 = ( ( ( A1 = nil_list_com )
% 0.31/1.89 & ( A22 = nil_state ) )
% 0.31/1.89 | ? [X4: list_com,Y5: state,Xs3: list_list_com,Ys4: list_state] :
% 0.31/1.89 ( ( A1
% 0.31/1.89 = ( cons_list_com @ X4 @ Xs3 ) )
% 0.31/1.89 & ( A22
% 0.31/1.89 = ( cons_state @ Y5 @ Ys4 ) )
% 0.31/1.89 & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y5 ) @ R )
% 0.31/1.89 & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys4 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_329_listrel_Osimps,axiom,
% 0.31/1.89 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.31/1.89 = ( ( ( A1 = nil_Pr1844458753_state )
% 0.31/1.89 & ( A22 = nil_Pr1844458753_state ) )
% 0.31/1.89 | ? [X4: produc2041926651_state,Y5: produc2041926651_state,Xs3: list_P1040014977_state,Ys4: list_P1040014977_state] :
% 0.31/1.89 ( ( A1
% 0.31/1.89 = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 0.31/1.89 & ( A22
% 0.31/1.89 = ( cons_P465369265_state @ Y5 @ Ys4 ) )
% 0.31/1.89 & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y5 ) @ R )
% 0.31/1.89 & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys4 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_330_irreflI,axiom,
% 0.31/1.89 ! [R2: set_Pr1165141447_state] :
% 0.31/1.89 ( ! [A3: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ A3 @ A3 ) @ R2 )
% 0.31/1.89 => ( irrefl654089520_state @ R2 ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_331_irrefl__def,axiom,
% 0.31/1.89 ( irrefl654089520_state
% 0.31/1.89 = ( ^ [R3: set_Pr1165141447_state] :
% 0.31/1.89 ! [A5: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_332_lenlex__append2,axiom,
% 0.31/1.89 ! [R2: set_Pr1822651163om_com,Us2: list_com,Xs: list_com,Ys: list_com] :
% 0.31/1.89 ( ( irrefl_com @ R2 )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us2 @ Xs ) @ ( append_com @ Us2 @ Ys ) ) @ ( lenlex_com @ R2 ) )
% 0.31/1.89 = ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_333_Nil__lenlex__iff1,axiom,
% 0.31/1.89 ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ns ) @ ( lenlex_com @ R ) )
% 0.31/1.89 = ( Ns != nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_334_Nil__notin__lex,axiom,
% 0.31/1.89 ! [Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ys ) @ ( lex_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_335_Nil2__notin__lex,axiom,
% 0.31/1.89 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( lex_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_336_lex__append__leftI,axiom,
% 0.31/1.89 ! [Ys: list_com,Zs: list_com,R: set_Pr1822651163om_com,Xs: list_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lex_com @ R ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lex_com @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_337_lenlex__irreflexive,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.31/1.89 ( ! [X3: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/1.89 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( lenlex295247238_state @ R ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_338_Nil__lenlex__iff2,axiom,
% 0.31/1.89 ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ~ ( member32358020st_com @ ( produc1307105171st_com @ Ns @ nil_com ) @ ( lenlex_com @ R ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_339_lex__append__leftD,axiom,
% 0.31/1.89 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ! [X3: com] :
% 0.31/1.89 ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lex_com @ R ) )
% 0.31/1.89 => ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lex_com @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_340_lex__append__leftD,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state,Zs: list_P1040014977_state] :
% 0.31/1.89 ( ! [X3: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ Ys ) @ ( append982487830_state @ Xs @ Zs ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/1.89 => ( member1267359376_state @ ( produc1298457559_state @ Ys @ Zs ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_341_lex__append__left__iff,axiom,
% 0.31/1.89 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys: list_com,Zs: list_com] :
% 0.31/1.89 ( ! [X3: com] :
% 0.31/1.89 ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.31/1.89 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys ) @ ( append_com @ Xs @ Zs ) ) @ ( lex_com @ R ) )
% 0.31/1.89 = ( member32358020st_com @ ( produc1307105171st_com @ Ys @ Zs ) @ ( lex_com @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_342_lex__append__left__iff,axiom,
% 0.31/1.89 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state,Zs: list_P1040014977_state] :
% 0.31/1.89 ( ! [X3: produc2041926651_state] :
% 0.31/1.89 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/1.89 => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ Ys ) @ ( append982487830_state @ Xs @ Zs ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/1.89 = ( member1267359376_state @ ( produc1298457559_state @ Ys @ Zs ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_343_Cons__in__lex,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com,Y: com,Ys: list_com,R: set_Pr1822651163om_com] :
% 0.31/1.89 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys ) ) @ ( lex_com @ R ) )
% 0.31/1.89 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/1.89 & ( ( size_size_list_com @ Xs )
% 0.31/1.89 = ( size_size_list_com @ Ys ) ) )
% 0.31/1.89 | ( ( X = Y )
% 0.31/1.89 & ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( lex_com @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_344_Cons__in__lex,axiom,
% 0.31/1.89 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Y: produc2041926651_state,Ys: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/1.89 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/1.89 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/1.89 & ( ( size_s213202669_state @ Xs )
% 0.31/1.89 = ( size_s213202669_state @ Ys ) ) )
% 0.31/1.89 | ( ( X = Y )
% 0.31/1.89 & ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( lex_Pr570247525_state @ R ) ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_345_rotate1_Osimps_I2_J,axiom,
% 0.31/1.89 ! [X: com,Xs: list_com] :
% 0.31/1.89 ( ( rotate1_com @ ( cons_com @ X @ Xs ) )
% 0.31/1.89 = ( append_com @ Xs @ ( cons_com @ X @ nil_com ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_346_append__eq__append__conv,axiom,
% 0.31/1.89 ! [Xs: list_com,Ys: list_com,Us2: list_com,Vs: list_com] :
% 0.31/1.89 ( ( ( ( size_size_list_com @ Xs )
% 0.31/1.89 = ( size_size_list_com @ Ys ) )
% 0.31/1.89 | ( ( size_size_list_com @ Us2 )
% 0.31/1.89 = ( size_size_list_com @ Vs ) ) )
% 0.31/1.89 => ( ( ( append_com @ Xs @ Us2 )
% 0.31/1.89 = ( append_com @ Ys @ Vs ) )
% 0.31/1.89 = ( ( Xs = Ys )
% 0.31/1.89 & ( Us2 = Vs ) ) ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_347_rotate1__is__Nil__conv,axiom,
% 0.31/1.89 ! [Xs: list_com] :
% 0.31/1.89 ( ( ( rotate1_com @ Xs )
% 0.31/1.89 = nil_com )
% 0.31/1.89 = ( Xs = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(fact_348_length__0__conv,axiom,
% 0.31/1.89 ! [Xs: list_com] :
% 0.31/1.89 ( ( ( size_size_list_com @ Xs )
% 0.31/1.89 = zero_zero_nat )
% 0.31/1.89 = ( Xs = nil_com ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(conj_0,hypothesis,
% 0.31/1.89 ( ( f @ zero_zero_nat )
% 0.31/1.89 = ( produc1204172211_state @ ( cons_com @ ( while @ b @ c ) @ cs ) @ s ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(conj_1,hypothesis,
% 0.31/1.89 ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ I3 ) @ ( f @ ( suc @ I3 ) ) ) @ pHoare259243666_exec1 ) ).
% 0.31/1.89
% 0.31/1.89 thf(conj_2,hypothesis,
% 0.31/1.89 member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ zero_zero_nat ) ) ) @ pHoare259243666_exec1 ).
% 0.31/1.89
% 0.31/1.89 thf(conj_3,hypothesis,
% 0.31/1.89 ( ( f @ ( suc @ zero_zero_nat ) )
% 0.31/1.89 = ( produc1204172211_state @ a @ ba ) ) ).
% 0.31/1.89
% 0.31/1.89 thf(conj_4,conjecture,
% 0.31/1.89 ( ~ ( b @ s )
% 0.31/1.89 | ? [F4: nat > produc2041926651_state] :
% 0.31/1.89 ( ( ( F4 @ zero_zero_nat )
% 0.31/1.89 = ( produc1204172211_state @ ( cons_com @ c @ ( cons_com @ ( while @ b @ c ) @ cs ) ) @ s ) )
% 0.31/1.89 & ! [I2: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F4 @ I2 ) @ ( F4 @ ( suc @ I2 ) ) ) @ pHoare259243666_exec1 ) ) ) ).
% 0.31/1.89 ------------------------
% 4.25/1.95 % (15998)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_15884 for (2999ds/275Mi)
% 4.25/1.95 % (15999)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/18Mi)
% 4.25/1.95 % (15995)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_15884 for (2999ds/27Mi)
% 4.25/1.95 % (15993)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/183Mi)
% 4.25/1.95 % (15997)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_15884 for (2999ds/2Mi)
% 4.25/1.95 % (15994)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_15884 for (2999ds/4Mi)
% 4.25/1.95 % (15996)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/2Mi)
% 4.25/1.95 % (15996)Instruction limit reached!
% 4.25/1.95 % (15996)------------------------------
% 4.25/1.95 % (15996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.95 % (15996)Termination reason: Unknown
% 4.25/1.95 % (15997)Instruction limit reached!
% 4.25/1.95 % (15997)------------------------------
% 4.25/1.95 % (15997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.95 % (15996)Termination phase: shuffling
% 4.25/1.95
% 4.25/1.95 % (15996)Memory used [KB]: 1663
% 4.25/1.95 % (15996)Time elapsed: 0.003 s
% 4.25/1.95 % (15996)Instructions burned: 2 (million)
% 4.25/1.95 % (15996)------------------------------
% 4.25/1.95 % (15996)------------------------------
% 4.25/1.95 % (15997)Termination reason: Unknown
% 4.25/1.95 % (15997)Termination phase: shuffling
% 4.25/1.95
% 4.25/1.95 % (15997)Memory used [KB]: 1663
% 4.25/1.95 % (15997)Time elapsed: 0.003 s
% 4.25/1.95 % (15997)Instructions burned: 2 (million)
% 4.25/1.95 % (15997)------------------------------
% 4.25/1.95 % (15997)------------------------------
% 4.25/1.95 % (15994)Instruction limit reached!
% 4.25/1.95 % (15994)------------------------------
% 4.25/1.95 % (15994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.95 % (15994)Termination reason: Unknown
% 4.25/1.95 % (15994)Termination phase: shuffling
% 4.25/1.95
% 4.25/1.95 % (15994)Memory used [KB]: 1663
% 4.25/1.95 % (15994)Time elapsed: 0.005 s
% 4.25/1.95 % (15994)Instructions burned: 5 (million)
% 4.25/1.95 % (15994)------------------------------
% 4.25/1.95 % (15994)------------------------------
% 4.25/1.96 % (15999)Instruction limit reached!
% 4.25/1.96 % (15999)------------------------------
% 4.25/1.96 % (15999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.96 % (15999)Termination reason: Unknown
% 4.25/1.96 % (15999)Termination phase: shuffling
% 4.25/1.96
% 4.25/1.96 % (15999)Memory used [KB]: 1918
% 4.25/1.96 % (15999)Time elapsed: 0.012 s
% 4.25/1.96 % (15999)Instructions burned: 19 (million)
% 4.25/1.96 % (15999)------------------------------
% 4.25/1.96 % (15999)------------------------------
% 4.25/1.96 % (15995)Instruction limit reached!
% 4.25/1.96 % (15995)------------------------------
% 4.25/1.96 % (15995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.96 % (15995)Termination reason: Unknown
% 4.25/1.96 % (15995)Termination phase: shuffling
% 4.25/1.96
% 4.25/1.96 % (15995)Memory used [KB]: 2174
% 4.25/1.96 % (15995)Time elapsed: 0.017 s
% 4.25/1.96 % (15995)Instructions burned: 27 (million)
% 4.25/1.96 % (15995)------------------------------
% 4.25/1.96 % (15995)------------------------------
% 4.25/1.97 % (16000)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/3Mi)
% 4.25/1.97 % (16001)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_15884 for (2999ds/37Mi)
% 4.25/1.97 % (16002)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_15884 for (2999ds/15Mi)
% 4.25/1.97 % (16000)Instruction limit reached!
% 4.25/1.97 % (16000)------------------------------
% 4.25/1.97 % (16000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.97 % (16000)Termination reason: Unknown
% 4.25/1.97 % (16000)Termination phase: shuffling
% 4.25/1.97
% 4.25/1.97 % (16000)Memory used [KB]: 1663
% 4.25/1.97 % (16000)Time elapsed: 0.004 s
% 4.25/1.97 % (16000)Instructions burned: 4 (million)
% 4.25/1.97 % (16000)------------------------------
% 4.25/1.97 % (16000)------------------------------
% 4.25/1.98 % (16002)Instruction limit reached!
% 4.25/1.98 % (16002)------------------------------
% 4.25/1.98 % (16002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.98 % (16002)Termination reason: Unknown
% 4.25/1.98 % (16002)Termination phase: shuffling
% 4.25/1.98
% 4.25/1.98 % (16002)Memory used [KB]: 1918
% 4.25/1.98 % (16002)Time elapsed: 0.010 s
% 4.25/1.98 % (16002)Instructions burned: 15 (million)
% 4.25/1.98 % (16002)------------------------------
% 4.25/1.98 % (16002)------------------------------
% 4.25/1.98 % (16003)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_15884 for (2999ds/3Mi)
% 4.25/1.98 % (16003)Instruction limit reached!
% 4.25/1.98 % (16003)------------------------------
% 4.25/1.98 % (16003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.98 % (16003)Termination reason: Unknown
% 4.25/1.98 % (16003)Termination phase: shuffling
% 4.25/1.98
% 4.25/1.98 % (16003)Memory used [KB]: 1663
% 4.25/1.98 % (16003)Time elapsed: 0.005 s
% 4.25/1.98 % (16003)Instructions burned: 4 (million)
% 4.25/1.98 % (16003)------------------------------
% 4.25/1.98 % (16003)------------------------------
% 4.25/1.98 % (16004)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_15884 for (2999ds/1041Mi)
% 4.25/1.99 % (16001)Instruction limit reached!
% 4.25/1.99 % (16001)------------------------------
% 4.25/1.99 % (16001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/1.99 % (16001)Termination reason: Unknown
% 4.25/1.99 % (16001)Termination phase: shuffling
% 4.25/1.99
% 4.25/1.99 % (16001)Memory used [KB]: 2302
% 4.25/1.99 % (16001)Time elapsed: 0.021 s
% 4.25/1.99 % (16001)Instructions burned: 37 (million)
% 4.25/1.99 % (16001)------------------------------
% 4.25/1.99 % (16001)------------------------------
% 4.25/1.99 % (16005)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/7Mi)
% 4.25/2.00 % (16005)Instruction limit reached!
% 4.25/2.00 % (16005)------------------------------
% 4.25/2.00 % (16005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/2.00 % (16005)Termination reason: Unknown
% 4.25/2.00 % (16005)Termination phase: shuffling
% 4.25/2.00
% 4.25/2.00 % (16005)Memory used [KB]: 1791
% 4.25/2.00 % (16005)Time elapsed: 0.006 s
% 4.25/2.00 % (16005)Instructions burned: 7 (million)
% 4.25/2.00 % (16005)------------------------------
% 4.25/2.00 % (16005)------------------------------
% 4.25/2.00 % (16006)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/16Mi)
% 4.25/2.00 % (16007)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_15884 for (2999ds/3Mi)
% 4.25/2.00 % (16007)Instruction limit reached!
% 4.25/2.00 % (16007)------------------------------
% 4.25/2.00 % (16007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/2.00 % (16007)Termination reason: Unknown
% 4.25/2.00 % (16007)Termination phase: shuffling
% 4.25/2.00
% 4.25/2.00 % (16007)Memory used [KB]: 1663
% 4.25/2.00 % (16007)Time elapsed: 0.004 s
% 4.25/2.00 % (16007)Instructions burned: 4 (million)
% 4.25/2.00 % (16007)------------------------------
% 4.25/2.00 % (16007)------------------------------
% 4.25/2.01 % (16006)Instruction limit reached!
% 4.25/2.01 % (16006)------------------------------
% 4.25/2.01 % (16006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/2.01 % (16006)Termination reason: Unknown
% 4.25/2.01 % (16006)Termination phase: shuffling
% 4.25/2.01
% 4.25/2.01 % (16006)Memory used [KB]: 1918
% 4.25/2.01 % (16006)Time elapsed: 0.011 s
% 4.25/2.01 % (16006)Instructions burned: 17 (million)
% 4.25/2.01 % (16006)------------------------------
% 4.25/2.01 % (16006)------------------------------
% 4.25/2.01 % (16008)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_15884 for (2999ds/3Mi)
% 4.25/2.01 % (16008)Instruction limit reached!
% 4.25/2.01 % (16008)------------------------------
% 4.25/2.01 % (16008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/2.01 % (16008)Termination reason: Unknown
% 4.25/2.01 % (16008)Termination phase: shuffling
% 4.25/2.01
% 4.25/2.01 % (16008)Memory used [KB]: 1663
% 4.25/2.01 % (16008)Time elapsed: 0.004 s
% 4.25/2.01 % (16008)Instructions burned: 4 (million)
% 4.25/2.01 % (16008)------------------------------
% 4.25/2.01 % (16008)------------------------------
% 4.25/2.02 % (16009)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15884 for (2999ds/7Mi)
% 4.25/2.02 % (16009)Instruction limit reached!
% 4.25/2.02 % (16009)------------------------------
% 4.25/2.02 % (16009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/2.02 % (16009)Termination reason: Unknown
% 4.25/2.02 % (16009)Termination phase: shuffling
% 4.25/2.02
% 4.25/2.02 % (16009)Memory used [KB]: 1791
% 4.25/2.02 % (16009)Time elapsed: 0.006 s
% 4.25/2.02 % (16009)Instructions burned: 7 (million)
% 4.25/2.02 % (16009)------------------------------
% 4.25/2.02 % (16009)------------------------------
% 4.25/2.02 % (16010)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/3Mi)
% 4.25/2.03 % (16010)Instruction limit reached!
% 4.25/2.03 % (16010)------------------------------
% 4.25/2.03 % (16010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.25/2.03 % (16010)Termination reason: Unknown
% 4.25/2.03 % (16010)Termination phase: shuffling
% 4.25/2.03
% 4.25/2.03 % (16010)Memory used [KB]: 1663
% 4.25/2.03 % (16010)Time elapsed: 0.004 s
% 4.25/2.03 % (16010)Instructions burned: 3 (million)
% 4.25/2.03 % (16010)------------------------------
% 4.25/2.03 % (16010)------------------------------
% 4.84/2.03 % (16011)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/4Mi)
% 4.84/2.03 % (16012)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/18Mi)
% 4.84/2.03 % (16011)Instruction limit reached!
% 4.84/2.03 % (16011)------------------------------
% 4.84/2.03 % (16011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.03 % (16011)Termination reason: Unknown
% 4.84/2.03 % (16011)Termination phase: shuffling
% 4.84/2.03
% 4.84/2.03 % (16011)Memory used [KB]: 1663
% 4.84/2.03 % (16011)Time elapsed: 0.005 s
% 4.84/2.03 % (16011)Instructions burned: 5 (million)
% 4.84/2.03 % (16011)------------------------------
% 4.84/2.03 % (16011)------------------------------
% 4.84/2.04 % (16013)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/710Mi)
% 4.84/2.04 % (16012)Instruction limit reached!
% 4.84/2.04 % (16012)------------------------------
% 4.84/2.04 % (16012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.04 % (16012)Termination reason: Unknown
% 4.84/2.04 % (16012)Termination phase: shuffling
% 4.84/2.04
% 4.84/2.04 % (16012)Memory used [KB]: 1918
% 4.84/2.04 % (16012)Time elapsed: 0.012 s
% 4.84/2.04 % (16012)Instructions burned: 18 (million)
% 4.84/2.04 % (16012)------------------------------
% 4.84/2.04 % (16012)------------------------------
% 4.84/2.05 % (15993)Instruction limit reached!
% 4.84/2.05 % (15993)------------------------------
% 4.84/2.05 % (15993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.05 % (15993)Termination reason: Unknown
% 4.84/2.05 % (15993)Termination phase: Property scanning
% 4.84/2.05
% 4.84/2.05 % (15993)Memory used [KB]: 3454
% 4.84/2.05 % (15993)Time elapsed: 0.098 s
% 4.84/2.05 % (15993)Instructions burned: 184 (million)
% 4.84/2.05 % (15993)------------------------------
% 4.84/2.05 % (15993)------------------------------
% 4.84/2.05 % (16014)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/6Mi)
% 4.84/2.05 % (16014)Instruction limit reached!
% 4.84/2.05 % (16014)------------------------------
% 4.84/2.05 % (16014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.05 % (16014)Termination reason: Unknown
% 4.84/2.05 % (16014)Termination phase: shuffling
% 4.84/2.05
% 4.84/2.05 % (16014)Memory used [KB]: 1663
% 4.84/2.05 % (16014)Time elapsed: 0.006 s
% 4.84/2.05 % (16014)Instructions burned: 6 (million)
% 4.84/2.05 % (16014)------------------------------
% 4.84/2.05 % (16014)------------------------------
% 4.84/2.05 % (16015)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_15884 for (2998ds/902Mi)
% 4.84/2.06 % (16016)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_15884 for (2998ds/21Mi)
% 4.84/2.07 % (16017)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/5Mi)
% 4.84/2.07 % (16017)Instruction limit reached!
% 4.84/2.07 % (16017)------------------------------
% 4.84/2.07 % (16017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.07 % (16017)Termination reason: Unknown
% 4.84/2.07 % (16017)Termination phase: shuffling
% 4.84/2.07
% 4.84/2.07 % (16017)Memory used [KB]: 1663
% 4.84/2.07 % (16017)Time elapsed: 0.005 s
% 4.84/2.07 % (16017)Instructions burned: 5 (million)
% 4.84/2.07 % (16017)------------------------------
% 4.84/2.07 % (16017)------------------------------
% 4.84/2.07 % (16018)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_15884 for (2998ds/6Mi)
% 4.84/2.07 % (16016)Instruction limit reached!
% 4.84/2.07 % (16016)------------------------------
% 4.84/2.07 % (16016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.07 % (16016)Termination reason: Unknown
% 4.84/2.07 % (16016)Termination phase: shuffling
% 4.84/2.07
% 4.84/2.07 % (16016)Memory used [KB]: 1918
% 4.84/2.07 % (16016)Time elapsed: 0.014 s
% 4.84/2.07 % (16016)Instructions burned: 21 (million)
% 4.84/2.07 % (16016)------------------------------
% 4.84/2.07 % (16016)------------------------------
% 4.84/2.07 % (16018)Instruction limit reached!
% 4.84/2.07 % (16018)------------------------------
% 4.84/2.07 % (16018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.07 % (16018)Termination reason: Unknown
% 4.84/2.07 % (16018)Termination phase: shuffling
% 4.84/2.07
% 4.84/2.07 % (16018)Memory used [KB]: 1663
% 4.84/2.07 % (16018)Time elapsed: 0.005 s
% 4.84/2.07 % (16018)Instructions burned: 6 (million)
% 4.84/2.07 % (16018)------------------------------
% 4.84/2.07 % (16018)------------------------------
% 4.84/2.09 % (16019)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/377Mi)
% 4.84/2.09 % (16021)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_15884 for (2998ds/19Mi)
% 4.84/2.09 % (16020)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_15884 for (2998ds/779Mi)
% 4.84/2.10 % (16021)Instruction limit reached!
% 4.84/2.10 % (16021)------------------------------
% 4.84/2.10 % (16021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.10 % (16021)Termination reason: Unknown
% 4.84/2.10 % (16021)Termination phase: shuffling
% 4.84/2.10
% 4.84/2.10 % (16021)Memory used [KB]: 2046
% 4.84/2.10 % (16021)Time elapsed: 0.012 s
% 4.84/2.10 % (16021)Instructions burned: 19 (million)
% 4.84/2.10 % (16021)------------------------------
% 4.84/2.10 % (16021)------------------------------
% 4.84/2.11 % (15998)Instruction limit reached!
% 4.84/2.11 % (15998)------------------------------
% 4.84/2.11 % (15998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.84/2.11 % (15998)Termination reason: Unknown
% 4.84/2.11 % (15998)Termination phase: Saturation
% 4.84/2.11
% 4.84/2.11 % (15998)Memory used [KB]: 8059
% 4.84/2.11 % (15998)Time elapsed: 0.159 s
% 4.84/2.11 % (15998)Instructions burned: 276 (million)
% 4.84/2.11 % (15998)------------------------------
% 4.84/2.11 % (15998)------------------------------
% 4.84/2.12 % (16022)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/879Mi)
% 5.26/2.13 % (16023)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15884 for (2998ds/17Mi)
% 5.26/2.14 % (16023)Instruction limit reached!
% 5.26/2.14 % (16023)------------------------------
% 5.26/2.14 % (16023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.14 % (16023)Termination reason: Unknown
% 5.26/2.14 % (16023)Termination phase: shuffling
% 5.26/2.14
% 5.26/2.14 % (16023)Memory used [KB]: 1918
% 5.26/2.14 % (16023)Time elapsed: 0.012 s
% 5.26/2.14 % (16023)Instructions burned: 18 (million)
% 5.26/2.14 % (16023)------------------------------
% 5.26/2.14 % (16023)------------------------------
% 5.26/2.16 % (16024)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15884 for (2997ds/3Mi)
% 5.26/2.16 % (16024)Instruction limit reached!
% 5.26/2.16 % (16024)------------------------------
% 5.26/2.16 % (16024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.16 % (16024)Termination reason: Unknown
% 5.26/2.16 % (16024)Termination phase: shuffling
% 5.26/2.16
% 5.26/2.16 % (16024)Memory used [KB]: 1663
% 5.26/2.16 % (16024)Time elapsed: 0.004 s
% 5.26/2.16 % (16024)Instructions burned: 3 (million)
% 5.26/2.16 % (16024)------------------------------
% 5.26/2.16 % (16024)------------------------------
% 5.26/2.18 % (16025)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15884 for (2997ds/30Mi)
% 5.39/2.20 % (16025)Instruction limit reached!
% 5.39/2.20 % (16025)------------------------------
% 5.39/2.20 % (16025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.20 % (16025)Termination reason: Unknown
% 5.39/2.20 % (16025)Termination phase: shuffling
% 5.39/2.20
% 5.39/2.20 % (16025)Memory used [KB]: 2174
% 5.39/2.20 % (16025)Time elapsed: 0.019 s
% 5.39/2.20 % (16025)Instructions burned: 30 (million)
% 5.39/2.20 % (16025)------------------------------
% 5.39/2.20 % (16025)------------------------------
% 5.39/2.22 % (16026)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15884 for (2996ds/127Mi)
% 5.39/2.29 % (16026)Instruction limit reached!
% 5.39/2.29 % (16026)------------------------------
% 5.39/2.29 % (16026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.29 % (16026)Termination reason: Unknown
% 5.39/2.29 % (16026)Termination phase: Property scanning
% 5.39/2.29
% 5.39/2.29 % (16026)Memory used [KB]: 3326
% 5.39/2.29 % (16026)Time elapsed: 0.073 s
% 5.39/2.29 % (16026)Instructions burned: 127 (million)
% 5.39/2.29 % (16026)------------------------------
% 5.39/2.29 % (16026)------------------------------
% 5.39/2.30 % (16019)Instruction limit reached!
% 5.39/2.30 % (16019)------------------------------
% 5.39/2.30 % (16019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.30 % (16019)Termination reason: Unknown
% 5.39/2.30 % (16019)Termination phase: Saturation
% 5.39/2.30
% 5.39/2.30 % (16019)Memory used [KB]: 9466
% 5.39/2.30 % (16019)Time elapsed: 0.208 s
% 5.39/2.30 % (16019)Instructions burned: 378 (million)
% 5.39/2.30 % (16019)------------------------------
% 5.39/2.30 % (16019)------------------------------
% 5.85/2.32 % (16027)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15884 for (2995ds/100Mi)
% 5.85/2.32 % (16028)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_15884 for (2995ds/3Mi)
% 5.85/2.32 % (16028)Instruction limit reached!
% 5.85/2.32 % (16028)------------------------------
% 5.85/2.32 % (16028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.32 % (16028)Termination reason: Unknown
% 5.85/2.32 % (16028)Termination phase: shuffling
% 5.85/2.32
% 5.85/2.32 % (16028)Memory used [KB]: 1663
% 5.85/2.32 % (16028)Time elapsed: 0.005 s
% 5.85/2.32 % (16028)Instructions burned: 4 (million)
% 5.85/2.32 % (16028)------------------------------
% 5.85/2.32 % (16028)------------------------------
% 5.85/2.34 % (16029)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_15884 for (2995ds/20Mi)
% 5.85/2.35 % (16029)Instruction limit reached!
% 5.85/2.35 % (16029)------------------------------
% 5.85/2.35 % (16029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.35 % (16029)Termination reason: Unknown
% 5.85/2.35 % (16029)Termination phase: shuffling
% 5.85/2.35
% 5.85/2.35 % (16029)Memory used [KB]: 1918
% 5.85/2.35 % (16029)Time elapsed: 0.014 s
% 5.85/2.35 % (16029)Instructions burned: 21 (million)
% 5.85/2.35 % (16029)------------------------------
% 5.85/2.35 % (16029)------------------------------
% 5.85/2.37 % (16027)Instruction limit reached!
% 5.85/2.37 % (16027)------------------------------
% 5.85/2.37 % (16027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.37 % (16027)Termination reason: Unknown
% 5.85/2.37 % (16027)Termination phase: Property scanning
% 5.85/2.37
% 5.85/2.37 % (16027)Memory used [KB]: 3198
% 5.85/2.37 % (16027)Time elapsed: 0.054 s
% 5.85/2.37 % (16027)Instructions burned: 101 (million)
% 5.85/2.37 % (16027)------------------------------
% 5.85/2.37 % (16027)------------------------------
% 5.85/2.38 % (16030)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_15884 for (2995ds/86Mi)
% 5.85/2.39 % (16031)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_15884 for (2995ds/107Mi)
% 6.09/2.42 % (16030)Instruction limit reached!
% 6.09/2.42 % (16030)------------------------------
% 6.09/2.42 % (16030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.42 % (16030)Termination reason: Unknown
% 6.09/2.42 % (16030)Termination phase: Preprocessing 3
% 6.09/2.42
% 6.09/2.42 % (16030)Memory used [KB]: 2814
% 6.09/2.42 % (16030)Time elapsed: 0.050 s
% 6.09/2.42 % (16030)Instructions burned: 87 (million)
% 6.09/2.42 % (16030)------------------------------
% 6.09/2.42 % (16030)------------------------------
% 6.09/2.45 % (16032)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_15884 for (2994ds/39Mi)
% 6.09/2.45 % (16031)Instruction limit reached!
% 6.09/2.45 % (16031)------------------------------
% 6.09/2.45 % (16031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.45 % (16031)Termination reason: Unknown
% 6.09/2.45 % (16031)Termination phase: Property scanning
% 6.09/2.45
% 6.09/2.45 % (16031)Memory used [KB]: 2942
% 6.09/2.45 % (16031)Time elapsed: 0.061 s
% 6.09/2.45 % (16031)Instructions burned: 108 (million)
% 6.09/2.45 % (16031)------------------------------
% 6.09/2.45 % (16031)------------------------------
% 6.09/2.45 % (16013)Instruction limit reached!
% 6.09/2.45 % (16013)------------------------------
% 6.09/2.45 % (16013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.45 % (16013)Termination reason: Unknown
% 6.09/2.45 % (16013)Termination phase: Saturation
% 6.09/2.45
% 6.09/2.45 % (16013)Memory used [KB]: 8443
% 6.09/2.45 % (16013)Time elapsed: 0.414 s
% 6.09/2.45 % (16013)Instructions burned: 710 (million)
% 6.09/2.45 % (16013)------------------------------
% 6.09/2.45 % (16013)------------------------------
% 6.09/2.47 % (16032)Instruction limit reached!
% 6.09/2.47 % (16032)------------------------------
% 6.09/2.47 % (16032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.47 % (16032)Termination reason: Unknown
% 6.09/2.47 % (16032)Termination phase: shuffling
% 6.09/2.47
% 6.09/2.47 % (16032)Memory used [KB]: 2302
% 6.09/2.47 % (16032)Time elapsed: 0.022 s
% 6.09/2.47 % (16032)Instructions burned: 39 (million)
% 6.09/2.47 % (16032)------------------------------
% 6.09/2.47 % (16032)------------------------------
% 6.09/2.47 % (16033)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_15884 for (2994ds/448Mi)
% 6.09/2.47 % (16034)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_15884 for (2994ds/46Mi)
% 6.09/2.49 % (16035)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_15884 for (2994ds/98Mi)
% 6.83/2.50 % (16034)Instruction limit reached!
% 6.83/2.50 % (16034)------------------------------
% 6.83/2.50 % (16034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.50 % (16034)Termination reason: Unknown
% 6.83/2.50 % (16034)Termination phase: Property scanning
% 6.83/2.50
% 6.83/2.50 % (16034)Memory used [KB]: 2430
% 6.83/2.50 % (16034)Time elapsed: 0.027 s
% 6.83/2.50 % (16034)Instructions burned: 46 (million)
% 6.83/2.50 % (16034)------------------------------
% 6.83/2.50 % (16034)------------------------------
% 6.83/2.52 % (16036)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_15884 for (2993ds/507Mi)
% 6.83/2.52 % (16020)Instruction limit reached!
% 6.83/2.52 % (16020)------------------------------
% 6.83/2.52 % (16020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.52 % (16020)Termination reason: Unknown
% 6.83/2.52 % (16020)Termination phase: Saturation
% 6.83/2.52
% 6.83/2.52 % (16020)Memory used [KB]: 9978
% 6.83/2.52 % (16020)Time elapsed: 0.433 s
% 6.83/2.52 % (16020)Instructions burned: 779 (million)
% 6.83/2.52 % (16020)------------------------------
% 6.83/2.52 % (16020)------------------------------
% 6.83/2.54 % (16035)Instruction limit reached!
% 6.83/2.54 % (16035)------------------------------
% 6.83/2.54 % (16035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.54 % (16035)Termination reason: Unknown
% 6.83/2.54 % (16035)Termination phase: Property scanning
% 6.83/2.54
% 6.83/2.54 % (16035)Memory used [KB]: 3198
% 6.83/2.54 % (16035)Time elapsed: 0.053 s
% 6.83/2.54 % (16035)Instructions burned: 99 (million)
% 6.83/2.54 % (16035)------------------------------
% 6.83/2.54 % (16035)------------------------------
% 6.83/2.54 % (16015)Instruction limit reached!
% 6.83/2.54 % (16015)------------------------------
% 6.83/2.54 % (16015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.54 % (16015)Termination reason: Unknown
% 6.83/2.54 % (16015)Termination phase: Saturation
% 6.83/2.54
% 6.83/2.54 % (16015)Memory used [KB]: 10874
% 6.83/2.54 % (16015)Time elapsed: 0.491 s
% 6.83/2.54 % (16015)Instructions burned: 903 (million)
% 6.83/2.54 % (16015)------------------------------
% 6.83/2.54 % (16015)------------------------------
% 6.83/2.55 % (16037)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_15884 for (2993ds/149Mi)
% 6.83/2.56 % (16039)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_15884 for (2993ds/6Mi)
% 6.83/2.56 % (16038)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_15884 for (2993ds/39Mi)
% 6.83/2.56 % (16039)Instruction limit reached!
% 6.83/2.56 % (16039)------------------------------
% 6.83/2.56 % (16039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.56 % (16039)Termination reason: Unknown
% 6.83/2.56 % (16039)Termination phase: shuffling
% 6.83/2.56
% 6.83/2.56 % (16039)Memory used [KB]: 1791
% 6.83/2.56 % (16039)Time elapsed: 0.006 s
% 6.83/2.56 % (16039)Instructions burned: 7 (million)
% 6.83/2.56 % (16039)------------------------------
% 6.83/2.56 % (16039)------------------------------
% 6.83/2.58 % (16038)Instruction limit reached!
% 6.83/2.58 % (16038)------------------------------
% 6.83/2.58 % (16038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.58 % (16038)Termination reason: Unknown
% 6.83/2.58 % (16038)Termination phase: shuffling
% 6.83/2.58
% 6.83/2.58 % (16038)Memory used [KB]: 2302
% 6.83/2.58 % (16038)Time elapsed: 0.023 s
% 6.83/2.58 % (16038)Instructions burned: 39 (million)
% 6.83/2.58 % (16038)------------------------------
% 6.83/2.58 % (16038)------------------------------
% 6.83/2.59 % (16040)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_15884 for (2993ds/1087Mi)
% 8.06/2.60 % (16004)Instruction limit reached!
% 8.06/2.60 % (16004)------------------------------
% 8.06/2.60 % (16004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.60 % (16004)Termination reason: Unknown
% 8.06/2.60 % (16004)Termination phase: Saturation
% 8.06/2.60
% 8.06/2.60 % (16004)Memory used [KB]: 10618
% 8.06/2.60 % (16004)Time elapsed: 0.622 s
% 8.06/2.60 % (16004)Instructions burned: 1042 (million)
% 8.06/2.60 % (16004)------------------------------
% 8.06/2.60 % (16004)------------------------------
% 8.06/2.60 % (16041)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_15884 for (2993ds/47Mi)
% 8.06/2.63 % (16037)Instruction limit reached!
% 8.06/2.63 % (16037)------------------------------
% 8.06/2.63 % (16037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.63 % (16037)Termination reason: Unknown
% 8.06/2.63 % (16037)Termination phase: Property scanning
% 8.06/2.63
% 8.06/2.63 % (16037)Memory used [KB]: 3454
% 8.06/2.63 % (16037)Time elapsed: 0.082 s
% 8.06/2.63 % (16037)Instructions burned: 149 (million)
% 8.06/2.63 % (16037)------------------------------
% 8.06/2.63 % (16037)------------------------------
% 8.06/2.63 % (16042)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_15884 for (2992ds/44Mi)
% 8.06/2.63 % (16022)Instruction limit reached!
% 8.06/2.63 % (16022)------------------------------
% 8.06/2.63 % (16022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.63 % (16022)Termination reason: Unknown
% 8.06/2.63 % (16022)Termination phase: Saturation
% 8.06/2.63
% 8.06/2.63 % (16022)Memory used [KB]: 8571
% 8.06/2.63 % (16022)Time elapsed: 0.529 s
% 8.06/2.63 % (16022)Instructions burned: 879 (million)
% 8.06/2.63 % (16022)------------------------------
% 8.06/2.63 % (16022)------------------------------
% 8.06/2.63 % (16041)Instruction limit reached!
% 8.06/2.63 % (16041)------------------------------
% 8.06/2.63 % (16041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.63 % (16041)Termination reason: Unknown
% 8.06/2.63 % (16041)Termination phase: Property scanning
% 8.06/2.63
% 8.06/2.63 % (16041)Memory used [KB]: 2430
% 8.06/2.63 % (16041)Time elapsed: 0.028 s
% 8.06/2.63 % (16041)Instructions burned: 47 (million)
% 8.06/2.63 % (16041)------------------------------
% 8.06/2.63 % (16041)------------------------------
% 8.06/2.65 % (16043)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_15884 for (2992ds/432Mi)
% 8.06/2.65 % (16045)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_15884 for (2992ds/31Mi)
% 8.06/2.65 % (16044)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_15884 for (2992ds/62Mi)
% 8.06/2.65 % (16042)Instruction limit reached!
% 8.06/2.65 % (16042)------------------------------
% 8.06/2.65 % (16042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.65 % (16042)Termination reason: Unknown
% 8.06/2.65 % (16042)Termination phase: shuffling
% 8.06/2.65
% 8.06/2.65 % (16042)Memory used [KB]: 2558
% 8.06/2.65 % (16042)Time elapsed: 0.026 s
% 8.06/2.65 % (16042)Instructions burned: 45 (million)
% 8.06/2.65 % (16042)------------------------------
% 8.06/2.65 % (16042)------------------------------
% 8.06/2.67 % (16045)Instruction limit reached!
% 8.06/2.67 % (16045)------------------------------
% 8.06/2.67 % (16045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.67 % (16045)Termination reason: Unknown
% 8.06/2.67 % (16045)Termination phase: shuffling
% 8.06/2.67
% 8.06/2.67 % (16045)Memory used [KB]: 2174
% 8.06/2.67 % (16045)Time elapsed: 0.019 s
% 8.06/2.67 % (16045)Instructions burned: 31 (million)
% 8.06/2.67 % (16045)------------------------------
% 8.06/2.67 % (16045)------------------------------
% 8.06/2.67 % (16046)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_15884 for (2992ds/96Mi)
% 8.06/2.68 % (16044)Instruction limit reached!
% 8.06/2.68 % (16044)------------------------------
% 8.06/2.68 % (16044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.68 % (16044)Termination reason: Unknown
% 8.06/2.68 % (16044)Termination phase: shuffling
% 8.06/2.68
% 8.06/2.68 % (16044)Memory used [KB]: 2814
% 8.06/2.68 % (16044)Time elapsed: 0.034 s
% 8.06/2.68 % (16044)Instructions burned: 62 (million)
% 8.06/2.68 % (16044)------------------------------
% 8.06/2.68 % (16044)------------------------------
% 8.06/2.69 % (16047)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_15884 for (2992ds/453Mi)
% 8.90/2.71 % (16048)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_15884 for (2992ds/71Mi)
% 8.90/2.71 % (16033)Instruction limit reached!
% 8.90/2.71 % (16033)------------------------------
% 8.90/2.71 % (16033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.71 % (16033)Termination reason: Unknown
% 8.90/2.71 % (16033)Termination phase: Saturation
% 8.90/2.71
% 8.90/2.71 % (16033)Memory used [KB]: 9850
% 8.90/2.71 % (16033)Time elapsed: 0.244 s
% 8.90/2.71 % (16033)Instructions burned: 448 (million)
% 8.90/2.71 % (16033)------------------------------
% 8.90/2.71 % (16033)------------------------------
% 8.90/2.73 % (16046)Instruction limit reached!
% 8.90/2.73 % (16046)------------------------------
% 8.90/2.73 % (16046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.73 % (16046)Termination reason: Unknown
% 8.90/2.73 % (16046)Termination phase: Preprocessing 3
% 8.90/2.73
% 8.90/2.73 % (16046)Memory used [KB]: 3198
% 8.90/2.73 % (16046)Time elapsed: 0.055 s
% 8.90/2.73 % (16046)Instructions burned: 96 (million)
% 8.90/2.73 % (16046)------------------------------
% 8.90/2.73 % (16046)------------------------------
% 8.90/2.73 % (16049)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_15884 for (2991ds/83Mi)
% 8.90/2.74 % (16048)Instruction limit reached!
% 8.90/2.74 % (16048)------------------------------
% 8.90/2.74 % (16048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.74 % (16048)Termination reason: Unknown
% 8.90/2.74 % (16048)Termination phase: Property scanning
% 8.90/2.74
% 8.90/2.74 % (16048)Memory used [KB]: 2558
% 8.90/2.74 % (16048)Time elapsed: 0.040 s
% 8.90/2.74 % (16048)Instructions burned: 72 (million)
% 8.90/2.74 % (16048)------------------------------
% 8.90/2.74 % (16048)------------------------------
% 8.90/2.75 % (16050)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_15884 for (2991ds/11Mi)
% 8.90/2.76 % (16050)Instruction limit reached!
% 8.90/2.76 % (16050)------------------------------
% 8.90/2.76 % (16050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.76 % (16050)Termination reason: Unknown
% 8.90/2.76 % (16050)Termination phase: shuffling
% 8.90/2.76
% 8.90/2.76 % (16050)Memory used [KB]: 1918
% 8.90/2.76 % (16050)Time elapsed: 0.009 s
% 8.90/2.76 % (16050)Instructions burned: 12 (million)
% 8.90/2.76 % (16050)------------------------------
% 8.90/2.76 % (16050)------------------------------
% 8.90/2.77 % (16051)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_15884 for (2991ds/41Mi)
% 8.90/2.78 % (16049)Instruction limit reached!
% 8.90/2.78 % (16049)------------------------------
% 8.90/2.78 % (16049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.78 % (16049)Termination reason: Unknown
% 8.90/2.78 % (16049)Termination phase: SInE selection
% 8.90/2.78
% 8.90/2.78 % (16049)Memory used [KB]: 2430
% 8.90/2.78 % (16049)Time elapsed: 0.048 s
% 8.90/2.78 % (16049)Instructions burned: 83 (million)
% 8.90/2.78 % (16049)------------------------------
% 8.90/2.78 % (16049)------------------------------
% 8.90/2.78 % (16052)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15884 for (2991ds/6Mi)
% 8.90/2.78 % (16052)Instruction limit reached!
% 8.90/2.78 % (16052)------------------------------
% 8.90/2.78 % (16052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.78 % (16052)Termination reason: Unknown
% 8.90/2.78 % (16052)Termination phase: shuffling
% 8.90/2.78
% 8.90/2.78 % (16052)Memory used [KB]: 1663
% 8.90/2.78 % (16052)Time elapsed: 0.006 s
% 8.90/2.78 % (16052)Instructions burned: 6 (million)
% 8.90/2.78 % (16052)------------------------------
% 8.90/2.78 % (16052)------------------------------
% 8.90/2.79 % (16051)Instruction limit reached!
% 8.90/2.79 % (16051)------------------------------
% 8.90/2.79 % (16051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.79 % (16051)Termination reason: Unknown
% 8.90/2.79 % (16051)Termination phase: shuffling
% 8.90/2.79
% 8.90/2.79 % (16051)Memory used [KB]: 2558
% 8.90/2.79 % (16051)Time elapsed: 0.024 s
% 8.90/2.79 % (16051)Instructions burned: 41 (million)
% 8.90/2.79 % (16051)------------------------------
% 8.90/2.79 % (16051)------------------------------
% 9.47/2.80 % (16053)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_15884 for (2991ds/150Mi)
% 9.47/2.80 % (16054)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_15884 for (2991ds/343Mi)
% 9.47/2.81 % (16055)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_15884 for (2991ds/109Mi)
% 9.47/2.81 % (16036)Instruction limit reached!
% 9.47/2.81 % (16036)------------------------------
% 9.47/2.81 % (16036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.81 % (16036)Termination reason: Unknown
% 9.47/2.81 % (16036)Termination phase: Saturation
% 9.47/2.81
% 9.47/2.81 % (16036)Memory used [KB]: 11001
% 9.47/2.81 % (16036)Time elapsed: 0.295 s
% 9.47/2.81 % (16036)Instructions burned: 508 (million)
% 9.47/2.81 % (16036)------------------------------
% 9.47/2.81 % (16036)------------------------------
% 9.47/2.84 % (16056)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_15884 for (2990ds/253Mi)
% 9.47/2.87 % (16055)Instruction limit reached!
% 9.47/2.87 % (16055)------------------------------
% 9.47/2.87 % (16055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.87 % (16055)Termination reason: Unknown
% 9.47/2.87 % (16055)Termination phase: Preprocessing 3
% 9.47/2.87
% 9.47/2.87 % (16055)Memory used [KB]: 3326
% 9.47/2.87 % (16055)Time elapsed: 0.062 s
% 9.47/2.87 % (16055)Instructions burned: 109 (million)
% 9.47/2.87 % (16055)------------------------------
% 9.47/2.87 % (16055)------------------------------
% 9.47/2.88 % (16053)Instruction limit reached!
% 9.47/2.88 % (16053)------------------------------
% 9.47/2.88 % (16053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.88 % (16053)Termination reason: Unknown
% 9.47/2.88 % (16053)Termination phase: Function definition elimination
% 9.47/2.88
% 9.47/2.88 % (16053)Memory used [KB]: 3454
% 9.47/2.88 % (16053)Time elapsed: 0.082 s
% 9.47/2.88 % (16053)Instructions burned: 150 (million)
% 9.47/2.88 % (16053)------------------------------
% 9.47/2.88 % (16053)------------------------------
% 9.47/2.89 % (16043)Instruction limit reached!
% 9.47/2.89 % (16043)------------------------------
% 9.47/2.89 % (16043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.89 % (16043)Termination reason: Unknown
% 9.47/2.89 % (16043)Termination phase: Saturation
% 9.47/2.89
% 9.47/2.89 % (16043)Memory used [KB]: 4733
% 9.47/2.89 % (16043)Time elapsed: 0.239 s
% 9.47/2.89 % (16043)Instructions burned: 432 (million)
% 9.47/2.89 % (16043)------------------------------
% 9.47/2.89 % (16043)------------------------------
% 9.47/2.89 % (16057)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_15884 for (2990ds/140Mi)
% 10.23/2.90 % (16058)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_15884 for (2990ds/614Mi)
% 10.23/2.91 % (16059)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_15884 for (2990ds/202Mi)
% 10.23/2.93 % (16047)Instruction limit reached!
% 10.23/2.93 % (16047)------------------------------
% 10.23/2.93 % (16047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/2.93 % (16047)Termination reason: Unknown
% 10.23/2.93 % (16047)Termination phase: Saturation
% 10.23/2.93
% 10.23/2.93 % (16047)Memory used [KB]: 9083
% 10.23/2.93 % (16047)Time elapsed: 0.248 s
% 10.23/2.93 % (16047)Instructions burned: 453 (million)
% 10.23/2.93 % (16047)------------------------------
% 10.23/2.93 % (16047)------------------------------
% 10.23/2.96 % (16060)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_15884 for (2989ds/339Mi)
% 10.23/2.97 % (16057)Instruction limit reached!
% 10.23/2.97 % (16057)------------------------------
% 10.23/2.97 % (16057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/2.97 % (16057)Termination reason: Unknown
% 10.23/2.97 % (16057)Termination phase: Saturation
% 10.23/2.97
% 10.23/2.97 % (16057)Memory used [KB]: 7419
% 10.23/2.97 % (16057)Time elapsed: 0.082 s
% 10.23/2.97 % (16057)Instructions burned: 140 (million)
% 10.23/2.97 % (16057)------------------------------
% 10.23/2.97 % (16057)------------------------------
% 10.23/2.98 % (16056)Instruction limit reached!
% 10.23/2.98 % (16056)------------------------------
% 10.23/2.98 % (16056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/2.98 % (16056)Termination reason: Unknown
% 10.23/2.98 % (16056)Termination phase: Saturation
% 10.23/2.98
% 10.23/2.98 % (16056)Memory used [KB]: 8187
% 10.23/2.98 % (16056)Time elapsed: 0.146 s
% 10.23/2.98 % (16056)Instructions burned: 254 (million)
% 10.23/2.98 % (16056)------------------------------
% 10.23/2.98 % (16056)------------------------------
% 10.23/2.99 % (16061)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_15884 for (2989ds/283Mi)
% 10.23/3.00 % (16054)Instruction limit reached!
% 10.23/3.00 % (16054)------------------------------
% 10.23/3.00 % (16054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/3.00 % (16054)Termination reason: Unknown
% 10.23/3.00 % (16054)Termination phase: Saturation
% 10.23/3.00
% 10.23/3.00 % (16054)Memory used [KB]: 8187
% 10.23/3.00 % (16054)Time elapsed: 0.199 s
% 10.23/3.00 % (16054)Instructions burned: 343 (million)
% 10.23/3.00 % (16054)------------------------------
% 10.23/3.00 % (16054)------------------------------
% 10.23/3.00 % (16062)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_15884 for (2989ds/134Mi)
% 10.23/3.02 % (16059)Instruction limit reached!
% 10.23/3.02 % (16059)------------------------------
% 10.23/3.02 % (16059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/3.02 % (16059)Termination reason: Unknown
% 10.23/3.02 % (16059)Termination phase: Saturation
% 10.23/3.02
% 10.23/3.02 % (16059)Memory used [KB]: 8187
% 10.23/3.02 % (16059)Time elapsed: 0.115 s
% 10.23/3.02 % (16059)Instructions burned: 203 (million)
% 10.23/3.02 % (16059)------------------------------
% 10.23/3.02 % (16059)------------------------------
% 10.23/3.03 % (16064)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_15884 for (2988ds/298Mi)
% 11.87/3.04 % (16065)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_15884 for (2988ds/192Mi)
% 11.87/3.08 % (16062)Instruction limit reached!
% 11.87/3.08 % (16062)------------------------------
% 11.87/3.08 % (16062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.08 % (16062)Termination reason: Unknown
% 11.87/3.08 % (16062)Termination phase: Property scanning
% 11.87/3.08
% 11.87/3.08 % (16062)Memory used [KB]: 3326
% 11.87/3.08 % (16062)Time elapsed: 0.074 s
% 11.87/3.08 % (16062)Instructions burned: 134 (million)
% 11.87/3.08 % (16062)------------------------------
% 11.87/3.08 % (16062)------------------------------
% 11.87/3.10 % (16066)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_15884 for (2988ds/258Mi)
% 12.33/3.14 % (16060)Instruction limit reached!
% 12.33/3.14 % (16060)------------------------------
% 12.33/3.14 % (16060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.14 % (16060)Termination reason: Unknown
% 12.33/3.14 % (16060)Termination phase: Saturation
% 12.33/3.14
% 12.33/3.14 % (16060)Memory used [KB]: 8187
% 12.33/3.14 % (16060)Time elapsed: 0.182 s
% 12.33/3.14 % (16060)Instructions burned: 340 (million)
% 12.33/3.14 % (16060)------------------------------
% 12.33/3.14 % (16060)------------------------------
% 12.33/3.14 % (16061)Instruction limit reached!
% 12.33/3.14 % (16061)------------------------------
% 12.33/3.14 % (16061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.14 % (16061)Termination reason: Unknown
% 12.33/3.14 % (16061)Termination phase: Saturation
% 12.33/3.14
% 12.33/3.14 % (16061)Memory used [KB]: 7931
% 12.33/3.14 % (16061)Time elapsed: 0.149 s
% 12.33/3.14 % (16061)Instructions burned: 283 (million)
% 12.33/3.14 % (16061)------------------------------
% 12.33/3.14 % (16061)------------------------------
% 12.33/3.15 % (16065)Instruction limit reached!
% 12.33/3.15 % (16065)------------------------------
% 12.33/3.15 % (16065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.15 % (16065)Termination reason: Unknown
% 12.33/3.15 % (16065)Termination phase: Saturation
% 12.33/3.15
% 12.33/3.15 % (16065)Memory used [KB]: 3582
% 12.33/3.15 % (16065)Time elapsed: 0.106 s
% 12.33/3.15 % (16065)Instructions burned: 192 (million)
% 12.33/3.15 % (16065)------------------------------
% 12.33/3.15 % (16065)------------------------------
% 12.33/3.16 % (16067)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_15884 for (2987ds/90Mi)
% 12.33/3.16 % (16068)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_15884 for (2987ds/231Mi)
% 12.33/3.17 % (16069)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_15884 for (2987ds/458Mi)
% 12.33/3.18 % (16064)Instruction limit reached!
% 12.33/3.18 % (16064)------------------------------
% 12.33/3.18 % (16064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.18 % (16064)Termination reason: Unknown
% 12.33/3.18 % (16064)Termination phase: Saturation
% 12.33/3.18
% 12.33/3.18 % (16064)Memory used [KB]: 8443
% 12.33/3.18 % (16064)Time elapsed: 0.155 s
% 12.33/3.18 % (16064)Instructions burned: 298 (million)
% 12.33/3.18 % (16064)------------------------------
% 12.33/3.18 % (16064)------------------------------
% 12.82/3.20 % (16070)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_15884 for (2987ds/31Mi)
% 12.82/3.21 % (16067)Instruction limit reached!
% 12.82/3.21 % (16067)------------------------------
% 12.82/3.21 % (16067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.21 % (16067)Termination reason: Unknown
% 12.82/3.21 % (16067)Termination phase: Preprocessing 3
% 12.82/3.21
% 12.82/3.21 % (16067)Memory used [KB]: 2942
% 12.82/3.21 % (16067)Time elapsed: 0.051 s
% 12.82/3.21 % (16067)Instructions burned: 90 (million)
% 12.82/3.21 % (16067)------------------------------
% 12.82/3.21 % (16067)------------------------------
% 12.82/3.22 % (16070)Instruction limit reached!
% 12.82/3.22 % (16070)------------------------------
% 12.82/3.22 % (16070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.22 % (16070)Termination reason: Unknown
% 12.82/3.22 % (16070)Termination phase: shuffling
% 12.82/3.22
% 12.82/3.22 % (16070)Memory used [KB]: 2174
% 12.82/3.22 % (16070)Time elapsed: 0.020 s
% 12.82/3.22 % (16070)Instructions burned: 32 (million)
% 12.82/3.22 % (16070)------------------------------
% 12.82/3.22 % (16070)------------------------------
% 12.82/3.22 % (16040)Instruction limit reached!
% 12.82/3.22 % (16040)------------------------------
% 12.82/3.22 % (16040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.22 % (16040)Termination reason: Unknown
% 12.82/3.22 % (16040)Termination phase: Saturation
% 12.82/3.22
% 12.82/3.22 % (16040)Memory used [KB]: 9850
% 12.82/3.22 % (16040)Time elapsed: 0.639 s
% 12.82/3.22 % (16040)Instructions burned: 1088 (million)
% 12.82/3.22 % (16040)------------------------------
% 12.82/3.22 % (16040)------------------------------
% 12.82/3.23 % (16071)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_15884 for (2986ds/297Mi)
% 12.82/3.24 % (16072)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_15884 for (2986ds/987Mi)
% 12.82/3.24 % (16066)Instruction limit reached!
% 12.82/3.24 % (16066)------------------------------
% 12.82/3.24 % (16066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.24 % (16066)Termination reason: Unknown
% 12.82/3.24 % (16066)Termination phase: Saturation
% 12.82/3.24
% 12.82/3.24 % (16066)Memory used [KB]: 8315
% 12.82/3.24 % (16066)Time elapsed: 0.147 s
% 12.82/3.24 % (16066)Instructions burned: 259 (million)
% 12.82/3.24 % (16066)------------------------------
% 12.82/3.24 % (16066)------------------------------
% 12.82/3.25 % (16073)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_15884 for (2986ds/182Mi)
% 12.82/3.25 % (16058)Instruction limit reached!
% 12.82/3.25 % (16058)------------------------------
% 12.82/3.25 % (16058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.25 % (16058)Termination reason: Unknown
% 12.82/3.25 % (16058)Termination phase: Saturation
% 12.82/3.25
% 12.82/3.25 % (16058)Memory used [KB]: 9722
% 12.82/3.25 % (16058)Time elapsed: 0.352 s
% 12.82/3.25 % (16058)Instructions burned: 614 (million)
% 12.82/3.25 % (16058)------------------------------
% 12.82/3.25 % (16058)------------------------------
% 12.82/3.27 % (16074)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_15884 for (2986ds/182Mi)
% 12.82/3.28 % (16075)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_15884 for (2986ds/154Mi)
% 12.82/3.28 % (16068)Instruction limit reached!
% 12.82/3.28 % (16068)------------------------------
% 12.82/3.28 % (16068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.28 % (16068)Termination reason: Unknown
% 12.82/3.28 % (16068)Termination phase: Property scanning
% 12.82/3.28
% 12.82/3.28 % (16068)Memory used [KB]: 3326
% 12.82/3.28 % (16068)Time elapsed: 0.120 s
% 12.82/3.28 % (16068)Instructions burned: 231 (million)
% 12.82/3.28 % (16068)------------------------------
% 12.82/3.28 % (16068)------------------------------
% 13.34/3.30 % (16076)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_15884 for (2986ds/79Mi)
% 13.34/3.34 % (16073)Instruction limit reached!
% 13.34/3.34 % (16073)------------------------------
% 13.34/3.34 % (16073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.34 % (16073)Termination reason: Unknown
% 13.34/3.34 % (16073)Termination phase: Property scanning
% 13.34/3.34
% 13.34/3.34 % (16073)Memory used [KB]: 3454
% 13.34/3.34 % (16073)Time elapsed: 0.099 s
% 13.34/3.34 % (16073)Instructions burned: 182 (million)
% 13.34/3.34 % (16073)------------------------------
% 13.34/3.34 % (16073)------------------------------
% 13.34/3.35 % (16076)Instruction limit reached!
% 13.34/3.35 % (16076)------------------------------
% 13.34/3.35 % (16076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.35 % (16076)Termination reason: Unknown
% 13.34/3.35 % (16076)Termination phase: Preprocessing 3
% 13.34/3.35
% 13.34/3.35 % (16076)Memory used [KB]: 2686
% 13.34/3.35 % (16076)Time elapsed: 0.045 s
% 13.34/3.35 % (16076)Instructions burned: 79 (million)
% 13.34/3.35 % (16076)------------------------------
% 13.34/3.35 % (16076)------------------------------
% 13.34/3.35 % (16075)Instruction limit reached!
% 13.34/3.35 % (16075)------------------------------
% 13.34/3.35 % (16075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.35 % (16075)Termination reason: Unknown
% 13.34/3.35 % (16075)Termination phase: Property scanning
% 13.34/3.35
% 13.34/3.35 % (16075)Memory used [KB]: 3198
% 13.34/3.35 % (16075)Time elapsed: 0.081 s
% 13.34/3.35 % (16075)Instructions burned: 154 (million)
% 13.34/3.35 % (16075)------------------------------
% 13.34/3.35 % (16075)------------------------------
% 13.34/3.36 % (16074)Instruction limit reached!
% 13.34/3.36 % (16074)------------------------------
% 13.34/3.36 % (16074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.36 % (16074)Termination reason: Unknown
% 13.34/3.36 % (16074)Termination phase: Property scanning
% 13.34/3.36
% 13.34/3.36 % (16074)Memory used [KB]: 3582
% 13.34/3.36 % (16074)Time elapsed: 0.100 s
% 13.34/3.36 % (16074)Instructions burned: 183 (million)
% 13.34/3.36 % (16074)------------------------------
% 13.34/3.36 % (16074)------------------------------
% 13.34/3.36 % (16077)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_15884 for (2985ds/216Mi)
% 13.34/3.37 % (16078)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_15884 for (2985ds/114Mi)
% 13.34/3.38 % (16079)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_15884 for (2985ds/922Mi)
% 13.34/3.39 % (16080)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_15884 for (2985ds/182Mi)
% 13.34/3.39 % (16071)Instruction limit reached!
% 13.34/3.39 % (16071)------------------------------
% 13.34/3.39 % (16071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.39 % (16071)Termination reason: Unknown
% 13.34/3.39 % (16071)Termination phase: Saturation
% 13.34/3.39
% 13.34/3.39 % (16071)Memory used [KB]: 8827
% 13.34/3.39 % (16071)Time elapsed: 0.164 s
% 13.34/3.39 % (16071)Instructions burned: 297 (million)
% 13.34/3.39 % (16071)------------------------------
% 13.34/3.39 % (16071)------------------------------
% 13.92/3.42 % (16081)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_15884 for (2985ds/164Mi)
% 13.92/3.43 % (16078)Instruction limit reached!
% 13.92/3.43 % (16078)------------------------------
% 13.92/3.43 % (16078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.43 % (16078)Termination reason: Unknown
% 13.92/3.43 % (16078)Termination phase: Property scanning
% 13.92/3.43
% 13.92/3.43 % (16078)Memory used [KB]: 3326
% 13.92/3.43 % (16078)Time elapsed: 0.064 s
% 13.92/3.43 % (16078)Instructions burned: 114 (million)
% 13.92/3.43 % (16078)------------------------------
% 13.92/3.43 % (16078)------------------------------
% 13.92/3.43 % (16069)Instruction limit reached!
% 13.92/3.43 % (16069)------------------------------
% 13.92/3.43 % (16069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.43 % (16069)Termination reason: Unknown
% 13.92/3.43 % (16069)Termination phase: Saturation
% 13.92/3.43
% 13.92/3.43 % (16069)Memory used [KB]: 9594
% 13.92/3.43 % (16069)Time elapsed: 0.262 s
% 13.92/3.43 % (16069)Instructions burned: 458 (million)
% 13.92/3.43 % (16069)------------------------------
% 13.92/3.43 % (16069)------------------------------
% 13.92/3.45 % (16082)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_15884 for (2984ds/50Mi)
% 13.92/3.45 % (16083)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_15884 for (2984ds/368Mi)
% 13.92/3.48 % (16082)Instruction limit reached!
% 13.92/3.48 % (16082)------------------------------
% 13.92/3.48 % (16082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.48 % (16082)Termination reason: Unknown
% 13.92/3.48 % (16082)Termination phase: shuffling
% 13.92/3.48
% 13.92/3.48 % (16082)Memory used [KB]: 2686
% 13.92/3.48 % (16082)Time elapsed: 0.028 s
% 13.92/3.48 % (16082)Instructions burned: 50 (million)
% 13.92/3.48 % (16082)------------------------------
% 13.92/3.48 % (16082)------------------------------
% 13.92/3.48 % (16080)Instruction limit reached!
% 13.92/3.48 % (16080)------------------------------
% 13.92/3.48 % (16080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.48 % (16080)Termination reason: Unknown
% 13.92/3.48 % (16080)Termination phase: Property scanning
% 13.92/3.48
% 13.92/3.48 % (16080)Memory used [KB]: 3198
% 13.92/3.48 % (16080)Time elapsed: 0.095 s
% 13.92/3.48 % (16080)Instructions burned: 182 (million)
% 13.92/3.48 % (16080)------------------------------
% 13.92/3.48 % (16080)------------------------------
% 13.92/3.48 % (16077)Instruction limit reached!
% 13.92/3.48 % (16077)------------------------------
% 13.92/3.48 % (16077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.48 % (16077)Termination reason: Unknown
% 13.92/3.48 % (16077)Termination phase: Saturation
% 13.92/3.48
% 13.92/3.48 % (16077)Memory used [KB]: 7803
% 13.92/3.48 % (16077)Time elapsed: 0.117 s
% 13.92/3.48 % (16077)Instructions burned: 216 (million)
% 13.92/3.48 % (16077)------------------------------
% 13.92/3.48 % (16077)------------------------------
% 14.59/3.50 % (16086)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_15884 for (2984ds/204Mi)
% 14.59/3.50 % (16084)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_15884 for (2984ds/1021Mi)
% 14.59/3.50 % (16085)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_15884 for (2984ds/267Mi)
% 14.59/3.50 % (16081)Instruction limit reached!
% 14.59/3.50 % (16081)------------------------------
% 14.59/3.50 % (16081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.50 % (16081)Termination reason: Unknown
% 14.59/3.50 % (16081)Termination phase: SInE selection
% 14.59/3.50
% 14.59/3.50 % (16081)Memory used [KB]: 3198
% 14.59/3.50 % (16081)Time elapsed: 0.089 s
% 14.59/3.50 % (16081)Instructions burned: 164 (million)
% 14.59/3.50 % (16081)------------------------------
% 14.59/3.50 % (16081)------------------------------
% 14.59/3.53 % (16087)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_15884 for (2983ds/26Mi)
% 14.59/3.54 % (16087)Instruction limit reached!
% 14.59/3.54 % (16087)------------------------------
% 14.59/3.54 % (16087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.54 % (16087)Termination reason: Unknown
% 14.59/3.54 % (16087)Termination phase: shuffling
% 14.59/3.54
% 14.59/3.54 % (16087)Memory used [KB]: 2174
% 14.59/3.54 % (16087)Time elapsed: 0.016 s
% 14.59/3.54 % (16087)Instructions burned: 26 (million)
% 14.59/3.54 % (16087)------------------------------
% 14.59/3.54 % (16087)------------------------------
% 14.59/3.56 % (16088)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_15884 for (2983ds/53Mi)
% 14.59/3.59 % (16088)Instruction limit reached!
% 14.59/3.59 % (16088)------------------------------
% 14.59/3.59 % (16088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.59 % (16088)Termination reason: Unknown
% 14.59/3.59 % (16088)Termination phase: shuffling
% 14.59/3.59
% 14.59/3.59 % (16088)Memory used [KB]: 2686
% 14.59/3.59 % (16088)Time elapsed: 0.030 s
% 14.59/3.59 % (16088)Instructions burned: 53 (million)
% 14.59/3.59 % (16088)------------------------------
% 14.59/3.59 % (16088)------------------------------
% 14.79/3.61 % (16086)Instruction limit reached!
% 14.79/3.61 % (16086)------------------------------
% 14.79/3.61 % (16086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.61 % (16086)Termination reason: Unknown
% 14.79/3.61 % (16086)Termination phase: Saturation
% 14.79/3.61
% 14.79/3.61 % (16086)Memory used [KB]: 7931
% 14.79/3.61 % (16086)Time elapsed: 0.114 s
% 14.79/3.61 % (16086)Instructions burned: 205 (million)
% 14.79/3.61 % (16086)------------------------------
% 14.79/3.61 % (16086)------------------------------
% 14.79/3.61 % (16089)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_15884 for (2983ds/4436Mi)
% 14.79/3.63 % (16090)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_15884 for (2982ds/1539Mi)
% 14.79/3.64 % (16085)Instruction limit reached!
% 14.79/3.64 % (16085)------------------------------
% 14.79/3.64 % (16085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.64 % (16085)Termination reason: Unknown
% 14.79/3.64 % (16085)Termination phase: Saturation
% 14.79/3.64
% 14.79/3.64 % (16085)Memory used [KB]: 7803
% 14.79/3.64 % (16085)Time elapsed: 0.139 s
% 14.79/3.64 % (16085)Instructions burned: 267 (million)
% 14.79/3.64 % (16085)------------------------------
% 14.79/3.64 % (16085)------------------------------
% 14.79/3.65 % (16083)Instruction limit reached!
% 14.79/3.65 % (16083)------------------------------
% 14.79/3.65 % (16083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.65 % (16083)Termination reason: Unknown
% 14.79/3.65 % (16083)Termination phase: Saturation
% 14.79/3.65
% 14.79/3.65 % (16083)Memory used [KB]: 9083
% 14.79/3.65 % (16083)Time elapsed: 0.204 s
% 14.79/3.65 % (16083)Instructions burned: 368 (million)
% 14.79/3.65 % (16083)------------------------------
% 14.79/3.65 % (16083)------------------------------
% 14.79/3.66 % (16091)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_15884 for (2982ds/408Mi)
% 14.79/3.68 % (16092)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_15884 for (2982ds/5205Mi)
% 15.30/3.83 % (16072)Instruction limit reached!
% 15.30/3.83 % (16072)------------------------------
% 15.30/3.83 % (16072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.30/3.83 % (16072)Termination reason: Unknown
% 15.30/3.83 % (16072)Termination phase: Saturation
% 15.30/3.83
% 15.30/3.83 % (16072)Memory used [KB]: 11001
% 15.30/3.83 % (16072)Time elapsed: 0.589 s
% 15.30/3.83 % (16072)Instructions burned: 988 (million)
% 15.30/3.83 % (16072)------------------------------
% 15.30/3.83 % (16072)------------------------------
% 15.30/3.85 % (16093)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_15884 for (2980ds/1913Mi)
% 15.30/3.88 % (16091)Instruction limit reached!
% 15.30/3.88 % (16091)------------------------------
% 15.30/3.88 % (16091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.30/3.88 % (16091)Termination reason: Unknown
% 15.30/3.88 % (16091)Termination phase: Saturation
% 15.30/3.88
% 15.30/3.88 % (16091)Memory used [KB]: 10874
% 15.30/3.88 % (16091)Time elapsed: 0.225 s
% 15.30/3.88 % (16091)Instructions burned: 409 (million)
% 15.30/3.88 % (16091)------------------------------
% 15.30/3.88 % (16091)------------------------------
% 15.30/3.88 % (16079)Instruction limit reached!
% 15.30/3.88 % (16079)------------------------------
% 15.30/3.88 % (16079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.30/3.88 % (16079)Termination reason: Unknown
% 15.30/3.88 % (16079)Termination phase: Saturation
% 15.30/3.88
% 15.30/3.88 % (16079)Memory used [KB]: 9083
% 15.30/3.88 % (16079)Time elapsed: 0.510 s
% 15.30/3.88 % (16079)Instructions burned: 923 (million)
% 15.30/3.88 % (16079)------------------------------
% 15.30/3.88 % (16079)------------------------------
% 15.30/3.89 % (16094)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_15884 for (2980ds/4350Mi)
% 16.69/3.90 % (16095)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_15884 for (2980ds/68Mi)
% 16.69/3.94 % (16095)Instruction limit reached!
% 16.69/3.94 % (16095)------------------------------
% 16.69/3.94 % (16095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.69/3.94 % (16095)Termination reason: Unknown
% 16.69/3.94 % (16095)Termination phase: Property scanning
% 16.69/3.94
% 16.69/3.94 % (16095)Memory used [KB]: 2430
% 16.69/3.94 % (16095)Time elapsed: 0.039 s
% 16.69/3.94 % (16095)Instructions burned: 68 (million)
% 16.69/3.94 % (16095)------------------------------
% 16.69/3.94 % (16095)------------------------------
% 16.69/3.96 % (16096)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_15884 for (2979ds/358Mi)
% 18.88/4.08 % (16084)Instruction limit reached!
% 18.88/4.08 % (16084)------------------------------
% 18.88/4.08 % (16084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.88/4.08 % (16084)Termination reason: Unknown
% 18.88/4.08 % (16084)Termination phase: Saturation
% 18.88/4.08
% 18.88/4.08 % (16084)Memory used [KB]: 10362
% 18.88/4.08 % (16084)Time elapsed: 0.581 s
% 18.88/4.08 % (16084)Instructions burned: 1021 (million)
% 18.88/4.08 % (16084)------------------------------
% 18.88/4.08 % (16084)------------------------------
% 18.88/4.10 % (16097)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_15884 for (2978ds/31Mi)
% 18.88/4.12 % (16097)Instruction limit reached!
% 18.88/4.12 % (16097)------------------------------
% 18.88/4.12 % (16097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.88/4.12 % (16097)Termination reason: Unknown
% 18.88/4.12 % (16097)Termination phase: shuffling
% 18.88/4.12
% 18.88/4.12 % (16097)Memory used [KB]: 2174
% 18.88/4.12 % (16097)Time elapsed: 0.020 s
% 18.88/4.12 % (16097)Instructions burned: 31 (million)
% 18.88/4.12 % (16097)------------------------------
% 18.88/4.12 % (16097)------------------------------
% 19.59/4.14 % (16098)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_15884 for (2977ds/279Mi)
% 19.59/4.17 % (16096)Instruction limit reached!
% 19.59/4.17 % (16096)------------------------------
% 19.59/4.17 % (16096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.59/4.17 % (16096)Termination reason: Unknown
% 19.59/4.17 % (16096)Termination phase: Saturation
% 19.59/4.17
% 19.59/4.17 % (16096)Memory used [KB]: 8187
% 19.59/4.17 % (16096)Time elapsed: 0.204 s
% 19.59/4.17 % (16096)Instructions burned: 358 (million)
% 19.59/4.17 % (16096)------------------------------
% 19.59/4.17 % (16096)------------------------------
% 19.59/4.19 % (16099)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_15884 for (2977ds/258Mi)
% 19.98/4.25 % (16098)Refutation not found, incomplete strategy
% 19.98/4.25 % (16098)------------------------------
% 19.98/4.25 % (16098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.98/4.25 % (16098)Termination reason: Refutation not found, incomplete strategy
% 19.98/4.25
% 19.98/4.25
% 19.98/4.25 % (16098)Memory used [KB]: 8059
% 19.98/4.25 % (16098)Time elapsed: 0.109 s
% 19.98/4.25 % (16098)Instructions burned: 204 (million)
% 19.98/4.25 % (16098)------------------------------
% 19.98/4.25 % (16098)------------------------------
% 19.98/4.27 % (16100)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_15884 for (2976ds/26Mi)
% 19.98/4.29 % (16100)Instruction limit reached!
% 19.98/4.29 % (16100)------------------------------
% 19.98/4.29 % (16100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.98/4.29 % (16100)Termination reason: Unknown
% 19.98/4.29 % (16100)Termination phase: shuffling
% 19.98/4.29
% 19.98/4.29 % (16100)Memory used [KB]: 2174
% 19.98/4.29 % (16100)Time elapsed: 0.016 s
% 19.98/4.29 % (16100)Instructions burned: 26 (million)
% 19.98/4.29 % (16100)------------------------------
% 19.98/4.29 % (16100)------------------------------
% 20.64/4.31 % (16101)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_15884 for (2976ds/995Mi)
% 20.64/4.33 % (16099)Instruction limit reached!
% 20.64/4.33 % (16099)------------------------------
% 20.64/4.33 % (16099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.64/4.33 % (16099)Termination reason: Unknown
% 20.64/4.33 % (16099)Termination phase: Saturation
% 20.64/4.33
% 20.64/4.33 % (16099)Memory used [KB]: 8443
% 20.64/4.33 % (16099)Time elapsed: 0.143 s
% 20.64/4.33 % (16099)Instructions burned: 259 (million)
% 20.64/4.33 % (16099)------------------------------
% 20.64/4.33 % (16099)------------------------------
% 20.64/4.35 % (16102)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_15884 for (2975ds/373Mi)
% 21.81/4.52 % (16090)Instruction limit reached!
% 21.81/4.52 % (16090)------------------------------
% 21.81/4.52 % (16090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.81/4.52 % (16090)Termination reason: Unknown
% 21.81/4.52 % (16090)Termination phase: Saturation
% 21.81/4.52
% 21.81/4.52 % (16090)Memory used [KB]: 10618
% 21.81/4.52 % (16090)Time elapsed: 0.889 s
% 21.81/4.52 % (16090)Instructions burned: 1539 (million)
% 21.81/4.52 % (16090)------------------------------
% 21.81/4.52 % (16090)------------------------------
% 21.81/4.54 % (16103)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_15884 for (2973ds/253Mi)
% 21.81/4.56 % (16102)Instruction limit reached!
% 21.81/4.56 % (16102)------------------------------
% 21.81/4.56 % (16102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.81/4.56 % (16102)Termination reason: Unknown
% 21.81/4.56 % (16102)Termination phase: Saturation
% 21.81/4.56
% 21.81/4.56 % (16102)Memory used [KB]: 8827
% 21.81/4.56 % (16102)Time elapsed: 0.236 s
% 21.81/4.56 % (16102)Instructions burned: 374 (million)
% 21.81/4.56 % (16102)------------------------------
% 21.81/4.56 % (16102)------------------------------
% 21.81/4.59 % (16104)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_15884 for (2973ds/832Mi)
% 22.49/4.68 % (16103)Instruction limit reached!
% 22.49/4.68 % (16103)------------------------------
% 22.49/4.68 % (16103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.49/4.68 % (16103)Termination reason: Unknown
% 22.49/4.68 % (16103)Termination phase: Saturation
% 22.49/4.68
% 22.49/4.68 % (16103)Memory used [KB]: 7803
% 22.49/4.68 % (16103)Time elapsed: 0.135 s
% 22.49/4.68 % (16103)Instructions burned: 253 (million)
% 22.49/4.68 % (16103)------------------------------
% 22.49/4.68 % (16103)------------------------------
% 23.04/4.70 % (16105)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_15884 for (2972ds/668Mi)
% 23.44/4.86 % (16101)Instruction limit reached!
% 23.44/4.86 % (16101)------------------------------
% 23.44/4.86 % (16101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.44/4.86 % (16101)Termination reason: Unknown
% 23.44/4.86 % (16101)Termination phase: Saturation
% 23.44/4.86
% 23.44/4.86 % (16101)Memory used [KB]: 12665
% 23.44/4.86 % (16101)Time elapsed: 0.551 s
% 23.44/4.86 % (16101)Instructions burned: 995 (million)
% 23.44/4.86 % (16101)------------------------------
% 23.44/4.86 % (16101)------------------------------
% 23.44/4.88 % (16106)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_15884 for (2970ds/40Mi)
% 24.41/4.90 % (16093)Instruction limit reached!
% 24.41/4.90 % (16093)------------------------------
% 24.41/4.90 % (16093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.41/4.90 % (16093)Termination reason: Unknown
% 24.41/4.90 % (16093)Termination phase: Saturation
% 24.41/4.90
% 24.41/4.90 % (16093)Memory used [KB]: 4221
% 24.41/4.90 % (16093)Time elapsed: 1.052 s
% 24.41/4.90 % (16093)Instructions burned: 1914 (million)
% 24.41/4.90 % (16093)------------------------------
% 24.41/4.90 % (16093)------------------------------
% 24.41/4.91 % (16106)Instruction limit reached!
% 24.41/4.91 % (16106)------------------------------
% 24.41/4.91 % (16106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.41/4.91 % (16106)Termination reason: Unknown
% 24.41/4.91 % (16106)Termination phase: shuffling
% 24.41/4.91
% 24.41/4.91 % (16106)Memory used [KB]: 2558
% 24.41/4.91 % (16106)Time elapsed: 0.024 s
% 24.41/4.91 % (16106)Instructions burned: 41 (million)
% 24.41/4.91 % (16106)------------------------------
% 24.41/4.91 % (16106)------------------------------
% 24.41/4.92 % (16107)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_15884 for (2969ds/294Mi)
% 24.41/4.93 % (16108)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_15884 for (2969ds/187Mi)
% 24.41/5.03 % (16108)Instruction limit reached!
% 24.41/5.03 % (16108)------------------------------
% 24.41/5.03 % (16108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.41/5.03 % (16108)Termination reason: Unknown
% 24.41/5.03 % (16108)Termination phase: Property scanning
% 24.41/5.03
% 24.41/5.03 % (16108)Memory used [KB]: 3454
% 24.41/5.03 % (16108)Time elapsed: 0.102 s
% 24.41/5.03 % (16108)Instructions burned: 187 (million)
% 24.41/5.03 % (16108)------------------------------
% 24.41/5.03 % (16108)------------------------------
% 25.84/5.05 % (16109)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_15884 for (2968ds/371Mi)
% 25.84/5.07 % (16104)Instruction limit reached!
% 25.84/5.07 % (16104)------------------------------
% 25.84/5.07 % (16104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.84/5.07 % (16104)Termination reason: Unknown
% 25.84/5.07 % (16104)Termination phase: Saturation
% 25.84/5.07
% 25.84/5.07 % (16104)Memory used [KB]: 11257
% 25.84/5.07 % (16104)Time elapsed: 0.502 s
% 25.84/5.07 % (16104)Instructions burned: 832 (million)
% 25.84/5.07 % (16104)------------------------------
% 25.84/5.07 % (16104)------------------------------
% 25.84/5.07 % (16105)Instruction limit reached!
% 25.84/5.07 % (16105)------------------------------
% 25.84/5.07 % (16105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.84/5.07 % (16105)Termination reason: Unknown
% 25.84/5.07 % (16105)Termination phase: Saturation
% 25.84/5.07
% 25.84/5.07 % (16105)Memory used [KB]: 16630
% 25.84/5.07 % (16105)Time elapsed: 0.368 s
% 25.84/5.07 % (16105)Instructions burned: 669 (million)
% 25.84/5.07 % (16105)------------------------------
% 25.84/5.07 % (16105)------------------------------
% 25.84/5.08 % (16107)Instruction limit reached!
% 25.84/5.08 % (16107)------------------------------
% 25.84/5.08 % (16107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.84/5.08 % (16107)Termination reason: Unknown
% 25.84/5.08 % (16107)Termination phase: Saturation
% 25.84/5.08
% 25.84/5.08 % (16107)Memory used [KB]: 8827
% 25.84/5.08 % (16107)Time elapsed: 0.162 s
% 25.84/5.08 % (16107)Instructions burned: 294 (million)
% 25.84/5.08 % (16107)------------------------------
% 25.84/5.08 % (16107)------------------------------
% 25.84/5.09 % (16110)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_15884 for (2968ds/1827Mi)
% 25.84/5.09 % (16111)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_15884 for (2968ds/70Mi)
% 25.84/5.11 % (16112)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_15884 for (2968ds/316Mi)
% 26.37/5.13 % (16111)Instruction limit reached!
% 26.37/5.13 % (16111)------------------------------
% 26.37/5.13 % (16111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.37/5.13 % (16111)Termination reason: Unknown
% 26.37/5.13 % (16111)Termination phase: shuffling
% 26.37/5.13
% 26.37/5.13 % (16111)Memory used [KB]: 2942
% 26.37/5.13 % (16111)Time elapsed: 0.039 s
% 26.37/5.13 % (16111)Instructions burned: 70 (million)
% 26.37/5.13 % (16111)------------------------------
% 26.37/5.13 % (16111)------------------------------
% 26.37/5.15 % (16113)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_15884 for (2967ds/932Mi)
% 26.62/5.26 % (16109)Instruction limit reached!
% 26.62/5.26 % (16109)------------------------------
% 26.62/5.26 % (16109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.62/5.26 % (16109)Termination reason: Unknown
% 26.62/5.26 % (16109)Termination phase: Saturation
% 26.62/5.26
% 26.62/5.26 % (16109)Memory used [KB]: 8315
% 26.62/5.26 % (16109)Time elapsed: 0.215 s
% 26.62/5.26 % (16109)Instructions burned: 372 (million)
% 26.62/5.26 % (16109)------------------------------
% 26.62/5.26 % (16109)------------------------------
% 26.62/5.27 % (16112)Refutation not found, incomplete strategy
% 26.62/5.27 % (16112)------------------------------
% 26.62/5.27 % (16112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.62/5.27 % (16112)Termination reason: Refutation not found, incomplete strategy
% 26.62/5.27
% 26.62/5.27
% 26.62/5.27 % (16112)Memory used [KB]: 8187
% 26.62/5.27 % (16112)Time elapsed: 0.163 s
% 26.62/5.27 % (16112)Instructions burned: 303 (million)
% 26.62/5.27 % (16112)------------------------------
% 26.62/5.27 % (16112)------------------------------
% 26.62/5.29 % (16114)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_15884 for (2966ds/4714Mi)
% 26.62/5.29 % (16115)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_15884 for (2966ds/8250Mi)
% 27.65/5.45 % (16114)Refutation not found, incomplete strategy
% 27.65/5.45 % (16114)------------------------------
% 27.65/5.45 % (16114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.65/5.45 % (16114)Termination reason: Refutation not found, incomplete strategy
% 27.65/5.45
% 27.65/5.45
% 27.65/5.45 % (16114)Memory used [KB]: 8315
% 27.65/5.45 % (16114)Time elapsed: 0.167 s
% 27.65/5.45 % (16114)Instructions burned: 306 (million)
% 27.65/5.45 % (16114)------------------------------
% 27.65/5.45 % (16114)------------------------------
% 27.65/5.48 % (16116)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_15884 for (2964ds/770Mi)
% 28.44/5.69 % (16113)Instruction limit reached!
% 28.44/5.69 % (16113)------------------------------
% 28.44/5.69 % (16113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.44/5.69 % (16113)Termination reason: Unknown
% 28.44/5.69 % (16113)Termination phase: Saturation
% 28.44/5.69
% 28.44/5.69 % (16113)Memory used [KB]: 12153
% 28.44/5.69 % (16113)Time elapsed: 0.537 s
% 28.44/5.69 % (16113)Instructions burned: 933 (million)
% 28.44/5.69 % (16113)------------------------------
% 28.44/5.69 % (16113)------------------------------
% 29.29/5.71 % (16117)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_15884 for (2962ds/794Mi)
% 29.89/5.93 % (16116)Instruction limit reached!
% 29.89/5.93 % (16116)------------------------------
% 29.89/5.93 % (16116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.89/5.93 % (16116)Termination reason: Unknown
% 29.89/5.93 % (16116)Termination phase: Saturation
% 29.89/5.93
% 29.89/5.93 % (16116)Memory used [KB]: 8315
% 29.89/5.93 % (16116)Time elapsed: 0.453 s
% 29.89/5.93 % (16116)Instructions burned: 771 (million)
% 29.89/5.93 % (16116)------------------------------
% 29.89/5.93 % (16116)------------------------------
% 29.89/5.95 % (16118)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_15884 for (2959ds/464Mi)
% 33.58/6.13 % (16110)Instruction limit reached!
% 33.58/6.13 % (16110)------------------------------
% 33.58/6.13 % (16110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.58/6.13 % (16110)Termination reason: Unknown
% 33.58/6.13 % (16110)Termination phase: Saturation
% 33.58/6.13
% 33.58/6.13 % (16110)Memory used [KB]: 10874
% 33.58/6.13 % (16110)Time elapsed: 1.047 s
% 33.58/6.13 % (16110)Instructions burned: 1827 (million)
% 33.58/6.13 % (16110)------------------------------
% 33.58/6.13 % (16110)------------------------------
% 33.58/6.16 % (16119)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_15884 for (2957ds/1376Mi)
% 33.58/6.17 % (16117)Instruction limit reached!
% 33.58/6.17 % (16117)------------------------------
% 33.58/6.17 % (16117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.58/6.17 % (16117)Termination reason: Unknown
% 33.58/6.17 % (16117)Termination phase: Saturation
% 33.58/6.17
% 33.58/6.17 % (16117)Memory used [KB]: 7803
% 33.58/6.17 % (16117)Time elapsed: 0.460 s
% 33.58/6.17 % (16117)Instructions burned: 794 (million)
% 33.58/6.17 % (16117)------------------------------
% 33.58/6.17 % (16117)------------------------------
% 33.58/6.17 % (16089)Instruction limit reached!
% 33.58/6.17 % (16089)------------------------------
% 33.58/6.17 % (16089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.58/6.17 % (16089)Termination reason: Unknown
% 33.58/6.17 % (16089)Termination phase: Saturation
% 33.58/6.17
% 33.58/6.17 % (16089)Memory used [KB]: 14200
% 33.58/6.17 % (16089)Time elapsed: 2.559 s
% 33.58/6.17 % (16089)Instructions burned: 4436 (million)
% 33.58/6.17 % (16089)------------------------------
% 33.58/6.17 % (16089)------------------------------
% 33.58/6.19 % (16121)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_15884 for (2957ds/434Mi)
% 33.58/6.19 % (16120)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_15884 for (2957ds/906Mi)
% 33.98/6.21 % (16118)Instruction limit reached!
% 33.98/6.21 % (16118)------------------------------
% 33.98/6.21 % (16118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.98/6.21 % (16118)Termination reason: Unknown
% 33.98/6.21 % (16118)Termination phase: Saturation
% 33.98/6.21
% 33.98/6.21 % (16118)Memory used [KB]: 8699
% 33.98/6.21 % (16118)Time elapsed: 0.265 s
% 33.98/6.21 % (16118)Instructions burned: 465 (million)
% 33.98/6.21 % (16118)------------------------------
% 33.98/6.21 % (16118)------------------------------
% 33.98/6.24 % (16122)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_15884 for (2956ds/865Mi)
% 33.98/6.29 % (16094)Refutation not found, non-redundant clauses discarded% (16094)------------------------------
% 33.98/6.29 % (16094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.98/6.29 % (16094)Termination reason: Refutation not found, non-redundant clauses discarded
% 33.98/6.29
% 33.98/6.29 % (16094)Memory used [KB]: 13048
% 33.98/6.29 % (16094)Time elapsed: 2.396 s
% 33.98/6.29 % (16094)Instructions burned: 4304 (million)
% 33.98/6.29 % (16094)------------------------------
% 33.98/6.29 % (16094)------------------------------
% 34.31/6.31 % (16123)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_15884 for (2956ds/593Mi)
% 34.51/6.43 % (16121)Instruction limit reached!
% 34.51/6.43 % (16121)------------------------------
% 34.51/6.43 % (16121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.51/6.43 % (16121)Termination reason: Unknown
% 34.51/6.43 % (16121)Termination phase: Saturation
% 34.51/6.43
% 34.51/6.43 % (16121)Memory used [KB]: 8443
% 34.51/6.43 % (16121)Time elapsed: 0.241 s
% 34.51/6.43 % (16121)Instructions burned: 435 (million)
% 34.51/6.43 % (16121)------------------------------
% 34.51/6.43 % (16121)------------------------------
% 34.51/6.46 % (16124)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_15884 for (2954ds/443Mi)
% 35.16/6.63 % (16123)Instruction limit reached!
% 35.16/6.63 % (16123)------------------------------
% 35.16/6.63 % (16123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.16/6.63 % (16123)Termination reason: Unknown
% 35.16/6.63 % (16123)Termination phase: Saturation
% 35.16/6.63
% 35.16/6.63 % (16123)Memory used [KB]: 11513
% 35.16/6.63 % (16123)Time elapsed: 0.320 s
% 35.16/6.63 % (16123)Instructions burned: 593 (million)
% 35.16/6.63 % (16123)------------------------------
% 35.16/6.63 % (16123)------------------------------
% 35.16/6.65 % (16125)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_15884 for (2952ds/594Mi)
% 35.71/6.71 % (16124)Instruction limit reached!
% 35.71/6.71 % (16124)------------------------------
% 35.71/6.71 % (16124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.71/6.71 % (16124)Termination reason: Unknown
% 35.71/6.71 % (16124)Termination phase: Saturation
% 35.71/6.71
% 35.71/6.71 % (16124)Memory used [KB]: 8571
% 35.71/6.71 % (16124)Time elapsed: 0.252 s
% 35.71/6.71 % (16124)Instructions burned: 443 (million)
% 35.71/6.71 % (16124)------------------------------
% 35.71/6.71 % (16124)------------------------------
% 35.71/6.72 % (16122)Instruction limit reached!
% 35.71/6.72 % (16122)------------------------------
% 35.71/6.72 % (16122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.71/6.72 % (16122)Termination reason: Unknown
% 35.71/6.72 % (16122)Termination phase: Saturation
% 35.71/6.72
% 35.71/6.72 % (16122)Memory used [KB]: 11513
% 35.71/6.72 % (16122)Time elapsed: 0.488 s
% 35.71/6.72 % (16122)Instructions burned: 866 (million)
% 35.71/6.72 % (16122)------------------------------
% 35.71/6.72 % (16122)------------------------------
% 35.71/6.73 % (16126)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_15884 for (2951ds/327Mi)
% 35.71/6.75 % (16127)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_15884 for (2951ds/5411Mi)
% 35.71/6.78 % (16120)Instruction limit reached!
% 35.71/6.78 % (16120)------------------------------
% 35.71/6.78 % (16120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.71/6.78 % (16120)Termination reason: Unknown
% 35.71/6.78 % (16120)Termination phase: Saturation
% 35.71/6.78
% 35.71/6.78 % (16120)Memory used [KB]: 13432
% 35.71/6.78 % (16120)Time elapsed: 0.592 s
% 35.71/6.78 % (16120)Instructions burned: 906 (million)
% 35.71/6.78 % (16120)------------------------------
% 35.71/6.78 % (16120)------------------------------
% 37.31/6.81 % (16128)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_15884 for (2951ds/1762Mi)
% 37.31/6.88 % (16092)Instruction limit reached!
% 37.31/6.88 % (16092)------------------------------
% 37.31/6.88 % (16092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.31/6.88 % (16092)Termination reason: Unknown
% 37.31/6.88 % (16092)Termination phase: Saturation
% 37.31/6.88
% 37.31/6.88 % (16092)Memory used [KB]: 15095
% 37.31/6.88 % (16092)Time elapsed: 3.204 s
% 37.31/6.88 % (16092)Instructions burned: 5206 (million)
% 37.31/6.88 % (16092)------------------------------
% 37.31/6.88 % (16092)------------------------------
% 37.49/6.90 % (16129)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_15884 for (2950ds/96Mi)
% 37.49/6.91 % (16126)Instruction limit reached!
% 37.49/6.91 % (16126)------------------------------
% 37.49/6.91 % (16126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.49/6.91 % (16126)Termination reason: Unknown
% 37.49/6.91 % (16126)Termination phase: Saturation
% 37.49/6.91
% 37.49/6.91 % (16126)Memory used [KB]: 8955
% 37.49/6.91 % (16126)Time elapsed: 0.184 s
% 37.49/6.91 % (16126)Instructions burned: 327 (million)
% 37.49/6.91 % (16126)------------------------------
% 37.49/6.91 % (16126)------------------------------
% 37.49/6.93 % (16130)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_15884 for (2949ds/503Mi)
% 37.49/6.95 % (16119)Instruction limit reached!
% 37.49/6.95 % (16119)------------------------------
% 37.49/6.95 % (16119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.49/6.95 % (16119)Termination reason: Unknown
% 37.49/6.95 % (16119)Termination phase: Saturation
% 37.49/6.95
% 37.49/6.95 % (16119)Memory used [KB]: 15095
% 37.49/6.95 % (16119)Time elapsed: 0.792 s
% 37.49/6.95 % (16119)Instructions burned: 1377 (million)
% 37.49/6.95 % (16119)------------------------------
% 37.49/6.95 % (16119)------------------------------
% 37.49/6.95 % (16129)Instruction limit reached!
% 37.49/6.95 % (16129)------------------------------
% 37.49/6.95 % (16129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.49/6.95 % (16129)Termination reason: Unknown
% 37.49/6.95 % (16129)Termination phase: Property scanning
% 37.49/6.95
% 37.49/6.95 % (16129)Memory used [KB]: 3198
% 37.49/6.95 % (16129)Time elapsed: 0.053 s
% 37.49/6.95 % (16129)Instructions burned: 97 (million)
% 37.49/6.95 % (16129)------------------------------
% 37.49/6.95 % (16129)------------------------------
% 37.49/6.97 % (16131)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_15884 for (2949ds/90Mi)
% 37.49/6.98 % (16132)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_15884 for (2949ds/593Mi)
% 37.49/6.99 % (16125)Instruction limit reached!
% 37.49/6.99 % (16125)------------------------------
% 37.49/6.99 % (16125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.49/6.99 % (16125)Termination reason: Unknown
% 37.49/6.99 % (16125)Termination phase: Saturation
% 37.49/6.99
% 37.49/6.99 % (16125)Memory used [KB]: 8443
% 37.49/6.99 % (16125)Time elapsed: 0.334 s
% 37.49/6.99 % (16125)Instructions burned: 595 (million)
% 37.49/6.99 % (16125)------------------------------
% 37.49/6.99 % (16125)------------------------------
% 37.49/7.01 % (16133)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_15884 for (2949ds/1512Mi)
% 37.49/7.02 % (16131)Instruction limit reached!
% 37.49/7.02 % (16131)------------------------------
% 37.49/7.02 % (16131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.49/7.02 % (16131)Termination reason: Unknown
% 37.49/7.02 % (16131)Termination phase: Preprocessing 3
% 37.49/7.02
% 37.49/7.02 % (16131)Memory used [KB]: 2942
% 37.49/7.02 % (16131)Time elapsed: 0.052 s
% 37.49/7.02 % (16131)Instructions burned: 90 (million)
% 37.49/7.02 % (16131)------------------------------
% 37.49/7.02 % (16131)------------------------------
% 39.86/7.04 % (16134)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_15884 for (2948ds/569Mi)
% 40.46/7.16 % (16130)First to succeed.
% 40.46/7.16 % (16130)Refutation found. Thanks to Tanya!
% 40.46/7.16 % SZS status Theorem for DTF2THF_15884
% 40.46/7.16 % SZS output start Proof for DTF2THF_15884
% 40.46/7.16 thf(type_def_5, type, nat: $tType).
% 40.46/7.16 thf(type_def_6, type, list_list_com: $tType).
% 40.46/7.16 thf(type_def_8, type, list_com: $tType).
% 40.46/7.16 thf(type_def_9, type, list_P1040014977_state: $tType).
% 40.46/7.16 thf(type_def_10, type, com: $tType).
% 40.46/7.16 thf(type_def_11, type, list_state: $tType).
% 40.46/7.16 thf(type_def_12, type, set_Pr1822651163om_com: $tType).
% 40.46/7.16 thf(type_def_13, type, set_Pr602326075st_com: $tType).
% 40.46/7.16 thf(type_def_14, type, set_Pr1165141447_state: $tType).
% 40.46/7.16 thf(type_def_15, type, set_Pr1142642759_state: $tType).
% 40.46/7.16 thf(type_def_16, type, state: $tType).
% 40.46/7.16 thf(type_def_17, type, produc2041926651_state: $tType).
% 40.46/7.16 thf(type_def_18, type, set_Pr849496667_state: $tType).
% 40.46/7.16 thf(type_def_19, type, set_Pr391631483_state: $tType).
% 40.46/7.16 thf(type_def_20, type, set_nat: $tType).
% 40.46/7.16 thf(type_def_21, type, set_state: $tType).
% 40.46/7.16 thf(type_def_22, type, produc2058209240st_com: $tType).
% 40.46/7.16 thf(type_def_23, type, produc1393453339_state: $tType).
% 40.46/7.16 thf(type_def_24, type, produc258871771st_com: $tType).
% 40.46/7.16 thf(type_def_25, type, produc1225889383_state: $tType).
% 40.46/7.16 thf(type_def_26, type, product_prod_com_com: $tType).
% 40.46/7.16 thf(type_def_27, type, produc1115495963_state: $tType).
% 40.46/7.16 thf(type_def_28, type, produc1440412305st_com: $tType).
% 40.46/7.16 thf(type_def_29, type, produc392316135_state: $tType).
% 40.46/7.16 thf(type_def_30, type, produc1762014951st_com: $tType).
% 40.46/7.16 thf(type_def_31, type, produc410756839_state: $tType).
% 40.46/7.16 thf(type_def_32, type, produc1519776487_state: $tType).
% 40.46/7.16 thf(type_def_33, type, produc1065433319om_com: $tType).
% 40.46/7.16 thf(type_def_34, type, produc186437863_state: $tType).
% 40.46/7.16 thf(type_def_35, type, set_Pr135335153st_com: $tType).
% 40.46/7.16 thf(type_def_36, type, set_Pr1419004359_state: $tType).
% 40.46/7.16 thf(type_def_37, type, set_Pr2083163591st_com: $tType).
% 40.46/7.16 thf(type_def_38, type, set_Pr1847866567_state: $tType).
% 40.46/7.16 thf(type_def_39, type, set_Pr1675528647om_com: $tType).
% 40.46/7.16 thf(type_def_40, type, set_Pr2096893127_state: $tType).
% 40.46/7.16 thf(type_def_41, type, set_Pr795498619_state: $tType).
% 40.46/7.16 thf(func_def_0, type, set_Pr1847866567_state: $tType).
% 40.46/7.16 thf(func_def_1, type, produc1519776487_state: $tType).
% 40.46/7.16 thf(func_def_2, type, set_Pr2096893127_state: $tType).
% 40.46/7.16 thf(func_def_3, type, produc186437863_state: $tType).
% 40.46/7.16 thf(func_def_4, type, set_Pr1419004359_state: $tType).
% 40.46/7.16 thf(func_def_5, type, set_Pr135335153st_com: $tType).
% 40.46/7.16 thf(func_def_6, type, produc392316135_state: $tType).
% 40.46/7.16 thf(func_def_7, type, produc1440412305st_com: $tType).
% 40.46/7.16 thf(func_def_8, type, set_Pr1142642759_state: $tType).
% 40.46/7.16 thf(func_def_9, type, set_Pr2083163591st_com: $tType).
% 40.46/7.16 thf(func_def_10, type, produc1225889383_state: $tType).
% 40.46/7.16 thf(func_def_11, type, produc1762014951st_com: $tType).
% 40.46/7.16 thf(func_def_12, type, set_Pr1165141447_state: $tType).
% 40.46/7.16 thf(func_def_13, type, produc410756839_state: $tType).
% 40.46/7.16 thf(func_def_14, type, set_Pr1675528647om_com: $tType).
% 40.46/7.16 thf(func_def_15, type, produc1065433319om_com: $tType).
% 40.46/7.16 thf(func_def_16, type, set_Pr391631483_state: $tType).
% 40.46/7.16 thf(func_def_17, type, produc1393453339_state: $tType).
% 40.46/7.16 thf(func_def_18, type, produc2058209240st_com: $tType).
% 40.46/7.16 thf(func_def_19, type, set_Pr602326075st_com: $tType).
% 40.46/7.16 thf(func_def_20, type, list_P1040014977_state: $tType).
% 40.46/7.16 thf(func_def_21, type, set_Pr849496667_state: $tType).
% 40.46/7.16 thf(func_def_22, type, produc258871771st_com: $tType).
% 40.46/7.16 thf(func_def_23, type, set_Pr795498619_state: $tType).
% 40.46/7.16 thf(func_def_24, type, produc2041926651_state: $tType).
% 40.46/7.16 thf(func_def_25, type, set_Pr1822651163om_com: $tType).
% 40.46/7.16 thf(func_def_26, type, produc1115495963_state: $tType).
% 40.46/7.16 thf(func_def_27, type, product_prod_com_com: $tType).
% 40.46/7.16 thf(func_def_28, type, list_list_com: $tType).
% 40.46/7.16 thf(func_def_29, type, list_state: $tType).
% 40.46/7.16 thf(func_def_30, type, set_state: $tType).
% 40.46/7.16 thf(func_def_31, type, list_com: $tType).
% 40.46/7.16 thf(func_def_32, type, set_nat: $tType).
% 40.46/7.16 thf(func_def_33, type, state: $tType).
% 40.46/7.16 thf(func_def_34, type, com: $tType).
% 40.46/7.16 thf(func_def_35, type, nat: $tType).
% 40.46/7.16 thf(func_def_36, type, zero_zero_nat: nat).
% 40.46/7.16 thf(func_def_37, type, append_list_com: list_list_com > list_list_com > list_list_com).
% 40.46/7.16 thf(func_def_38, type, append_com: list_com > list_com > list_com).
% 40.46/7.16 thf(func_def_39, type, append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state).
% 40.46/7.16 thf(func_def_40, type, bind_com_com: list_com > (com > list_com) > list_com).
% 40.46/7.16 thf(func_def_41, type, concat_com: list_list_com > list_com).
% 40.46/7.16 thf(func_def_42, type, gen_length_list_com: nat > list_list_com > nat).
% 40.46/7.16 thf(func_def_43, type, gen_length_com: nat > list_com > nat).
% 40.46/7.16 thf(func_def_44, type, gen_length_state: nat > list_state > nat).
% 40.46/7.16 thf(func_def_45, type, gen_le1266608782_state: nat > list_P1040014977_state > nat).
% 40.46/7.16 thf(func_def_46, type, insert_com: com > list_com > list_com).
% 40.46/7.16 thf(func_def_47, type, lenlex_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_48, type, lenlex295247238_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_49, type, lex_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_50, type, lex_Pr570247525_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_51, type, lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_52, type, lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_53, type, cons_list_com: list_com > list_list_com > list_list_com).
% 40.46/7.16 thf(func_def_54, type, cons_com: com > list_com > list_com).
% 40.46/7.16 thf(func_def_55, type, cons_state: state > list_state > list_state).
% 40.46/7.16 thf(func_def_56, type, cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state).
% 40.46/7.16 thf(func_def_57, type, nil_list_com: list_list_com).
% 40.46/7.16 thf(func_def_58, type, nil_com: list_com).
% 40.46/7.16 thf(func_def_59, type, nil_state: list_state).
% 40.46/7.16 thf(func_def_60, type, nil_Pr1844458753_state: list_P1040014977_state).
% 40.46/7.16 thf(func_def_61, type, listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_62, type, listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_63, type, listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state).
% 40.46/7.16 thf(func_def_64, type, listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_65, type, listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_66, type, maps_com_com: (com > list_com) > list_com > list_com).
% 40.46/7.16 thf(func_def_67, type, n_lists_com: nat > list_com > list_list_com).
% 40.46/7.16 thf(func_def_68, type, nths_com: list_com > set_nat > list_com).
% 40.46/7.16 thf(func_def_69, type, product_lists_com: list_list_com > list_list_com).
% 40.46/7.16 thf(func_def_70, type, rotate1_com: list_com > list_com).
% 40.46/7.16 thf(func_def_71, type, subseqs_com: list_com > list_list_com).
% 40.46/7.16 thf(func_def_72, type, suc: nat > nat).
% 40.46/7.16 thf(func_def_73, type, size_size_list_com: list_com > nat).
% 40.46/7.16 thf(func_def_74, type, size_s213202669_state: list_P1040014977_state > nat).
% 40.46/7.16 thf(func_def_75, type, pHoare259243666_exec1: set_Pr1165141447_state).
% 40.46/7.16 thf(func_def_76, type, pHoare202237534exec1p: list_com > state > list_com > state > $o).
% 40.46/7.16 thf(func_def_77, type, pHoare259243732_execs: state > list_com > state > $o).
% 40.46/7.16 thf(func_def_78, type, pHoare2126160787le_inf: list_com > state > $o).
% 40.46/7.16 thf(func_def_79, type, pHoare806997636termis: list_com > state > $o).
% 40.46/7.16 thf(func_def_80, type, cond: (state > $o) > com > com > com).
% 40.46/7.16 thf(func_def_81, type, do: (state > set_state) > com).
% 40.46/7.16 thf(func_def_82, type, semi: com > com > com).
% 40.46/7.16 thf(func_def_83, type, while: (state > $o) > com > com).
% 40.46/7.16 thf(func_def_84, type, exec: state > com > state > $o).
% 40.46/7.16 thf(func_def_85, type, termi: com > state > $o).
% 40.46/7.16 thf(func_def_86, type, produc1914379986st_com: (com > com > $o) > list_com > produc2058209240st_com).
% 40.46/7.16 thf(func_def_87, type, produc1742567891_state: list_list_com > list_state > produc1393453339_state).
% 40.46/7.16 thf(func_def_88, type, produc1307105171st_com: list_com > list_com > produc258871771st_com).
% 40.46/7.16 thf(func_def_89, type, produc1204172211_state: list_com > state > produc2041926651_state).
% 40.46/7.16 thf(func_def_90, type, produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state).
% 40.46/7.16 thf(func_def_91, type, product_Pair_com_com: com > com > product_prod_com_com).
% 40.46/7.16 thf(func_def_92, type, produc64584659_state: state > state > produc1115495963_state).
% 40.46/7.16 thf(func_def_93, type, produc67337417st_com: produc2058209240st_com > produc2058209240st_com > produc1440412305st_com).
% 40.46/7.16 thf(func_def_94, type, produc67381847_state: produc1393453339_state > produc1393453339_state > produc392316135_state).
% 40.46/7.16 thf(func_def_95, type, produc313736791st_com: produc258871771st_com > produc258871771st_com > produc1762014951st_com).
% 40.46/7.16 thf(func_def_96, type, produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state).
% 40.46/7.16 thf(func_def_97, type, produc984060759_state: produc1225889383_state > produc1225889383_state > produc1519776487_state).
% 40.46/7.16 thf(func_def_98, type, produc1140939351om_com: product_prod_com_com > product_prod_com_com > produc1065433319om_com).
% 40.46/7.16 thf(func_def_99, type, produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state).
% 40.46/7.16 thf(func_def_100, type, irrefl_com: set_Pr1822651163om_com > $o).
% 40.46/7.16 thf(func_def_101, type, irrefl654089520_state: set_Pr1165141447_state > $o).
% 40.46/7.16 thf(func_def_102, type, collect_nat: (nat > $o) > set_nat).
% 40.46/7.16 thf(func_def_103, type, collect_state: (state > $o) > set_state).
% 40.46/7.16 thf(func_def_104, type, collec924674566_state: (produc1393453339_state > $o) > set_Pr391631483_state).
% 40.46/7.16 thf(func_def_105, type, collec328862150st_com: (produc258871771st_com > $o) > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_106, type, collec1409185766_state: (produc2041926651_state > $o) > set_Pr849496667_state).
% 40.46/7.16 thf(func_def_107, type, collec183560402_state: (produc1225889383_state > $o) > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_108, type, collec300063826_state: (produc410756839_state > $o) > set_Pr1165141447_state).
% 40.46/7.16 thf(func_def_109, type, transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com).
% 40.46/7.16 thf(func_def_110, type, transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state).
% 40.46/7.16 thf(func_def_111, type, transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com).
% 40.46/7.16 thf(func_def_112, type, transi1592315797st_com: set_Pr135335153st_com > set_Pr135335153st_com).
% 40.46/7.16 thf(func_def_113, type, transi89280670_state: set_Pr1419004359_state > set_Pr1419004359_state).
% 40.46/7.16 thf(func_def_114, type, transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com).
% 40.46/7.16 thf(func_def_115, type, transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state).
% 40.46/7.16 thf(func_def_116, type, transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state).
% 40.46/7.16 thf(func_def_117, type, transi1042416958om_com: set_Pr1675528647om_com > set_Pr1675528647om_com).
% 40.46/7.16 thf(func_def_118, type, transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state).
% 40.46/7.16 thf(func_def_119, type, same_f855297288_state: (list_com > $o) > (list_com > set_Pr795498619_state) > set_Pr1165141447_state).
% 40.46/7.16 thf(func_def_120, type, same_f1258458156_state: (produc2041926651_state > $o) > (produc2041926651_state > set_Pr1165141447_state) > set_Pr2096893127_state).
% 40.46/7.16 thf(func_def_121, type, member_nat: nat > set_nat > $o).
% 40.46/7.16 thf(func_def_122, type, member_state: state > set_state > $o).
% 40.46/7.16 thf(func_def_123, type, member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o).
% 40.46/7.16 thf(func_def_124, type, member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o).
% 40.46/7.16 thf(func_def_125, type, member64234660_state: produc2041926651_state > set_Pr849496667_state > $o).
% 40.46/7.16 thf(func_def_126, type, member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o).
% 40.46/7.16 thf(func_def_127, type, member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o).
% 40.46/7.16 thf(func_def_128, type, member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o).
% 40.46/7.16 thf(func_def_129, type, member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o).
% 40.46/7.16 thf(func_def_130, type, member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o).
% 40.46/7.16 thf(func_def_131, type, member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o).
% 40.46/7.16 thf(func_def_132, type, member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o).
% 40.46/7.16 thf(func_def_133, type, member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o).
% 40.46/7.16 thf(func_def_134, type, member2105207824om_com: produc1065433319om_com > set_Pr1675528647om_com > $o).
% 40.46/7.16 thf(func_def_135, type, member512523024_state: produc186437863_state > set_Pr2096893127_state > $o).
% 40.46/7.16 thf(func_def_136, type, a: list_com).
% 40.46/7.16 thf(func_def_137, type, b: state > $o).
% 40.46/7.16 thf(func_def_138, type, ba: state).
% 40.46/7.16 thf(func_def_139, type, c: com).
% 40.46/7.16 thf(func_def_140, type, cs: list_com).
% 40.46/7.16 thf(func_def_141, type, f: nat > produc2041926651_state).
% 40.46/7.16 thf(func_def_142, type, s: state).
% 40.46/7.16 thf(func_def_162, type, sK0: list_com > list_com).
% 40.46/7.16 thf(func_def_163, type, sK1: list_com > com).
% 40.46/7.16 thf(func_def_164, type, sK2: list_com > com).
% 40.46/7.16 thf(func_def_165, type, sK3: list_com > com).
% 40.46/7.16 thf(func_def_166, type, sK4: (nat > nat > $o) > nat).
% 40.46/7.16 thf(func_def_167, type, sK5: (nat > nat > $o) > nat).
% 40.46/7.16 thf(func_def_168, type, sK6: (nat > nat > $o) > nat).
% 40.46/7.16 thf(func_def_169, type, sK7: (nat > nat > $o) > nat).
% 40.46/7.16 thf(func_def_170, type, sK8: (produc410756839_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_171, type, sK9: (produc410756839_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_172, type, sK10: produc410756839_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_173, type, sK11: produc410756839_state > list_com).
% 40.46/7.16 thf(func_def_174, type, sK12: produc410756839_state > state).
% 40.46/7.16 thf(func_def_175, type, sK13: set_Pr1165141447_state > produc2041926651_state > (nat > produc2041926651_state) > nat).
% 40.46/7.16 thf(func_def_176, type, sK14: set_Pr1165141447_state > produc2041926651_state > nat > produc2041926651_state).
% 40.46/7.16 thf(func_def_177, type, sK15: (list_com > state > $o) > set_Pr1165141447_state > list_com > state > list_com).
% 40.46/7.16 thf(func_def_178, type, sK16: (list_com > state > $o) > set_Pr1165141447_state > list_com > state > state).
% 40.46/7.16 thf(func_def_179, type, sK17: (list_com > state > $o) > set_Pr1165141447_state > list_com > state > state).
% 40.46/7.16 thf(func_def_180, type, sK18: (list_com > state > $o) > set_Pr1165141447_state > list_com > state > list_com).
% 40.46/7.16 thf(func_def_181, type, sK19: produc2041926651_state > list_com).
% 40.46/7.16 thf(func_def_182, type, sK20: produc2041926651_state > state).
% 40.46/7.16 thf(func_def_183, type, sK21: list_com > list_com).
% 40.46/7.16 thf(func_def_184, type, sK22: list_com > com).
% 40.46/7.16 thf(func_def_185, type, sK23: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_186, type, sK24: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_187, type, sK25: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_188, type, sK26: (list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_189, type, sK27: (produc410756839_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_190, type, sK28: (produc410756839_state > $o) > list_com).
% 40.46/7.16 thf(func_def_191, type, sK29: (produc410756839_state > $o) > state).
% 40.46/7.16 thf(func_def_192, type, sK30: set_Pr1165141447_state > (produc2041926651_state > $o) > produc2041926651_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_193, type, sK31: set_Pr1165141447_state > (produc2041926651_state > $o) > produc2041926651_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_194, type, sK32: (produc258871771st_com > $o) > list_com).
% 40.46/7.16 thf(func_def_195, type, sK33: (produc258871771st_com > $o) > list_com).
% 40.46/7.16 thf(func_def_196, type, sK34: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_197, type, sK35: (produc410756839_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_198, type, sK36: (produc410756839_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_199, type, sK37: (produc2041926651_state > $o) > state).
% 40.46/7.16 thf(func_def_200, type, sK38: (produc2041926651_state > $o) > list_com).
% 40.46/7.16 thf(func_def_201, type, sK39: (produc2041926651_state > $o) > state).
% 40.46/7.16 thf(func_def_202, type, sK40: (produc2041926651_state > $o) > list_com).
% 40.46/7.16 thf(func_def_203, type, sK41: (produc258871771st_com > $o) > list_com).
% 40.46/7.16 thf(func_def_204, type, sK42: (produc258871771st_com > $o) > list_com).
% 40.46/7.16 thf(func_def_205, type, sK43: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_206, type, sK44: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_207, type, sK45: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_208, type, sK46: (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 40.46/7.16 thf(func_def_209, type, sK47: nat > nat).
% 40.46/7.16 thf(func_def_210, type, sK48: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_211, type, sK49: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_212, type, sK50: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_213, type, sK51: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_214, type, sK52: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_215, type, sK53: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_216, type, sK54: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_217, type, sK55: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_218, type, sK56: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_219, type, sK57: produc258871771st_com > com).
% 40.46/7.16 thf(func_def_220, type, sK58: produc258871771st_com > com).
% 40.46/7.16 thf(func_def_221, type, sK59: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_222, type, sK60: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_223, type, sK61: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_224, type, sK62: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_225, type, sK63: (list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_226, type, sK64: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_227, type, sK65: list_com > list_com).
% 40.46/7.16 thf(func_def_228, type, sK66: list_com > com).
% 40.46/7.16 thf(func_def_229, type, sK67: produc2041926651_state > list_com).
% 40.46/7.16 thf(func_def_230, type, sK68: produc2041926651_state > state).
% 40.46/7.16 thf(func_def_231, type, sK69: set_Pr1165141447_state > state > (list_com > state > $o) > list_com > state).
% 40.46/7.16 thf(func_def_232, type, sK70: set_Pr1165141447_state > state > (list_com > state > $o) > list_com > list_com).
% 40.46/7.16 thf(func_def_233, type, sK71: set_Pr1165141447_state > state > (list_com > state > $o) > list_com > list_com).
% 40.46/7.16 thf(func_def_234, type, sK72: set_Pr1165141447_state > state > (list_com > state > $o) > list_com > state).
% 40.46/7.16 thf(func_def_235, type, sK73: (nat > produc2041926651_state) > nat).
% 40.46/7.16 thf(func_def_236, type, sK74: ((com > com > $o) > list_com > $o) > com > com > $o).
% 40.46/7.16 thf(func_def_237, type, sK75: ((com > com > $o) > list_com > $o) > com).
% 40.46/7.16 thf(func_def_238, type, sK76: ((com > com > $o) > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_239, type, sK77: ((com > com > $o) > list_com > $o) > com).
% 40.46/7.16 thf(func_def_240, type, sK78: ((com > com > $o) > list_com > $o) > com > com > $o).
% 40.46/7.16 thf(func_def_241, type, sK79: ((com > com > $o) > list_com > $o) > com > com > $o).
% 40.46/7.16 thf(func_def_242, type, sK80: ((com > com > $o) > list_com > $o) > com).
% 40.46/7.16 thf(func_def_243, type, sK81: ((com > com > $o) > list_com > $o) > com > com > $o).
% 40.46/7.16 thf(func_def_244, type, sK82: ((com > com > $o) > list_com > $o) > com > com > $o).
% 40.46/7.16 thf(func_def_245, type, sK83: ((com > com > $o) > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_246, type, sK84: ((com > com > $o) > list_com > $o) > com).
% 40.46/7.16 thf(func_def_247, type, sK85: (nat > $o) > nat).
% 40.46/7.16 thf(func_def_248, type, sK86: state > list_com > list_com > set_Pr1165141447_state > state > list_com).
% 40.46/7.16 thf(func_def_249, type, sK87: state > list_com > list_com > set_Pr1165141447_state > state > state).
% 40.46/7.16 thf(func_def_250, type, sK88: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_251, type, sK89: (list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_252, type, sK90: produc410756839_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_253, type, sK91: produc410756839_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_254, type, sK92: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_255, type, sK93: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_256, type, sK94: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_257, type, sK95: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_258, type, sK96: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_259, type, sK97: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_260, type, sK98: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_261, type, sK99: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_262, type, sK100: nat > nat).
% 40.46/7.16 thf(func_def_263, type, sK101: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_264, type, sK102: (list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_265, type, sK103: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_266, type, sK104: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_267, type, sK105: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_268, type, sK106: (list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_269, type, sK107: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_270, type, sK108: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_271, type, sK109: (list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_272, type, sK110: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_273, type, sK111: (list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_274, type, sK112: (nat > $o) > nat).
% 40.46/7.16 thf(func_def_275, type, sK113: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_276, type, sK114: produc2041926651_state > (nat > produc2041926651_state) > set_Pr1165141447_state > nat).
% 40.46/7.16 thf(func_def_277, type, sK115: produc2041926651_state > set_Pr1165141447_state > nat > produc2041926651_state).
% 40.46/7.16 thf(func_def_278, type, sK116: produc410756839_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_279, type, sK117: produc410756839_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_280, type, sK118: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_281, type, sK119: produc258871771st_com > com).
% 40.46/7.16 thf(func_def_282, type, sK120: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_283, type, sK121: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_284, type, sK122: ((com > com) > list_com > list_com > $o) > com > com).
% 40.46/7.16 thf(func_def_285, type, sK123: ((com > com) > list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_286, type, sK124: ((com > com) > list_com > list_com > $o) > com).
% 40.46/7.16 thf(func_def_287, type, sK125: ((com > com) > list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_288, type, sK126: ((com > com) > list_com > list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_289, type, sK127: ((com > com) > list_com > list_com > $o) > com > com).
% 40.46/7.16 thf(func_def_290, type, sK128: (nat > $o) > nat).
% 40.46/7.16 thf(func_def_291, type, sK129: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 40.46/7.16 thf(func_def_292, type, sK130: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_293, type, sK131: produc258871771st_com > list_com).
% 40.46/7.16 thf(func_def_294, type, sK132: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_295, type, sK133: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_296, type, sK134: (list_com > $o) > list_com).
% 40.46/7.16 thf(func_def_297, type, sK135: (list_com > $o) > com).
% 40.46/7.16 thf(func_def_299, type, ph137: !>[X0: $tType]:(X0)).
% 40.46/7.16 thf(f1723,plain,(
% 40.46/7.16 $false),
% 40.46/7.16 inference(trivial_inequality_removal,[status(thm)],[f1719])).
% 40.46/7.16 thf(f1719,plain,(
% 40.46/7.16 ((produc1204172211_state @ a @ s) != (produc1204172211_state @ a @ s))),
% 40.46/7.16 inference(backward_demodulation,[status(thm)],[f1696,f1713])).
% 40.46/7.16 thf(f1713,plain,(
% 40.46/7.16 (a = (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)))),
% 40.46/7.16 inference(trivial_inequality_removal,[status(thm)],[f1711])).
% 40.46/7.16 thf(f1711,plain,(
% 40.46/7.16 ($true != $true) | (a = (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)))),
% 40.46/7.16 inference(superposition,[status(thm)],[f1625,f1632])).
% 40.46/7.16 thf(f1632,plain,(
% 40.46/7.16 ((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (produc1204172211_state @ a @ s)) @ pHoare259243666_exec1) = $true)),
% 40.46/7.16 inference(backward_demodulation,[status(thm)],[f1314,f1630])).
% 40.46/7.16 thf(f1630,plain,(
% 40.46/7.16 (s = ba)),
% 40.46/7.16 inference(trivial_inequality_removal,[status(thm)],[f1629])).
% 40.46/7.16 thf(f1629,plain,(
% 40.46/7.16 (s = ba) | ($true != $true)),
% 40.46/7.16 inference(superposition,[status(thm)],[f1624,f1314])).
% 40.46/7.16 thf(f1624,plain,(
% 40.46/7.16 ( ! [X0 : list_com,X1 : state] : (((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (produc1204172211_state @ X0 @ X1)) @ pHoare259243666_exec1) != $true) | (s = X1)) )),
% 40.46/7.16 inference(subsumption_resolution,[status(thm)],[f1615,f1217])).
% 40.46/7.16 thf(f1217,plain,(
% 40.46/7.16 ((b @ s) = $true)),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f1080])).
% 40.46/7.16 thf(f1080,plain,(
% 40.46/7.16 ((b @ s) = $true) & ! [X0 : nat > produc2041926651_state] : (((member1069318160_state @ (produc1909270103_state @ (X0 @ (sK73 @ X0)) @ (X0 @ (suc @ (sK73 @ X0)))) @ pHoare259243666_exec1) != $true) | ((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) != (X0 @ zero_zero_nat)))),
% 40.46/7.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f974,f1079])).
% 40.46/7.16 thf(f1079,plain,(
% 40.46/7.16 ! [X0 : nat > produc2041926651_state] : (? [X1 : nat] : ((member1069318160_state @ (produc1909270103_state @ (X0 @ X1) @ (X0 @ (suc @ X1))) @ pHoare259243666_exec1) != $true) => ((member1069318160_state @ (produc1909270103_state @ (X0 @ (sK73 @ X0)) @ (X0 @ (suc @ (sK73 @ X0)))) @ pHoare259243666_exec1) != $true))),
% 40.46/7.16 introduced(definition,[],[choice_axiom])).
% 40.46/7.16 thf(f974,plain,(
% 40.46/7.16 ((b @ s) = $true) & ! [X0 : nat > produc2041926651_state] : (? [X1 : nat] : ((member1069318160_state @ (produc1909270103_state @ (X0 @ X1) @ (X0 @ (suc @ X1))) @ pHoare259243666_exec1) != $true) | ((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) != (X0 @ zero_zero_nat)))),
% 40.46/7.16 inference(ennf_transformation,[status(thm)],[f865])).
% 40.46/7.16 thf(f865,plain,(
% 40.46/7.16 ~(((b @ s) != $true) | ? [X0 : nat > produc2041926651_state] : (((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) = (X0 @ zero_zero_nat)) & ! [X1 : nat] : ((member1069318160_state @ (produc1909270103_state @ (X0 @ X1) @ (X0 @ (suc @ X1))) @ pHoare259243666_exec1) = $true)))),
% 40.46/7.16 inference(flattening,[status(thm)],[f756])).
% 40.46/7.16 thf(f756,plain,(
% 40.46/7.16 ~(~((b @ s) = $true) | ? [X0 : nat > produc2041926651_state] : (((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) = (X0 @ zero_zero_nat)) & ! [X1 : nat] : ((member1069318160_state @ (produc1909270103_state @ (X0 @ X1) @ (X0 @ (suc @ X1))) @ pHoare259243666_exec1) = $true)))),
% 40.46/7.16 inference(fool_elimination,[status(thm)],[f755])).
% 40.46/7.16 thf(f755,plain,(
% 40.46/7.16 ~(~(b @ s) | ? [X0 : nat > produc2041926651_state] : (! [X1 : nat] : (member1069318160_state @ (produc1909270103_state @ (X0 @ X1) @ (X0 @ (suc @ X1))) @ pHoare259243666_exec1) & ((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) = (X0 @ zero_zero_nat))))),
% 40.46/7.16 inference(rectify,[status(thm)],[f355])).
% 40.46/7.16 thf(f355,negated_conjecture,(
% 40.46/7.16 ~(~(b @ s) | ? [X139 : nat > produc2041926651_state] : (! [X58 : nat] : (member1069318160_state @ (produc1909270103_state @ (X139 @ X58) @ (X139 @ (suc @ X58))) @ pHoare259243666_exec1) & ((X139 @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s))))),
% 40.46/7.16 inference(negated_conjecture,[status(cth)],[f354])).
% 40.46/7.16 thf(f354,conjecture,(
% 40.46/7.16 ~(b @ s) | ? [X139 : nat > produc2041926651_state] : (! [X58 : nat] : (member1069318160_state @ (produc1909270103_state @ (X139 @ X58) @ (X139 @ (suc @ X58))) @ pHoare259243666_exec1) & ((X139 @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s)))),
% 40.46/7.16 file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_4)).
% 40.46/7.16 thf(f1615,plain,(
% 40.46/7.16 ( ! [X0 : list_com,X1 : state] : (((b @ s) != $true) | ((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (produc1204172211_state @ X0 @ X1)) @ pHoare259243666_exec1) != $true) | (s = X1)) )),
% 40.46/7.16 inference(superposition,[status(thm)],[f1286,f1301])).
% 40.46/7.16 thf(f1301,plain,(
% 40.46/7.16 ((f @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ (while @ b @ c) @ cs) @ s))),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f350])).
% 40.46/7.16 thf(f350,axiom,(
% 40.46/7.16 ((f @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ (while @ b @ c) @ cs) @ s))),
% 40.46/7.16 file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_0)).
% 40.46/7.16 thf(f1286,plain,(
% 40.46/7.16 ( ! [X2 : state > $o,X3 : com,X0 : list_com,X1 : list_com,X4 : state,X5 : state] : (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) != $true) | (X4 = X5) | ((X2 @ X4) != $true)) )),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f996])).
% 40.46/7.16 thf(f996,plain,(
% 40.46/7.16 ! [X0 : list_com,X1 : list_com,X2 : state > $o,X3 : com,X4 : state,X5 : state] : (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) != $true) | (((X2 @ X4) = $true) & ((cons_com @ X3 @ (cons_com @ (while @ X2 @ X3) @ X1)) = X0) & (X4 = X5)) | ((X0 = X1) & (X4 = X5) & ((X2 @ X4) != $true)))),
% 40.46/7.16 inference(flattening,[status(thm)],[f995])).
% 40.46/7.16 thf(f995,plain,(
% 40.46/7.16 ! [X0 : list_com,X1 : list_com,X2 : state > $o,X3 : com,X4 : state,X5 : state] : ((((((X2 @ X4) = $true) & (X4 = X5)) & ((cons_com @ X3 @ (cons_com @ (while @ X2 @ X3) @ X1)) = X0)) | ((((X2 @ X4) != $true) & (X4 = X5)) & (X0 = X1))) | ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) != $true))),
% 40.46/7.16 inference(ennf_transformation,[status(thm)],[f883])).
% 40.46/7.16 thf(f883,plain,(
% 40.46/7.16 ! [X0 : list_com,X1 : list_com,X2 : state > $o,X3 : com,X4 : state,X5 : state] : (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) = $true) => (((X0 = X1) => ((X4 = X5) => ((X2 @ X4) = $true))) => ~(((cons_com @ X3 @ (cons_com @ (while @ X2 @ X3) @ X1)) = X0) => ((X4 = X5) => ((X2 @ X4) != $true)))))),
% 40.46/7.16 inference(flattening,[status(thm)],[f410])).
% 40.46/7.16 thf(f410,plain,(
% 40.46/7.16 ! [X0 : list_com,X1 : list_com,X2 : state > $o,X3 : com,X4 : state,X5 : state] : (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) = $true) => (((X0 = X1) => ((X4 = X5) => ((X2 @ X4) = $true))) => ~(((cons_com @ X3 @ (cons_com @ (while @ X2 @ X3) @ X1)) = X0) => ((X4 = X5) => ~((X2 @ X4) = $true)))))),
% 40.46/7.16 inference(fool_elimination,[status(thm)],[f409])).
% 40.46/7.16 thf(f409,plain,(
% 40.46/7.16 ! [X0 : list_com,X1 : list_com,X2 : state > $o,X3 : com,X4 : state,X5 : state] : ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) => (((X0 = X1) => ((X4 = X5) => (X2 @ X4))) => ~(((cons_com @ X3 @ (cons_com @ (while @ X2 @ X3) @ X1)) = X0) => ((X4 = X5) => ~(X2 @ X4)))))),
% 40.46/7.16 inference(rectify,[status(thm)],[f1])).
% 40.46/7.16 thf(f1,axiom,(
% 40.46/7.16 ! [X4 : list_com,X2 : list_com,X0 : state > $o,X1 : com,X3 : state,X5 : state] : ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X0 @ X1) @ X2) @ X3) @ (produc1204172211_state @ X4 @ X5)) @ pHoare259243666_exec1) => (((X2 = X4) => ((X3 = X5) => (X0 @ X3))) => ~(((cons_com @ X1 @ (cons_com @ (while @ X0 @ X1) @ X2)) = X4) => ((X3 = X5) => ~(X0 @ X3)))))),
% 40.46/7.16 file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',fact_0_exec1E_I5_J)).
% 40.46/7.16 thf(f1314,plain,(
% 40.46/7.16 ((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (produc1204172211_state @ a @ ba)) @ pHoare259243666_exec1) = $true)),
% 40.46/7.16 inference(forward_demodulation,[status(thm)],[f1143,f1233])).
% 40.46/7.16 thf(f1233,plain,(
% 40.46/7.16 ((f @ (suc @ zero_zero_nat)) = (produc1204172211_state @ a @ ba))),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f353])).
% 40.46/7.16 thf(f353,axiom,(
% 40.46/7.16 ((f @ (suc @ zero_zero_nat)) = (produc1204172211_state @ a @ ba))),
% 40.46/7.16 file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_3)).
% 40.46/7.16 thf(f1143,plain,(
% 40.46/7.16 ((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ zero_zero_nat))) @ pHoare259243666_exec1) = $true)),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f358])).
% 40.46/7.16 thf(f358,plain,(
% 40.46/7.16 ((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ zero_zero_nat))) @ pHoare259243666_exec1) = $true)),
% 40.46/7.16 inference(fool_elimination,[status(thm)],[f357])).
% 40.46/7.16 thf(f357,plain,(
% 40.46/7.16 (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ zero_zero_nat))) @ pHoare259243666_exec1)),
% 40.46/7.16 inference(rectify,[status(thm)],[f352])).
% 40.46/7.16 thf(f352,axiom,(
% 40.46/7.16 (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ zero_zero_nat))) @ pHoare259243666_exec1)),
% 40.46/7.16 file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_2)).
% 40.46/7.16 thf(f1625,plain,(
% 40.46/7.16 ( ! [X0 : list_com,X1 : state] : (((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (produc1204172211_state @ X0 @ X1)) @ pHoare259243666_exec1) != $true) | ((cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) = X0)) )),
% 40.46/7.16 inference(subsumption_resolution,[status(thm)],[f1617,f1217])).
% 40.46/7.16 thf(f1617,plain,(
% 40.46/7.16 ( ! [X0 : list_com,X1 : state] : (((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (produc1204172211_state @ X0 @ X1)) @ pHoare259243666_exec1) != $true) | ((cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) = X0) | ((b @ s) != $true)) )),
% 40.46/7.16 inference(superposition,[status(thm)],[f1289,f1301])).
% 40.46/7.16 thf(f1289,plain,(
% 40.46/7.16 ( ! [X2 : state > $o,X3 : com,X0 : list_com,X1 : list_com,X4 : state,X5 : state] : (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ X2 @ X3) @ X1) @ X4) @ (produc1204172211_state @ X0 @ X5)) @ pHoare259243666_exec1) != $true) | ((X2 @ X4) != $true) | ((cons_com @ X3 @ (cons_com @ (while @ X2 @ X3) @ X1)) = X0)) )),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f996])).
% 40.46/7.16 thf(f1696,plain,(
% 40.46/7.16 ((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) != (produc1204172211_state @ a @ s))),
% 40.46/7.16 inference(subsumption_resolution,[status(thm)],[f1693,f1299])).
% 40.46/7.16 thf(f1299,plain,(
% 40.46/7.16 ( ! [X0 : nat] : (((member1069318160_state @ (produc1909270103_state @ (f @ X0) @ (f @ (suc @ X0))) @ pHoare259243666_exec1) = $true)) )),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f680])).
% 40.46/7.16 thf(f680,plain,(
% 40.46/7.16 ! [X0 : nat] : ((member1069318160_state @ (produc1909270103_state @ (f @ X0) @ (f @ (suc @ X0))) @ pHoare259243666_exec1) = $true)),
% 40.46/7.16 inference(fool_elimination,[status(thm)],[f679])).
% 40.46/7.16 thf(f679,plain,(
% 40.46/7.16 ! [X0 : nat] : (member1069318160_state @ (produc1909270103_state @ (f @ X0) @ (f @ (suc @ X0))) @ pHoare259243666_exec1)),
% 40.46/7.16 inference(rectify,[status(thm)],[f351])).
% 40.46/7.16 thf(f351,axiom,(
% 40.46/7.16 ! [X60 : nat] : (member1069318160_state @ (produc1909270103_state @ (f @ X60) @ (f @ (suc @ X60))) @ pHoare259243666_exec1)),
% 40.46/7.16 file('/export/starexec/sandbox/tmp/tmp.MtfLAatXJE/DTF2THF_15884.p',conj_1)).
% 40.46/7.16 thf(f1693,plain,(
% 40.46/7.16 ((member1069318160_state @ (produc1909270103_state @ (f @ (suc @ (sK73 @ (^[Y0 : nat]: (f @ (suc @ Y0)))))) @ (f @ (suc @ (suc @ (sK73 @ (^[Y0 : nat]: (f @ (suc @ Y0)))))))) @ pHoare259243666_exec1) != $true) | ((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) != (produc1204172211_state @ a @ s))),
% 40.46/7.16 inference(beta_eta_normalization,[status(thm)],[f1688])).
% 40.46/7.16 thf(f1688,plain,(
% 40.46/7.16 ((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) != (produc1204172211_state @ a @ s)) | ((member1069318160_state @ (produc1909270103_state @ ((^[Y0 : nat]: (f @ ((^[Y1 : nat]: (suc @ ((^[Y2 : nat]: (Y2)) @ Y1))) @ Y0))) @ (sK73 @ (^[Y0 : nat]: (f @ ((^[Y1 : nat]: (suc @ ((^[Y2 : nat]: (Y2)) @ Y1))) @ Y0))))) @ ((^[Y0 : nat]: (f @ ((^[Y1 : nat]: (suc @ ((^[Y2 : nat]: (Y2)) @ Y1))) @ Y0))) @ (suc @ (sK73 @ (^[Y0 : nat]: (f @ ((^[Y1 : nat]: (suc @ ((^[Y2 : nat]: (Y2)) @ Y1))) @ Y0))))))) @ pHoare259243666_exec1) != $true)),
% 40.46/7.16 inference(superposition,[status(thm)],[f1216,f1631])).
% 40.46/7.16 thf(f1631,plain,(
% 40.46/7.16 ((f @ (suc @ zero_zero_nat)) = (produc1204172211_state @ a @ s))),
% 40.46/7.16 inference(backward_demodulation,[status(thm)],[f1233,f1630])).
% 40.46/7.16 thf(f1216,plain,(
% 40.46/7.16 ( ! [X0 : nat > produc2041926651_state] : (((produc1204172211_state @ (cons_com @ c @ (cons_com @ (while @ b @ c) @ cs)) @ s) != (X0 @ zero_zero_nat)) | ((member1069318160_state @ (produc1909270103_state @ (X0 @ (sK73 @ X0)) @ (X0 @ (suc @ (sK73 @ X0)))) @ pHoare259243666_exec1) != $true)) )),
% 40.46/7.16 inference(cnf_transformation,[status(thm)],[f1080])).
% 40.46/7.16 % SZS output end Proof for DTF2THF_15884
% 40.46/7.16 % (16130)------------------------------
% 40.46/7.16 % (16130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.46/7.16 % (16130)Termination reason: Refutation
% 40.46/7.16
% 40.46/7.16 % (16130)Memory used [KB]: 8699
% 40.46/7.16 % (16130)Time elapsed: 0.229 s
% 40.46/7.16 % (16130)Instructions burned: 404 (million)
% 40.46/7.16 % (16130)------------------------------
% 40.46/7.16 % (16130)------------------------------
% 40.46/7.16 % (15992)Success in time 5.256 s
%------------------------------------------------------------------------------