%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP145^1 : 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 : n003.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 08:55:54 AM UTC 2026
% Result : Theorem 13.24s 3.20s
% Output : Refutation 12.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 24 unt; 0 typ; 1 def)
% Number of atoms : 197 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 537 ( 40 ~; 28 |; 5 &; 451 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 30 ( 29 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 319 ( 316 usr; 13 con; 0-6 aty)
% Number of variables : 63 ( 0 ^; 63 !; 0 ?; 63 :)
% 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,
list_P890094829_state: $tType ).
thf(type_def_11,type,
com: $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,
set_Pr2096893127_state: $tType ).
thf(type_def_17,type,
set_Pr1325664839_state: $tType ).
thf(type_def_18,type,
state: $tType ).
thf(type_def_19,type,
list_state: $tType ).
thf(type_def_20,type,
produc2041926651_state: $tType ).
thf(type_def_21,type,
produc410756839_state: $tType ).
thf(type_def_22,type,
set_Pr849496667_state: $tType ).
thf(type_def_23,type,
set_Pr391631483_state: $tType ).
thf(type_def_24,type,
set_nat: $tType ).
thf(type_def_25,type,
set_state: $tType ).
thf(type_def_26,type,
produc2058209240st_com: $tType ).
thf(type_def_27,type,
produc1393453339_state: $tType ).
thf(type_def_28,type,
produc258871771st_com: $tType ).
thf(type_def_29,type,
produc1225889383_state: $tType ).
thf(type_def_30,type,
produc1586269031_state: $tType ).
thf(type_def_31,type,
product_prod_com_com: $tType ).
thf(type_def_32,type,
produc186437863_state: $tType ).
thf(type_def_33,type,
produc2046512871_state: $tType ).
thf(type_def_34,type,
set_Pr541394119_state: $tType ).
thf(func_def_0,type,
set_Pr541394119_state: $tType ).
thf(func_def_1,type,
produc2046512871_state: $tType ).
thf(func_def_2,type,
set_Pr1325664839_state: $tType ).
thf(func_def_3,type,
produc1586269031_state: $tType ).
thf(func_def_4,type,
set_Pr2096893127_state: $tType ).
thf(func_def_5,type,
produc186437863_state: $tType ).
thf(func_def_6,type,
set_Pr1142642759_state: $tType ).
thf(func_def_7,type,
produc1225889383_state: $tType ).
thf(func_def_8,type,
list_P890094829_state: $tType ).
thf(func_def_9,type,
set_Pr1165141447_state: $tType ).
thf(func_def_10,type,
produc410756839_state: $tType ).
thf(func_def_11,type,
set_Pr391631483_state: $tType ).
thf(func_def_12,type,
produc1393453339_state: $tType ).
thf(func_def_13,type,
produc2058209240st_com: $tType ).
thf(func_def_14,type,
set_Pr602326075st_com: $tType ).
thf(func_def_15,type,
list_P1040014977_state: $tType ).
thf(func_def_16,type,
set_Pr849496667_state: $tType ).
thf(func_def_17,type,
produc258871771st_com: $tType ).
thf(func_def_18,type,
produc2041926651_state: $tType ).
thf(func_def_19,type,
set_Pr1822651163om_com: $tType ).
thf(func_def_20,type,
product_prod_com_com: $tType ).
thf(func_def_21,type,
list_list_com: $tType ).
thf(func_def_22,type,
list_state: $tType ).
thf(func_def_23,type,
set_state: $tType ).
thf(func_def_24,type,
list_com: $tType ).
thf(func_def_25,type,
set_nat: $tType ).
thf(func_def_26,type,
state: $tType ).
thf(func_def_27,type,
com: $tType ).
thf(func_def_28,type,
nat: $tType ).
thf(func_def_29,type,
zero_zero_nat: nat ).
thf(func_def_30,type,
append_list_com: list_list_com > list_list_com > list_list_com ).
thf(func_def_31,type,
append_com: list_com > list_com > list_com ).
thf(func_def_32,type,
append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state ).
thf(func_def_33,type,
append221843330_state: list_P890094829_state > list_P890094829_state > list_P890094829_state ).
thf(func_def_34,type,
bind_com_com: list_com > ( com > list_com ) > list_com ).
thf(func_def_35,type,
concat_com: list_list_com > list_com ).
thf(func_def_36,type,
gen_length_com: nat > list_com > nat ).
thf(func_def_37,type,
insert_com: com > list_com > list_com ).
thf(func_def_38,type,
lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_39,type,
lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_40,type,
lexord1893203674_state: set_Pr2096893127_state > set_Pr1325664839_state ).
thf(func_def_41,type,
cons_list_com: list_com > list_list_com > list_list_com ).
thf(func_def_42,type,
cons_com: com > list_com > list_com ).
thf(func_def_43,type,
cons_state: state > list_state > list_state ).
thf(func_def_44,type,
cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state ).
thf(func_def_45,type,
cons_P438230685_state: produc410756839_state > list_P890094829_state > list_P890094829_state ).
thf(func_def_46,type,
nil_list_com: list_list_com ).
thf(func_def_47,type,
nil_com: list_com ).
thf(func_def_48,type,
nil_state: list_state ).
thf(func_def_49,type,
nil_Pr1844458753_state: list_P1040014977_state ).
thf(func_def_50,type,
nil_Pr1347322605_state: list_P890094829_state ).
thf(func_def_51,type,
listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_52,type,
listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_53,type,
listre1725776070_state: set_Pr2096893127_state > set_Pr1325664839_state ).
thf(func_def_54,type,
listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state ).
thf(func_def_55,type,
listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
thf(func_def_56,type,
listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state ).
thf(func_def_57,type,
listre1244407729_state: set_Pr2096893127_state > set_Pr1325664839_state ).
thf(func_def_58,type,
maps_com_com: ( com > list_com ) > list_com > list_com ).
thf(func_def_59,type,
n_lists_com: nat > list_com > list_list_com ).
thf(func_def_60,type,
nths_com: list_com > set_nat > list_com ).
thf(func_def_61,type,
product_lists_com: list_list_com > list_list_com ).
thf(func_def_62,type,
subseqs_com: list_com > list_list_com ).
thf(func_def_63,type,
suc: nat > nat ).
thf(func_def_64,type,
pHoare259243666_exec1: set_Pr1165141447_state ).
thf(func_def_65,type,
pHoare259243732_execs: state > list_com > state > $o ).
thf(func_def_66,type,
pHoare2126160787le_inf: list_com > state > $o ).
thf(func_def_67,type,
pHoare806997636termis: list_com > state > $o ).
thf(func_def_68,type,
cond: ( state > $o ) > com > com > com ).
thf(func_def_69,type,
do: ( state > set_state ) > com ).
thf(func_def_70,type,
semi: com > com > com ).
thf(func_def_71,type,
while: ( state > $o ) > com > com ).
thf(func_def_72,type,
exec: state > com > state > $o ).
thf(func_def_73,type,
termi: com > state > $o ).
thf(func_def_74,type,
produc1914379986st_com: ( com > com > $o ) > list_com > produc2058209240st_com ).
thf(func_def_75,type,
produc1742567891_state: list_list_com > list_state > produc1393453339_state ).
thf(func_def_76,type,
produc1307105171st_com: list_com > list_com > produc258871771st_com ).
thf(func_def_77,type,
produc1204172211_state: list_com > state > produc2041926651_state ).
thf(func_def_78,type,
produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state ).
thf(func_def_79,type,
produc1354769367_state: list_P890094829_state > list_P890094829_state > produc1586269031_state ).
thf(func_def_80,type,
product_Pair_com_com: com > com > product_prod_com_com ).
thf(func_def_81,type,
produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).
thf(func_def_82,type,
produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state ).
thf(func_def_83,type,
produc2049704791_state: produc186437863_state > produc186437863_state > produc2046512871_state ).
thf(func_def_84,type,
irrefl_com: set_Pr1822651163om_com > $o ).
thf(func_def_85,type,
collect_state: ( state > $o ) > set_state ).
thf(func_def_86,type,
collec300063826_state: ( produc410756839_state > $o ) > set_Pr1165141447_state ).
thf(func_def_87,type,
collec489924946_state: ( produc186437863_state > $o ) > set_Pr2096893127_state ).
thf(func_def_88,type,
transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com ).
thf(func_def_89,type,
transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state ).
thf(func_def_90,type,
transi1965148016_state: set_Pr1325664839_state > set_Pr1325664839_state ).
thf(func_def_91,type,
transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com ).
thf(func_def_92,type,
transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(func_def_93,type,
transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).
thf(func_def_94,type,
transi152726506_state: set_Pr541394119_state > set_Pr541394119_state ).
thf(func_def_95,type,
transi1726587420_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(func_def_96,type,
transi1666849160_state: set_Pr2096893127_state > set_Pr2096893127_state ).
thf(func_def_97,type,
transi1995721864_state: set_Pr541394119_state > set_Pr541394119_state ).
thf(func_def_98,type,
member_nat: nat > set_nat > $o ).
thf(func_def_99,type,
member_state: state > set_state > $o ).
thf(func_def_100,type,
member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
thf(func_def_101,type,
member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
thf(func_def_102,type,
member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
thf(func_def_103,type,
member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).
thf(func_def_104,type,
member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o ).
thf(func_def_105,type,
member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
thf(func_def_106,type,
member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
thf(func_def_107,type,
member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
thf(func_def_108,type,
member284400400_state: produc2046512871_state > set_Pr541394119_state > $o ).
thf(func_def_109,type,
c: com ).
thf(func_def_110,type,
f: nat > produc2041926651_state ).
thf(func_def_111,type,
n: nat ).
thf(func_def_112,type,
s: state ).
thf(func_def_130,type,
sP0: state > ( state > $o ) > state > com > list_com > list_com > $o ).
thf(func_def_131,type,
sP1: state > com > list_com > list_com > ( state > $o ) > state > $o ).
thf(func_def_132,type,
sP2: ( list_com > $o ) > $o ).
thf(func_def_133,type,
sP3: list_com > list_com > com > list_com > $o ).
thf(func_def_134,type,
sP4: com > list_com > list_com > list_com > $o ).
thf(func_def_135,type,
sP5: ( state > $o ) > state > state > list_com > list_com > $o ).
thf(func_def_136,type,
sP6: com > list_com > list_com > ( state > $o ) > state > state > $o ).
thf(func_def_137,type,
sP7: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > $o ).
thf(func_def_138,type,
sP8: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > $o ).
thf(func_def_139,type,
sP9: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > $o ).
thf(func_def_140,type,
sP10: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > $o ).
thf(func_def_141,type,
sP11: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > $o ).
thf(func_def_142,type,
sP12: ( list_com > $o ) > $o ).
thf(func_def_143,type,
sP13: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o ).
thf(func_def_144,type,
sP14: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o ).
thf(func_def_145,type,
sP15: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o ).
thf(func_def_146,type,
sP16: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > $o ).
thf(func_def_147,type,
sP17: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > $o ).
thf(func_def_148,type,
sP18: ( produc2041926651_state > $o ) > produc2041926651_state > set_Pr1165141447_state > $o ).
thf(func_def_149,type,
sP19: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > $o ).
thf(func_def_150,type,
sP20: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o ).
thf(func_def_151,type,
sP21: ( list_com > $o ) > $o ).
thf(func_def_152,type,
sP22: ( list_com > list_com > $o ) > $o ).
thf(func_def_153,type,
sP23: ( list_com > state > $o ) > list_com > state > set_Pr1165141447_state > $o ).
thf(func_def_154,type,
sP24: list_com > com > list_com > list_com > $o ).
thf(func_def_155,type,
sP25: list_com > list_com > com > list_com > $o ).
thf(func_def_156,type,
sP26: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > $o ).
thf(func_def_157,type,
sP27: ( list_com > $o ) > $o ).
thf(func_def_158,type,
sK28: list_com > com ).
thf(func_def_159,type,
sK29: list_com > list_com ).
thf(func_def_160,type,
sK30: produc186437863_state > produc2041926651_state ).
thf(func_def_161,type,
sK31: produc186437863_state > produc2041926651_state ).
thf(func_def_162,type,
sK32: produc186437863_state > produc410756839_state ).
thf(func_def_163,type,
sK33: produc2041926651_state > ( nat > produc2041926651_state ) > set_Pr1165141447_state > nat ).
thf(func_def_164,type,
sK34: produc2041926651_state > set_Pr1165141447_state > nat > produc2041926651_state ).
thf(func_def_165,type,
sK35: ( list_com > list_com > $o ) > list_com ).
thf(func_def_166,type,
sK36: ( list_com > list_com > $o ) > list_com ).
thf(func_def_167,type,
sK37: ( list_com > list_com > $o ) > com ).
thf(func_def_168,type,
sK38: ( list_com > list_com > $o ) > list_com ).
thf(func_def_169,type,
sK39: nat > nat ).
thf(func_def_170,type,
sK40: produc2041926651_state > list_com ).
thf(func_def_171,type,
sK41: produc2041926651_state > state ).
thf(func_def_172,type,
sK42: ( list_com > list_com > $o ) > list_com ).
thf(func_def_173,type,
sK43: ( list_com > list_com > $o ) > com ).
thf(func_def_174,type,
sK44: ( list_com > list_com > $o ) > list_com ).
thf(func_def_175,type,
sK45: ( list_com > list_com > $o ) > com ).
thf(func_def_176,type,
sK46: ( list_com > list_com > $o ) > list_com ).
thf(func_def_177,type,
sK47: ( list_com > list_com > $o ) > com ).
thf(func_def_178,type,
sK48: ( list_com > list_com > $o ) > com ).
thf(func_def_179,type,
sK49: ( list_com > list_com > $o ) > list_com ).
thf(func_def_180,type,
sK50: produc258871771st_com > list_com ).
thf(func_def_181,type,
sK51: produc258871771st_com > list_com ).
thf(func_def_182,type,
sK52: produc258871771st_com > com ).
thf(func_def_183,type,
sK53: produc258871771st_com > list_com ).
thf(func_def_184,type,
sK54: ( list_com > $o ) > com ).
thf(func_def_185,type,
sK55: ( list_com > $o ) > list_com ).
thf(func_def_186,type,
sK56: ( list_com > $o ) > com ).
thf(func_def_187,type,
sK57: list_com > list_com > com > list_com > list_com ).
thf(func_def_188,type,
sK58: ( list_com > $o ) > com ).
thf(func_def_189,type,
sK59: ( list_com > $o ) > list_com ).
thf(func_def_190,type,
sK60: produc258871771st_com > list_com ).
thf(func_def_191,type,
sK61: produc258871771st_com > com ).
thf(func_def_192,type,
sK62: produc258871771st_com > list_com ).
thf(func_def_193,type,
sK63: produc258871771st_com > com ).
thf(func_def_194,type,
sK64: produc258871771st_com > list_com ).
thf(func_def_195,type,
sK65: produc258871771st_com > list_com ).
thf(func_def_196,type,
sK66: ( produc186437863_state > $o ) > list_com ).
thf(func_def_197,type,
sK67: ( produc186437863_state > $o ) > produc2041926651_state ).
thf(func_def_198,type,
sK68: ( produc186437863_state > $o ) > produc410756839_state ).
thf(func_def_199,type,
sK69: ( produc186437863_state > $o ) > state ).
thf(func_def_200,type,
sK70: ( list_com > $o ) > com ).
thf(func_def_201,type,
sK71: ( list_com > $o ) > list_com ).
thf(func_def_202,type,
sK72: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_203,type,
sK73: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_204,type,
sK74: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_205,type,
sK75: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_206,type,
sK76: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_207,type,
sK77: state > com > ( state > $o ) > state ).
thf(func_def_208,type,
sK78: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_209,type,
sK79: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_210,type,
sK80: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_211,type,
sK81: ( ( com > com > $o ) > list_com > $o ) > list_com ).
thf(func_def_212,type,
sK82: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_213,type,
sK83: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_214,type,
sK84: nat > nat ).
thf(func_def_215,type,
sK85: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_216,type,
sK86: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_217,type,
sK87: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_218,type,
sK88: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_219,type,
sK89: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_220,type,
sK90: ( nat > $o ) > nat ).
thf(func_def_221,type,
sK91: ( nat > state ) > com > nat ).
thf(func_def_222,type,
sK92: ( state > $o ) > ( nat > state ) > nat ).
thf(func_def_223,type,
sK93: ( nat > $o ) > nat ).
thf(func_def_224,type,
sK94: ( nat > state ) > ( state > $o ) > nat ).
thf(func_def_225,type,
sK95: ( nat > state ) > com > nat ).
thf(func_def_226,type,
sK96: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_227,type,
sK97: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_228,type,
sK98: set_Pr1165141447_state > ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_229,type,
sK99: ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_230,type,
sK100: ( ( com > com ) > list_com > list_com > $o ) > com ).
thf(func_def_231,type,
sK101: ( ( com > com ) > list_com > list_com > $o ) > com > com ).
thf(func_def_232,type,
sK102: ( ( com > com ) > list_com > list_com > $o ) > list_com ).
thf(func_def_233,type,
sK103: ( ( com > com ) > list_com > list_com > $o ) > list_com ).
thf(func_def_234,type,
sK104: ( ( com > com ) > list_com > list_com > $o ) > list_com ).
thf(func_def_235,type,
sK105: ( ( com > com ) > list_com > list_com > $o ) > com > com ).
thf(func_def_236,type,
sK106: ( produc186437863_state > $o ) > produc410756839_state ).
thf(func_def_237,type,
sK107: ( produc186437863_state > $o ) > produc410756839_state ).
thf(func_def_238,type,
sK108: produc186437863_state > produc410756839_state ).
thf(func_def_239,type,
sK109: produc186437863_state > produc410756839_state ).
thf(func_def_240,type,
sK110: list_com > list_com > list_com ).
thf(func_def_241,type,
sK111: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_242,type,
sK112: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_243,type,
sK113: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_244,type,
sK114: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_245,type,
sK115: ( ( com > com > $o ) > list_com > $o ) > list_com ).
thf(func_def_246,type,
sK116: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).
thf(func_def_247,type,
sK117: ( ( com > com > $o ) > list_com > $o ) > com ).
thf(func_def_248,type,
sK118: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_249,type,
sK119: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_250,type,
sK120: produc2041926651_state > set_Pr1165141447_state > ( produc2041926651_state > $o ) > produc2041926651_state ).
thf(func_def_251,type,
sK121: list_com > list_com > list_com ).
thf(func_def_252,type,
sK122: ( nat > produc410756839_state ) > set_Pr2096893127_state > produc410756839_state > nat ).
thf(func_def_253,type,
sK123: set_Pr2096893127_state > produc410756839_state > nat > produc410756839_state ).
thf(func_def_254,type,
sK124: com > com > state > state ).
thf(func_def_255,type,
sK125: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_256,type,
sK126: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_257,type,
sK127: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_258,type,
sK128: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_259,type,
sK129: ( produc186437863_state > $o ) > produc410756839_state ).
thf(func_def_260,type,
sK130: ( produc186437863_state > $o ) > produc2041926651_state ).
thf(func_def_261,type,
sK131: ( produc186437863_state > $o ) > produc2041926651_state ).
thf(func_def_262,type,
sK132: ( nat > $o ) > nat ).
thf(func_def_263,type,
sK133: ( list_com > $o ) > list_com ).
thf(func_def_264,type,
sK134: ( list_com > $o ) > com ).
thf(func_def_265,type,
sK135: ( list_com > $o ) > com ).
thf(func_def_266,type,
sK136: ( list_com > $o ) > com ).
thf(func_def_267,type,
sK137: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_268,type,
sK138: produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_269,type,
sK139: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_270,type,
sK140: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_271,type,
sK141: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_272,type,
sK142: list_com > list_com ).
thf(func_def_273,type,
sK143: list_com > com ).
thf(func_def_274,type,
sK144: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_275,type,
sK145: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_276,type,
sK146: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_277,type,
sK147: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_278,type,
sK148: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_279,type,
sK149: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_280,type,
sK150: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_281,type,
sK151: ( produc2041926651_state > $o ) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_282,type,
sK152: ( produc2041926651_state > $o ) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_283,type,
sK153: produc2041926651_state > ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_284,type,
sK154: set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_285,type,
sK155: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > state ).
thf(func_def_286,type,
sK156: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com ).
thf(func_def_287,type,
sK157: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > state ).
thf(func_def_288,type,
sK158: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com ).
thf(func_def_289,type,
sK159: ( list_com > state > $o ) > list_com > set_Pr1165141447_state > state > state ).
thf(func_def_290,type,
sK160: ( list_com > state > $o ) > list_com > set_Pr1165141447_state > state > list_com ).
thf(func_def_291,type,
sK161: state > list_com > set_Pr1165141447_state > state > list_com > list_com ).
thf(func_def_292,type,
sK162: state > list_com > set_Pr1165141447_state > state > list_com > state ).
thf(func_def_293,type,
sK163: produc410756839_state > produc2041926651_state ).
thf(func_def_294,type,
sK164: produc410756839_state > produc2041926651_state ).
thf(func_def_295,type,
sK165: ( list_com > $o ) > com ).
thf(func_def_296,type,
sK166: ( list_com > $o ) > list_com ).
thf(func_def_297,type,
sK167: ( list_com > $o ) > com ).
thf(func_def_298,type,
sK168: ( list_com > $o ) > com ).
thf(func_def_299,type,
sK169: produc410756839_state > set_Pr2096893127_state > nat > produc410756839_state ).
thf(func_def_300,type,
sK170: ( nat > produc410756839_state ) > produc410756839_state > set_Pr2096893127_state > nat ).
thf(func_def_301,type,
sK171: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_302,type,
sK172: ( produc186437863_state > $o ) > produc410756839_state ).
thf(func_def_303,type,
sK173: ( produc186437863_state > $o ) > produc410756839_state ).
thf(func_def_304,type,
sK174: ( list_com > list_com > $o ) > com ).
thf(func_def_305,type,
sK175: ( list_com > list_com > $o ) > com ).
thf(func_def_306,type,
sK176: ( list_com > list_com > $o ) > list_com ).
thf(func_def_307,type,
sK177: ( list_com > list_com > $o ) > list_com ).
thf(func_def_308,type,
sK178: ( list_com > list_com > $o ) > list_com ).
thf(func_def_309,type,
sK179: ( list_com > list_com > $o ) > list_com ).
thf(func_def_310,type,
sK180: list_com > com ).
thf(func_def_311,type,
sK181: list_com > com ).
thf(func_def_312,type,
sK182: list_com > list_com ).
thf(func_def_313,type,
sK183: list_com > com ).
thf(func_def_314,type,
sK184: produc410756839_state > produc2041926651_state ).
thf(func_def_315,type,
sK185: produc410756839_state > produc2041926651_state ).
thf(func_def_316,type,
sK186: ( list_com > state > $o ) > list_com > state > set_Pr1165141447_state > list_com ).
thf(func_def_317,type,
sK187: ( list_com > state > $o ) > list_com > state > set_Pr1165141447_state > list_com ).
thf(func_def_318,type,
sK188: ( list_com > state > $o ) > list_com > state > set_Pr1165141447_state > state ).
thf(func_def_319,type,
sK189: ( list_com > state > $o ) > list_com > state > set_Pr1165141447_state > state ).
thf(func_def_320,type,
sK190: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_321,type,
sK191: list_com > list_com > com > list_com > list_com ).
thf(func_def_322,type,
sK192: ( produc2041926651_state > $o ) > list_com ).
thf(func_def_323,type,
sK193: ( produc2041926651_state > $o ) > state ).
thf(func_def_324,type,
sK194: produc186437863_state > produc410756839_state ).
thf(func_def_325,type,
sK195: produc186437863_state > produc410756839_state ).
thf(func_def_326,type,
sK196: ( produc410756839_state > $o ) > list_com ).
thf(func_def_327,type,
sK197: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_328,type,
sK198: ( produc410756839_state > $o ) > state ).
thf(func_def_329,type,
sK199: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).
thf(func_def_330,type,
sK200: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > state ).
thf(func_def_331,type,
sK201: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > state ).
thf(func_def_332,type,
sK202: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com ).
thf(func_def_333,type,
sK203: list_com > state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com ).
thf(func_def_334,type,
sK204: produc2041926651_state > list_com ).
thf(func_def_335,type,
sK205: produc2041926651_state > state ).
thf(func_def_336,type,
sK206: ( nat > nat > $o ) > nat ).
thf(func_def_337,type,
sK207: ( nat > nat > $o ) > nat ).
thf(func_def_338,type,
sK208: ( nat > nat > $o ) > nat ).
thf(func_def_339,type,
sK209: ( nat > nat > $o ) > nat ).
thf(func_def_340,type,
sK210: set_Pr1165141447_state > produc2041926651_state > ( nat > produc2041926651_state ) > nat ).
thf(func_def_341,type,
sK211: set_Pr1165141447_state > produc2041926651_state > nat > produc2041926651_state ).
thf(func_def_342,type,
sK212: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_343,type,
sK213: ( produc2041926651_state > $o ) > list_com ).
thf(func_def_344,type,
sK214: ( produc2041926651_state > $o ) > state ).
thf(func_def_345,type,
sK215: produc186437863_state > produc410756839_state ).
thf(func_def_346,type,
sK216: produc186437863_state > state ).
thf(func_def_347,type,
sK217: produc186437863_state > list_com ).
thf(func_def_348,type,
sK218: produc186437863_state > produc2041926651_state ).
thf(func_def_349,type,
sK219: ( list_com > $o ) > list_com ).
thf(func_def_350,type,
sK220: ( list_com > $o ) > com ).
thf(func_def_351,type,
sK221: ( list_com > $o ) > com ).
thf(func_def_352,type,
sK222: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_353,type,
sK223: ( produc410756839_state > $o ) > produc2041926651_state ).
thf(func_def_354,type,
sK224: list_com > list_com ).
thf(func_def_355,type,
sK225: list_com > com ).
thf(func_def_356,type,
sK226: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).
thf(func_def_357,type,
sK227: produc410756839_state > list_com ).
thf(func_def_358,type,
sK228: produc410756839_state > state ).
thf(func_def_359,type,
sK229: produc410756839_state > produc2041926651_state ).
thf(func_def_362,type,
ph231:
!>[X0: $tType] : X0 ).
thf(f6077,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f6053,f6076]) ).
thf(f6076,plain,
~ spl230_45,
inference(avatar_contradiction_clause,[status(thm)],[f6075]) ).
thf(f6075,plain,
( $false
| ~ spl230_45 ),
inference(subsumption_resolution,[status(thm)],[f6074,f3345]) ).
thf(f3345,plain,
( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3339]) ).
thf(f3339,plain,
( ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2123,f1627]) ).
thf(f1627,plain,
! [X2: produc2041926651_state,X0: set_Pr1165141447_state,X1: produc2041926651_state] :
( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1302705790_state @ X0 ) ) )
| ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1044]) ).
thf(f1044,plain,
! [X0: set_Pr1165141447_state,X1: produc2041926651_state,X2: produc2041926651_state] :
( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1302705790_state @ X0 ) ) )
| ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f411]) ).
thf(f411,plain,
! [X0: set_Pr1165141447_state,X1: produc2041926651_state,X2: produc2041926651_state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X0 ) )
= $true )
=> ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1302705790_state @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f410]) ).
thf(f410,plain,
! [X0: set_Pr1165141447_state,X1: produc2041926651_state,X2: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X0 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1302705790_state @ X0 ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
! [X5: set_Pr1165141447_state,X9: produc2041926651_state,X3: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X3 @ X9 ) @ ( transi1726587420_state @ X5 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X3 @ X9 ) @ ( transi1302705790_state @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',fact_29_trancl__into__rtrancl) ).
thf(f2123,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
!= $true ),
inference(backward_demodulation,[status(thm)],[f1585,f1583]) ).
thf(f1583,plain,
( ( f @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
thf(f352,axiom,
( ( f @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_1) ).
thf(f1585,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f912]) ).
thf(f912,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
!= $true ),
inference(flattening,[status(thm)],[f393]) ).
thf(f393,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f392]) ).
thf(f392,plain,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_4) ).
thf(f6074,plain,
( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) )
| ~ spl230_45 ),
inference(superposition,[status(thm)],[f1631,f6050]) ).
thf(f6050,plain,
( ( ( f @ zero_zero_nat )
= ( f @ n ) )
| ~ spl230_45 ),
inference(avatar_component_clause,[status(thm)],[f6049]) ).
thf(f6049,definition,
( spl230_45
<=> ( ( f @ zero_zero_nat )
= ( f @ n ) ) ),
introduced(definition,[new_symbols(naming,[spl230_45])],[avatar_definition]) ).
thf(f1631,plain,
! [X0: nat] :
( $true
= ( member1069318160_state @ ( produc1909270103_state @ ( f @ X0 ) @ ( f @ ( suc @ X0 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ),
inference(cnf_transformation,[status(thm)],[f509]) ).
thf(f509,plain,
! [X0: nat] :
( $true
= ( member1069318160_state @ ( produc1909270103_state @ ( f @ X0 ) @ ( f @ ( suc @ X0 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ),
inference(fool_elimination,[status(thm)],[f508]) ).
thf(f508,plain,
! [X0: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X0 ) @ ( f @ ( suc @ X0 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ),
inference(rectify,[status(thm)],[f353]) ).
thf(f353,axiom,
! [X8: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X8 ) @ ( f @ ( suc @ X8 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_2) ).
thf(f6053,plain,
spl230_45,
inference(avatar_split_clause,[status(thm)],[f6052,f6049]) ).
thf(f6052,plain,
( ( f @ zero_zero_nat )
= ( f @ n ) ),
inference(subsumption_resolution,[status(thm)],[f6032,f2990]) ).
thf(f2990,plain,
( $true
= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
inference(forward_demodulation,[status(thm)],[f1664,f1583]) ).
thf(f1664,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f429]) ).
thf(f429,plain,
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f428]) ).
thf(f428,plain,
member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,axiom,
member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_3) ).
thf(f6032,plain,
( ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
| ( ( f @ zero_zero_nat )
= ( f @ n ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6025]) ).
thf(f6025,plain,
( ( ( f @ zero_zero_nat )
= ( f @ n ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f5999,f1626]) ).
thf(f1626,plain,
! [X2: produc2041926651_state,X0: produc2041926651_state,X1: set_Pr1165141447_state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X1 ) )
= $true )
| ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1302705790_state @ X1 ) )
!= $true )
| ( X0 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f981]) ).
thf(f981,plain,
! [X0: produc2041926651_state,X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1302705790_state @ X1 ) )
!= $true )
| ( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X1 ) )
= $true )
& ( X0 != X2 ) )
| ( X0 = X2 ) ),
inference(flattening,[status(thm)],[f980]) ).
thf(f980,plain,
! [X0: produc2041926651_state,X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( X0 = X2 )
| ( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X1 ) )
= $true )
& ( X0 != X2 ) )
| ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1302705790_state @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f525]) ).
thf(f525,plain,
! [X0: produc2041926651_state,X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1302705790_state @ X1 ) )
= $true )
=> ( ( X0 = X2 )
| ( ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X1 ) )
= $true )
& ( X0 != X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f524]) ).
thf(f524,plain,
! [X0: produc2041926651_state,X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1302705790_state @ X1 ) )
=> ( ( X0 = X2 )
| ( ( X0 != X2 )
& ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,axiom,
! [X9: produc2041926651_state,X12: set_Pr1165141447_state,X3: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X3 @ X9 ) @ ( transi1302705790_state @ X12 ) )
=> ( ( X3 = X9 )
| ( ( X3 != X9 )
& ( member1069318160_state @ ( produc1909270103_state @ X3 @ X9 ) @ ( transi1726587420_state @ X12 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',fact_25_rtranclD) ).
thf(f5999,plain,
( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5964]) ).
thf(f5964,plain,
( ( $true != $true )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ) ),
inference(superposition,[status(thm)],[f5271,f1631]) ).
thf(f5271,plain,
! [X0: produc2041926651_state] :
( ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X0 @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X0 ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5266]) ).
thf(f5266,plain,
! [X0: produc2041926651_state] :
( ( $true != $true )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X0 ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X0 @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ) ),
inference(superposition,[status(thm)],[f3345,f1567]) ).
thf(f1567,plain,
! [X2: produc2041926651_state,X3: set_Pr1165141447_state,X0: produc2041926651_state,X1: produc2041926651_state] :
( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X3 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X3 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X0 @ X1 ) @ ( transi1726587420_state @ X3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f999]) ).
thf(f999,plain,
! [X0: produc2041926651_state,X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state] :
( ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X3 ) ) )
| ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X3 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X0 @ X1 ) @ ( transi1726587420_state @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f998]) ).
thf(f998,plain,
! [X0: produc2041926651_state,X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state] :
( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X3 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X0 @ X1 ) @ ( transi1726587420_state @ X3 ) ) )
| ( $true
!= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f753]) ).
thf(f753,plain,
! [X0: produc2041926651_state,X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state] :
( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X3 ) ) )
=> ( ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X0 @ X1 ) @ ( transi1726587420_state @ X3 ) ) )
=> ( $true
= ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f752]) ).
thf(f752,plain,
! [X0: produc2041926651_state,X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X0 ) @ ( transi1726587420_state @ X3 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X0 @ X1 ) @ ( transi1726587420_state @ X3 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X2 @ X1 ) @ ( transi1726587420_state @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f82]) ).
thf(f82,axiom,
! [X31: produc2041926651_state,X35: produc2041926651_state,X30: produc2041926651_state,X5: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X30 @ X31 ) @ ( transi1726587420_state @ X5 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X31 @ X35 ) @ ( transi1726587420_state @ X5 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X30 @ X35 ) @ ( transi1726587420_state @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',fact_81_trancl__trans) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP145^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:27:40 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : ITP145^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.44 % Domain : Interactive Theorem Proving
% 0.20/0.44 % Problem : Sledgehammer PHoareTotal problem prob_632__3264706_1
% 0.20/0.44 % Version : Especial.
% 0.20/0.44 % English :
% 0.20/0.44
% 0.20/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.44 % Source : [Des21]
% 0.20/0.44 % Names : PHoareTotal/prob_632__3264706_1 [Des21]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% 0.20/0.44 % Syntax : Number of formulae : 468 ( 133 unt; 113 typ; 0 def)
% 0.20/0.44 % Number of atoms : 1002 ( 421 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 7 ( 2 avg)
% 0.20/0.44 % Number of connectives : 5196 ( 215 ~; 35 |; 108 &;4218 @)
% 0.20/0.44 % ( 0 <=>; 620 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 22 ( 10 avg)
% 0.20/0.44 % Number of types : 30 ( 29 usr)
% 0.20/0.44 % Number of type conns : 299 ( 299 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 85 ( 84 usr; 10 con; 0-3 aty)
% 0.20/0.44 % Number of variables : 1551 ( 8 ^;1465 !; 78 ?;1551 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:29.764
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % Could-be-implicit typings (29)
% 0.20/0.44 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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_Mt__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_J,type,
% 0.20/0.44 set_Pr541394119_state: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Product____Type__Oprod_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_Mt__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,
% 0.20/0.44 produc2046512871_state: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_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_Mt__List__Olist_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_J_J,type,
% 0.20/0.44 set_Pr1325664839_state: $tType ).
% 0.20/0.44
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% 0.20/0.44 ( ( ( F2 @ zero_zero_nat )
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% 0.20/0.44 % renumber
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% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F @ I ) ) @ ( transi463013610_state @ R ) )
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% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ R )
% 0.20/0.44 => ( P @ A2 @ B2 ) )
% 0.20/0.44 => ( ! [A2: produc410756839_state,B2: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ ( transi1995721864_state @ R ) )
% 0.20/0.44 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( P @ Aa @ Ba ) ) ) )
% 0.20/0.44 => ( P @ Bx @ By ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_induct2
% 0.20/0.44 thf(fact_11_trancl__induct2,axiom,
% 0.20/0.44 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ R )
% 0.20/0.44 => ( P @ A2 @ B2 ) )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( P @ Aa @ Ba ) ) ) )
% 0.20/0.44 => ( P @ Bx @ By ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_induct2
% 0.20/0.44 thf(fact_12_trancl__induct2,axiom,
% 0.20/0.44 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ! [A2: list_com,B2: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ R )
% 0.20/0.44 => ( P @ A2 @ B2 ) )
% 0.20/0.44 => ( ! [A2: list_com,B2: state,Aa: list_com,Ba: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( P @ Aa @ Ba ) ) ) )
% 0.20/0.44 => ( P @ Bx @ By ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_induct2
% 0.20/0.44 thf(fact_13_inf__def,axiom,
% 0.20/0.44 ( pHoare2126160787le_inf
% 0.20/0.44 = ( ^ [Cs2: list_com,S3: state] :
% 0.20/0.44 ? [F3: nat > produc2041926651_state] :
% 0.20/0.44 ( ( ( F3 @ zero_zero_nat )
% 0.20/0.44 = ( produc1204172211_state @ Cs2 @ S3 ) )
% 0.20/0.44 & ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ pHoare259243666_exec1 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % inf_def
% 0.20/0.44 thf(fact_14_rtrancl__induct2,axiom,
% 0.20/0.44 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.20/0.44 => ( ( P @ Ax @ Ay )
% 0.20/0.44 => ( ! [A2: produc410756839_state,B2: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ ( transi152726506_state @ R ) )
% 0.20/0.44 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( P @ Aa @ Ba ) ) ) )
% 0.20/0.44 => ( P @ Bx @ By ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_induct2
% 0.20/0.44 thf(fact_15_rtrancl__induct2,axiom,
% 0.20/0.44 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ Ax @ Ay )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( P @ Aa @ Ba ) ) ) )
% 0.20/0.44 => ( P @ Bx @ By ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_induct2
% 0.20/0.44 thf(fact_16_rtrancl__induct2,axiom,
% 0.20/0.44 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ Ax @ Ay )
% 0.20/0.44 => ( ! [A2: list_com,B2: state,Aa: list_com,Ba: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( P @ Aa @ Ba ) ) ) )
% 0.20/0.44 => ( P @ Bx @ By ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_induct2
% 0.20/0.44 thf(fact_17_converse__rtranclE2,axiom,
% 0.20/0.44 ! [Xa: produc410756839_state,Xb: produc410756839_state,Za: produc410756839_state,Zb: produc410756839_state,R: set_Pr541394119_state] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) )
% 0.20/0.44 => ( ( ( produc2065881943_state @ Xa @ Xb )
% 0.20/0.44 != ( produc2065881943_state @ Za @ Zb ) )
% 0.20/0.44 => ~ ! [A2: produc410756839_state,B2: produc410756839_state] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ R )
% 0.20/0.44 => ~ ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtranclE2
% 0.20/0.44 thf(fact_18_converse__rtranclE2,axiom,
% 0.20/0.44 ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( ( produc1909270103_state @ Xa @ Xb )
% 0.20/0.44 != ( produc1909270103_state @ Za @ Zb ) )
% 0.20/0.44 => ~ ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ R )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtranclE2
% 0.20/0.44 thf(fact_19_converse__rtranclE2,axiom,
% 0.20/0.44 ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( ( produc1204172211_state @ Xa @ Xb )
% 0.20/0.44 != ( produc1204172211_state @ Za @ Zb ) )
% 0.20/0.44 => ~ ! [A2: list_com,B2: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ R )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtranclE2
% 0.20/0.44 thf(fact_20_converse__rtrancl__induct2,axiom,
% 0.20/0.44 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.20/0.44 => ( ( P @ Bx @ By )
% 0.20/0.44 => ( ! [A2: produc410756839_state,B2: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.20/0.44 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Aa @ Ba ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.20/0.44 => ( ( P @ Aa @ Ba )
% 0.20/0.44 => ( P @ A2 @ B2 ) ) ) )
% 0.20/0.44 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_induct2
% 0.20/0.44 thf(fact_21_converse__rtrancl__induct2,axiom,
% 0.20/0.44 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ Bx @ By )
% 0.20/0.44 => ( ! [A2: list_com,B2: state,Aa: list_com,Ba: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ Aa @ Ba )
% 0.20/0.44 => ( P @ A2 @ B2 ) ) ) )
% 0.20/0.44 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_induct2
% 0.20/0.44 thf(fact_22_converse__rtrancl__induct2,axiom,
% 0.20/0.44 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ Bx @ By )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ Aa @ Ba )
% 0.20/0.44 => ( P @ A2 @ B2 ) ) ) )
% 0.20/0.44 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_induct2
% 0.20/0.44 thf(fact_23_tranclD,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R2: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R2 ) )
% 0.20/0.44 => ? [Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z ) @ R2 )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ Z @ Y ) @ ( transi1302705790_state @ R2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % tranclD
% 0.20/0.44 thf(fact_24_tranclD,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R2: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R2 ) )
% 0.20/0.44 => ? [Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z ) @ R2 )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ Z @ Y ) @ ( transi463013610_state @ R2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % tranclD
% 0.20/0.44 thf(fact_25_rtranclD,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R2: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R2 ) )
% 0.20/0.44 => ( ( A = B )
% 0.20/0.44 | ( ( A != B )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R2 ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtranclD
% 0.20/0.44 thf(fact_26_rtranclD,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R2: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R2 ) )
% 0.20/0.44 => ( ( A = B )
% 0.20/0.44 | ( ( A != B )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R2 ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtranclD
% 0.20/0.44 thf(fact_27_tranclD2,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R2: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R2 ) )
% 0.20/0.44 => ? [Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z ) @ ( transi1302705790_state @ R2 ) )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ Z @ Y ) @ R2 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % tranclD2
% 0.20/0.44 thf(fact_28_tranclD2,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R2: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R2 ) )
% 0.20/0.44 => ? [Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z ) @ ( transi463013610_state @ R2 ) )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ Z @ Y ) @ R2 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % tranclD2
% 0.20/0.44 thf(fact_29_trancl__into__rtrancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_into_rtrancl
% 0.20/0.44 thf(fact_30_trancl__into__rtrancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_into_rtrancl
% 0.20/0.44 thf(fact_31_rtrancl__eq__or__trancl,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R2: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R2 ) )
% 0.20/0.44 = ( ( X = Y )
% 0.20/0.44 | ( ( X != Y )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R2 ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_eq_or_trancl
% 0.20/0.44 thf(fact_32_rtrancl__eq__or__trancl,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R2: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R2 ) )
% 0.20/0.44 = ( ( X = Y )
% 0.20/0.44 | ( ( X != Y )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R2 ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_eq_or_trancl
% 0.20/0.44 thf(fact_33_r__into__rtrancl,axiom,
% 0.20/0.44 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ P2 @ R )
% 0.20/0.44 => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % r_into_rtrancl
% 0.20/0.44 thf(fact_34_r__into__rtrancl,axiom,
% 0.20/0.44 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ P2 @ R )
% 0.20/0.44 => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % r_into_rtrancl
% 0.20/0.44 thf(fact_35_rtrancl__idemp,axiom,
% 0.20/0.44 ! [R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 0.20/0.44 = ( transi1302705790_state @ R ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_idemp
% 0.20/0.44 thf(fact_36_rtrancl__idemp,axiom,
% 0.20/0.44 ! [R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 0.20/0.44 = ( transi463013610_state @ R ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_idemp
% 0.20/0.44 thf(fact_37_r__into__trancl_H,axiom,
% 0.20/0.44 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ P2 @ R )
% 0.20/0.44 => ( member1069318160_state @ P2 @ ( transi1726587420_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % r_into_trancl'
% 0.20/0.44 thf(fact_38_r__into__trancl_H,axiom,
% 0.20/0.44 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ P2 @ R )
% 0.20/0.44 => ( member512523024_state @ P2 @ ( transi1666849160_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % r_into_trancl'
% 0.20/0.44 thf(fact_39_converse__rtrancl__into__rtrancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_into_rtrancl
% 0.20/0.44 thf(fact_40_converse__rtrancl__into__rtrancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_into_rtrancl
% 0.20/0.44 thf(fact_41_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.rtrancl_into_rtrancl
% 0.20/0.44 thf(fact_42_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.rtrancl_into_rtrancl
% 0.20/0.44 thf(fact_43_converse__rtrancl__induct,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ B )
% 0.20/0.44 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ Z )
% 0.20/0.44 => ( P @ Y2 ) ) ) )
% 0.20/0.44 => ( P @ A ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_induct
% 0.20/0.44 thf(fact_44_converse__rtrancl__induct,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ B )
% 0.20/0.44 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ Z )
% 0.20/0.44 => ( P @ Y2 ) ) ) )
% 0.20/0.44 => ( P @ A ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtrancl_induct
% 0.20/0.44 thf(fact_45_rtrancl_Ortrancl__refl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ ( transi1302705790_state @ R ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.rtrancl_refl
% 0.20/0.44 thf(fact_46_rtrancl_Ortrancl__refl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,R: set_Pr2096893127_state] : ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ ( transi463013610_state @ R ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.rtrancl_refl
% 0.20/0.44 thf(fact_47_converse__rtranclE,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( X != Z2 )
% 0.20/0.44 => ~ ! [Y2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y2 ) @ R )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtranclE
% 0.20/0.44 thf(fact_48_converse__rtranclE,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( X != Z2 )
% 0.20/0.44 => ~ ! [Y2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y2 ) @ R )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_rtranclE
% 0.20/0.44 thf(fact_49_rtrancl_Oinducts,axiom,
% 0.20/0.44 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ! [A2: produc2041926651_state] : ( P @ A2 @ A2 )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,C3: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C3 ) @ R )
% 0.20/0.44 => ( P @ A2 @ C3 ) ) ) )
% 0.20/0.44 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.inducts
% 0.20/0.44 thf(fact_50_rtrancl_Oinducts,axiom,
% 0.20/0.44 ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ! [A2: produc410756839_state] : ( P @ A2 @ A2 )
% 0.20/0.44 => ( ! [A2: produc410756839_state,B2: produc410756839_state,C3: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C3 ) @ R )
% 0.20/0.44 => ( P @ A2 @ C3 ) ) ) )
% 0.20/0.44 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.inducts
% 0.20/0.44 thf(fact_51_rtrancl__induct,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( P @ A )
% 0.20/0.44 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( P @ Y2 )
% 0.20/0.44 => ( P @ Z ) ) ) )
% 0.20/0.44 => ( P @ B ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_induct
% 0.20/0.44 thf(fact_52_rtrancl__induct,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( P @ A )
% 0.20/0.44 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( P @ Y2 )
% 0.20/0.44 => ( P @ Z ) ) ) )
% 0.20/0.44 => ( P @ B ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_induct
% 0.20/0.44 thf(fact_53_rtrancl__trans,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_trans
% 0.20/0.44 thf(fact_54_rtrancl__trans,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_trans
% 0.20/0.44 thf(fact_55_rtrancl_Osimps,axiom,
% 0.20/0.44 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 = ( ? [A3: produc2041926651_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = A3 ) )
% 0.20/0.44 | ? [A3: produc2041926651_state,B3: produc2041926651_state,C4: produc2041926651_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = C4 )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.simps
% 0.20/0.44 thf(fact_56_rtrancl_Osimps,axiom,
% 0.20/0.44 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 = ( ? [A3: produc410756839_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = A3 ) )
% 0.20/0.44 | ? [A3: produc410756839_state,B3: produc410756839_state,C4: produc410756839_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = C4 )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ A3 @ B3 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.simps
% 0.20/0.44 thf(fact_57_rtrancl_Ocases,axiom,
% 0.20/0.44 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( A22 != A1 )
% 0.20/0.44 => ~ ! [B2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.cases
% 0.20/0.44 thf(fact_58_rtrancl_Ocases,axiom,
% 0.20/0.44 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( A22 != A1 )
% 0.20/0.44 => ~ ! [B2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl.cases
% 0.20/0.44 thf(fact_59_rtranclE,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( A != B )
% 0.20/0.44 => ~ ! [Y2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y2 @ B ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtranclE
% 0.20/0.44 thf(fact_60_rtranclE,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( A != B )
% 0.20/0.44 => ~ ! [Y2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ Y2 @ B ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtranclE
% 0.20/0.44 thf(fact_61_trancl_Otrancl__into__trancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.trancl_into_trancl
% 0.20/0.44 thf(fact_62_trancl_Otrancl__into__trancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.trancl_into_trancl
% 0.20/0.44 thf(fact_63_converse__trancl__induct,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ! [Y2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ B ) @ R )
% 0.20/0.44 => ( P @ Y2 ) )
% 0.20/0.44 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( P @ Z )
% 0.20/0.44 => ( P @ Y2 ) ) ) )
% 0.20/0.44 => ( P @ A ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_trancl_induct
% 0.20/0.44 thf(fact_64_converse__trancl__induct,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ! [Y2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ B ) @ R )
% 0.20/0.44 => ( P @ Y2 ) )
% 0.20/0.44 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( P @ Z )
% 0.20/0.44 => ( P @ Y2 ) ) ) )
% 0.20/0.44 => ( P @ A ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_trancl_induct
% 0.20/0.44 thf(fact_65_trancl_Or__into__trancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.r_into_trancl
% 0.20/0.44 thf(fact_66_trancl_Or__into__trancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.r_into_trancl
% 0.20/0.44 thf(fact_67_trancl__trans__induct,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ! [X3: produc2041926651_state,Y2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 0.20/0.44 => ( P @ X3 @ Y2 ) )
% 0.20/0.44 => ( ! [X3: produc2041926651_state,Y2: produc2041926651_state,Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( P @ X3 @ Y2 )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( P @ Y2 @ Z )
% 0.20/0.44 => ( P @ X3 @ Z ) ) ) ) )
% 0.20/0.44 => ( P @ X @ Y ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_trans_induct
% 0.20/0.44 thf(fact_68_trancl__trans__induct,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ! [X3: produc410756839_state,Y2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 0.20/0.44 => ( P @ X3 @ Y2 ) )
% 0.20/0.44 => ( ! [X3: produc410756839_state,Y2: produc410756839_state,Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( P @ X3 @ Y2 )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( P @ Y2 @ Z )
% 0.20/0.44 => ( P @ X3 @ Z ) ) ) ) )
% 0.20/0.44 => ( P @ X @ Y ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_trans_induct
% 0.20/0.44 thf(fact_69_trancl__into__trancl2,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_into_trancl2
% 0.20/0.44 thf(fact_70_trancl__into__trancl2,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_into_trancl2
% 0.20/0.44 thf(fact_71_irrefl__trancl__rD,axiom,
% 0.20/0.44 ! [R: set_Pr1165141447_state,X: produc2041926651_state,Y: produc2041926651_state] :
% 0.20/0.44 ( ! [X3: produc2041926651_state] :
% 0.20/0.44 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.20/0.44 => ( X != Y ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % irrefl_trancl_rD
% 0.20/0.44 thf(fact_72_irrefl__trancl__rD,axiom,
% 0.20/0.44 ! [R: set_Pr2096893127_state,X: produc410756839_state,Y: produc410756839_state] :
% 0.20/0.44 ( ! [X3: produc410756839_state] :
% 0.20/0.44 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.20/0.44 => ( X != Y ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % irrefl_trancl_rD
% 0.20/0.44 thf(fact_73_converse__tranclE,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ R )
% 0.20/0.44 => ~ ! [Y2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y2 ) @ R )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z2 ) @ ( transi1726587420_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_tranclE
% 0.20/0.44 thf(fact_74_converse__tranclE,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ~ ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ R )
% 0.20/0.44 => ~ ! [Y2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y2 ) @ R )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z2 ) @ ( transi1666849160_state @ R ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % converse_tranclE
% 0.20/0.44 thf(fact_75_r__r__into__trancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R2: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R2 )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R2 )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % r_r_into_trancl
% 0.20/0.44 thf(fact_76_r__r__into__trancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R2: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R2 )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R2 )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % r_r_into_trancl
% 0.20/0.44 thf(fact_77_trancl_Oinducts,axiom,
% 0.20/0.44 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.20/0.44 => ( P @ A2 @ B2 ) )
% 0.20/0.44 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,C3: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C3 ) @ R )
% 0.20/0.44 => ( P @ A2 @ C3 ) ) ) )
% 0.20/0.44 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.inducts
% 0.20/0.44 thf(fact_78_trancl_Oinducts,axiom,
% 0.20/0.44 ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ! [A2: produc410756839_state,B2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.20/0.44 => ( P @ A2 @ B2 ) )
% 0.20/0.44 => ( ! [A2: produc410756839_state,B2: produc410756839_state,C3: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( P @ A2 @ B2 )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C3 ) @ R )
% 0.20/0.44 => ( P @ A2 @ C3 ) ) ) )
% 0.20/0.44 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.inducts
% 0.20/0.44 thf(fact_79_trancl__induct,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ! [Y2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ R )
% 0.20/0.44 => ( P @ Y2 ) )
% 0.20/0.44 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( P @ Y2 )
% 0.20/0.44 => ( P @ Z ) ) ) )
% 0.20/0.44 => ( P @ B ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_induct
% 0.20/0.44 thf(fact_80_trancl__induct,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ! [Y2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ R )
% 0.20/0.44 => ( P @ Y2 ) )
% 0.20/0.44 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 0.20/0.44 => ( ( P @ Y2 )
% 0.20/0.44 => ( P @ Z ) ) ) )
% 0.20/0.44 => ( P @ B ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_induct
% 0.20/0.44 thf(fact_81_trancl__trans,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_trans
% 0.20/0.44 thf(fact_82_trancl__trans,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_trans
% 0.20/0.44 thf(fact_83_trancl_Osimps,axiom,
% 0.20/0.44 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 = ( ? [A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = B3 )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ R ) )
% 0.20/0.44 | ? [A3: produc2041926651_state,B3: produc2041926651_state,C4: produc2041926651_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = C4 )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 & ( member1069318160_state @ ( produc1909270103_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.simps
% 0.20/0.44 thf(fact_84_trancl_Osimps,axiom,
% 0.20/0.44 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 = ( ? [A3: produc410756839_state,B3: produc410756839_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = B3 )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ A3 @ B3 ) @ R ) )
% 0.20/0.44 | ? [A3: produc410756839_state,B3: produc410756839_state,C4: produc410756839_state] :
% 0.20/0.44 ( ( A1 = A3 )
% 0.20/0.44 & ( A22 = C4 )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ A3 @ B3 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 & ( member512523024_state @ ( produc2065881943_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.simps
% 0.20/0.44 thf(fact_85_trancl_Ocases,axiom,
% 0.20/0.44 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ~ ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ R )
% 0.20/0.44 => ~ ! [B2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.cases
% 0.20/0.44 thf(fact_86_trancl_Ocases,axiom,
% 0.20/0.44 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ~ ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ R )
% 0.20/0.44 => ~ ! [B2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl.cases
% 0.20/0.44 thf(fact_87_tranclE,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ~ ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.44 => ~ ! [C3: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ C3 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ~ ( member1069318160_state @ ( produc1909270103_state @ C3 @ B ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % tranclE
% 0.20/0.44 thf(fact_88_tranclE,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ~ ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.44 => ~ ! [C3: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ C3 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ~ ( member512523024_state @ ( produc2065881943_state @ C3 @ B ) @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % tranclE
% 0.20/0.44 thf(fact_89_termi__impl__not__inf,axiom,
% 0.20/0.44 ! [C: com,S: state] :
% 0.20/0.44 ( ( termi @ C @ S )
% 0.20/0.44 => ~ ( pHoare2126160787le_inf @ ( cons_com @ C @ nil_com ) @ S ) ) ).
% 0.20/0.44
% 0.20/0.44 % termi_impl_not_inf
% 0.20/0.44 thf(fact_90_mem__Collect__eq,axiom,
% 0.20/0.44 ! [A: produc410756839_state,P: produc410756839_state > $o] :
% 0.20/0.44 ( ( member1069318160_state @ A @ ( collec300063826_state @ P ) )
% 0.20/0.44 = ( P @ A ) ) ).
% 0.20/0.44
% 0.20/0.44 % mem_Collect_eq
% 0.20/0.44 thf(fact_91_mem__Collect__eq,axiom,
% 0.20/0.44 ! [A: state,P: state > $o] :
% 0.20/0.44 ( ( member_state @ A @ ( collect_state @ P ) )
% 0.20/0.44 = ( P @ A ) ) ).
% 0.20/0.44
% 0.20/0.44 % mem_Collect_eq
% 0.20/0.44 thf(fact_92_mem__Collect__eq,axiom,
% 0.20/0.44 ! [A: produc186437863_state,P: produc186437863_state > $o] :
% 0.20/0.44 ( ( member512523024_state @ A @ ( collec489924946_state @ P ) )
% 0.20/0.44 = ( P @ A ) ) ).
% 0.20/0.44
% 0.20/0.44 % mem_Collect_eq
% 0.20/0.44 thf(fact_93_Collect__mem__eq,axiom,
% 0.20/0.44 ! [A4: set_Pr1165141447_state] :
% 0.20/0.44 ( ( collec300063826_state
% 0.20/0.44 @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 0.20/0.44 = A4 ) ).
% 0.20/0.44
% 0.20/0.44 % Collect_mem_eq
% 0.20/0.44 thf(fact_94_Collect__mem__eq,axiom,
% 0.20/0.44 ! [A4: set_state] :
% 0.20/0.44 ( ( collect_state
% 0.20/0.44 @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 0.20/0.44 = A4 ) ).
% 0.20/0.44
% 0.20/0.44 % Collect_mem_eq
% 0.20/0.44 thf(fact_95_Collect__mem__eq,axiom,
% 0.20/0.44 ! [A4: set_Pr2096893127_state] :
% 0.20/0.44 ( ( collec489924946_state
% 0.20/0.44 @ ^ [X4: produc186437863_state] : ( member512523024_state @ X4 @ A4 ) )
% 0.20/0.44 = A4 ) ).
% 0.20/0.44
% 0.20/0.44 % Collect_mem_eq
% 0.20/0.44 thf(fact_96_trancl__rtrancl__trancl,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_rtrancl_trancl
% 0.20/0.44 thf(fact_97_trancl__rtrancl__trancl,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % trancl_rtrancl_trancl
% 0.20/0.44 thf(fact_98_rtrancl__trancl__trancl,axiom,
% 0.20/0.44 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1726587420_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_trancl_trancl
% 0.20/0.44 thf(fact_99_rtrancl__trancl__trancl,axiom,
% 0.20/0.44 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi1666849160_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_trancl_trancl
% 0.20/0.44 thf(fact_100_rtrancl__into__trancl2,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_into_trancl2
% 0.20/0.44 thf(fact_101_rtrancl__into__trancl2,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_into_trancl2
% 0.20/0.44 thf(fact_102_rtrancl__into__trancl1,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.20/0.44 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 0.20/0.44 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_into_trancl1
% 0.20/0.44 thf(fact_103_rtrancl__into__trancl1,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.20/0.44 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.20/0.44 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R )
% 0.20/0.44 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % rtrancl_into_trancl1
% 0.20/0.44 thf(fact_104_exec1s__impl__execs,axiom,
% 0.20/0.44 ! [Cs3: list_com,S: state,T: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.20/0.44 => ( pHoare259243732_execs @ S @ Cs3 @ T ) ) ).
% 0.20/0.44
% 0.20/0.44 % exec1s_impl_execs
% 0.20/0.44 thf(fact_105_execs__pres__termis,axiom,
% 0.20/0.44 ! [Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.20/0.44 => ( ( pHoare806997636termis @ Cs3 @ S )
% 0.20/0.44 => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % execs_pres_termis
% 0.20/0.44 thf(fact_106_old_Onat_Oinject,axiom,
% 0.20/0.44 ! [Nat: nat,Nat2: nat] :
% 0.20/0.44 ( ( ( suc @ Nat )
% 0.20/0.44 = ( suc @ Nat2 ) )
% 0.20/0.44 = ( Nat = Nat2 ) ) ).
% 0.20/0.44
% 0.20/0.44 % old.nat.inject
% 0.20/0.44 thf(fact_107_nat_Oinject,axiom,
% 0.20/0.44 ! [X2: nat,Y22: nat] :
% 0.20/0.44 ( ( ( suc @ X2 )
% 0.20/0.44 = ( suc @ Y22 ) )
% 0.20/0.44 = ( X2 = Y22 ) ) ).
% 0.20/0.44
% 0.20/0.44 % nat.inject
% 0.20/0.44 thf(fact_108_list_Oinject,axiom,
% 0.20/0.44 ! [X21: com,X22: list_com,Y21: com,Y222: list_com] :
% 0.20/0.44 ( ( ( cons_com @ X21 @ X22 )
% 0.20/0.44 = ( cons_com @ Y21 @ Y222 ) )
% 0.20/0.44 = ( ( X21 = Y21 )
% 0.20/0.44 & ( X22 = Y222 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % list.inject
% 0.20/0.44 thf(fact_109_exec1s__impl__exec,axiom,
% 0.20/0.44 ! [C: com,S: state,T: state] :
% 0.20/0.44 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.20/0.44 => ( exec @ S @ C @ T ) ) ).
% 0.20/0.44
% 0.20/0.44 % exec1s_impl_exec
% 0.20/0.44 thf(fact_110_old_Oprod_Oinject,axiom,
% 0.20/0.44 ! [A: list_com,B: state,A5: list_com,B4: state] :
% 0.20/0.44 ( ( ( produc1204172211_state @ A @ B )
% 0.20/0.44 = ( produc1204172211_state @ A5 @ B4 ) )
% 0.20/0.44 = ( ( A = A5 )
% 0.20/0.44 & ( B = B4 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % old.prod.inject
% 0.20/0.44 thf(fact_111_old_Oprod_Oinject,axiom,
% 0.20/0.44 ! [A: produc2041926651_state,B: produc2041926651_state,A5: produc2041926651_state,B4: produc2041926651_state] :
% 0.20/0.44 ( ( ( produc1909270103_state @ A @ B )
% 0.20/0.44 = ( produc1909270103_state @ A5 @ B4 ) )
% 0.20/0.44 = ( ( A = A5 )
% 0.20/0.44 & ( B = B4 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % old.prod.inject
% 0.20/0.44 thf(fact_112_old_Oprod_Oinject,axiom,
% 0.20/0.44 ! [A: produc410756839_state,B: produc410756839_state,A5: produc410756839_state,B4: produc410756839_state] :
% 0.20/0.44 ( ( ( produc2065881943_state @ A @ B )
% 0.20/0.44 = ( produc2065881943_state @ A5 @ B4 ) )
% 0.20/0.44 = ( ( A = A5 )
% 0.20/0.44 & ( B = B4 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % old.prod.inject
% 0.20/0.44 thf(fact_113_prod_Oinject,axiom,
% 0.20/0.44 ! [X1: list_com,X2: state,Y1: list_com,Y22: state] :
% 0.20/0.44 ( ( ( produc1204172211_state @ X1 @ X2 )
% 0.20/0.44 = ( produc1204172211_state @ Y1 @ Y22 ) )
% 0.20/0.44 = ( ( X1 = Y1 )
% 0.20/0.44 & ( X2 = Y22 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % prod.inject
% 0.20/0.44 thf(fact_114_prod_Oinject,axiom,
% 0.20/0.44 ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y22: produc2041926651_state] :
% 0.20/0.44 ( ( ( produc1909270103_state @ X1 @ X2 )
% 0.20/0.44 = ( produc1909270103_state @ Y1 @ Y22 ) )
% 0.20/0.44 = ( ( X1 = Y1 )
% 0.20/0.44 & ( X2 = Y22 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % prod.inject
% 0.20/0.44 thf(fact_115_prod_Oinject,axiom,
% 0.20/0.44 ! [X1: produc410756839_state,X2: produc410756839_state,Y1: produc410756839_state,Y22: produc410756839_state] :
% 0.20/0.44 ( ( ( produc2065881943_state @ X1 @ X2 )
% 0.20/0.44 = ( produc2065881943_state @ Y1 @ Y22 ) )
% 0.20/0.44 = ( ( X1 = Y1 )
% 0.20/0.44 & ( X2 = Y22 ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % prod.inject
% 0.20/0.44 thf(fact_116_execs_Ointros_I2_J,axiom,
% 0.20/0.44 ! [S: state,C: com,T: state,Cs3: list_com,U: state] :
% 0.20/0.44 ( ( exec @ S @ C @ T )
% 0.20/0.44 => ( ( pHoare259243732_execs @ T @ Cs3 @ U )
% 0.20/0.44 => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs3 ) @ U ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % execs.intros(2)
% 0.20/0.44 thf(fact_117_execs_Ocases,axiom,
% 0.20/0.44 ! [A1: state,A22: list_com,A32: state] :
% 0.20/0.44 ( ( pHoare259243732_execs @ A1 @ A22 @ A32 )
% 0.20/0.44 => ( ( ( A22 = nil_com )
% 0.20/0.44 => ( A32 != A1 ) )
% 0.20/0.44 => ~ ! [C3: com,T2: state,Cs4: list_com] :
% 0.20/0.44 ( ( A22
% 0.20/0.44 = ( cons_com @ C3 @ Cs4 ) )
% 0.20/0.44 => ( ( exec @ A1 @ C3 @ T2 )
% 0.20/0.44 => ~ ( pHoare259243732_execs @ T2 @ Cs4 @ A32 ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % execs.cases
% 0.20/0.44 thf(fact_118_execs_Osimps,axiom,
% 0.20/0.44 ( pHoare259243732_execs
% 0.20/0.44 = ( ^ [A12: state,A23: list_com,A33: state] :
% 0.20/0.44 ( ? [S3: state] :
% 0.20/0.44 ( ( A12 = S3 )
% 0.20/0.44 & ( A23 = nil_com )
% 0.20/0.44 & ( A33 = S3 ) )
% 0.20/0.44 | ? [S3: state,C4: com,T3: state,Cs2: list_com,U2: state] :
% 0.20/0.44 ( ( A12 = S3 )
% 0.20/0.44 & ( A23
% 0.20/0.44 = ( cons_com @ C4 @ Cs2 ) )
% 0.20/0.44 & ( A33 = U2 )
% 0.20/0.44 & ( exec @ S3 @ C4 @ T3 )
% 0.20/0.44 & ( pHoare259243732_execs @ T3 @ Cs2 @ U2 ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 % execs.simps
% 0.20/0.44 thf(fact_119_execs_Oinducts,axiom,
% 0.20/0.44 ! [X1: state,X2: list_com,X32: state,P: state > list_com > state > $o] :
% 0.20/0.44 ( ( pHoare259243732_execs @ X1 @ X2 @ X32 )
% 0.20/0.44 => ( ! [S4: state] : ( P @ S4 @ nil_com @ S4 )
% 0.20/0.44 => ( ! [S4: state,C3: com,T2: state,Cs4: list_com,U3: state] :
% 0.20/0.44 ( ( exec @ S4 @ C3 @ T2 )
% 0.20/0.44 => ( ( pHoare259243732_execs @ T2 @ Cs4 @ U3 )
% 0.20/0.44 => ( ( P @ T2 @ Cs4 @ U3 )
% 0.20/0.44 => ( P @ S4 @ ( cons_com @ C3 @ Cs4 ) @ U3 ) ) ) )
% 0.20/0.44 => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % execs.inducts
% 0.20/0.45 thf(fact_120_termis_Osimps_I2_J,axiom,
% 0.20/0.45 ! [C: com,Cs3: list_com,S: state] :
% 0.20/0.45 ( ( pHoare806997636termis @ ( cons_com @ C @ Cs3 ) @ S )
% 0.20/0.45 = ( ( termi @ C @ S )
% 0.20/0.45 & ! [T3: state] :
% 0.20/0.45 ( ( exec @ S @ C @ T3 )
% 0.20/0.45 => ( pHoare806997636termis @ Cs3 @ T3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termis.simps(2)
% 0.20/0.45 thf(fact_121_execs_Ointros_I1_J,axiom,
% 0.20/0.45 ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 0.20/0.45
% 0.20/0.45 % execs.intros(1)
% 0.20/0.45 thf(fact_122_termis_Osimps_I1_J,axiom,
% 0.20/0.45 ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 0.20/0.45
% 0.20/0.45 % termis.simps(1)
% 0.20/0.45 thf(fact_123_zero__reorient,axiom,
% 0.20/0.45 ! [X: nat] :
% 0.20/0.45 ( ( zero_zero_nat = X )
% 0.20/0.45 = ( X = zero_zero_nat ) ) ).
% 0.20/0.45
% 0.20/0.45 % zero_reorient
% 0.20/0.45 thf(fact_124_surj__pair,axiom,
% 0.20/0.45 ! [P2: produc2041926651_state] :
% 0.20/0.45 ? [X3: list_com,Y2: state] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc1204172211_state @ X3 @ Y2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % surj_pair
% 0.20/0.45 thf(fact_125_surj__pair,axiom,
% 0.20/0.45 ! [P2: produc410756839_state] :
% 0.20/0.45 ? [X3: produc2041926651_state,Y2: produc2041926651_state] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc1909270103_state @ X3 @ Y2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % surj_pair
% 0.20/0.45 thf(fact_126_surj__pair,axiom,
% 0.20/0.45 ! [P2: produc186437863_state] :
% 0.20/0.45 ? [X3: produc410756839_state,Y2: produc410756839_state] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc2065881943_state @ X3 @ Y2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % surj_pair
% 0.20/0.45 thf(fact_127_prod__cases,axiom,
% 0.20/0.45 ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 0.20/0.45 ( ! [A2: list_com,B2: state] : ( P @ ( produc1204172211_state @ A2 @ B2 ) )
% 0.20/0.45 => ( P @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases
% 0.20/0.45 thf(fact_128_prod__cases,axiom,
% 0.20/0.45 ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 0.20/0.45 ( ! [A2: produc2041926651_state,B2: produc2041926651_state] : ( P @ ( produc1909270103_state @ A2 @ B2 ) )
% 0.20/0.45 => ( P @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases
% 0.20/0.45 thf(fact_129_prod__cases,axiom,
% 0.20/0.45 ! [P: produc186437863_state > $o,P2: produc186437863_state] :
% 0.20/0.45 ( ! [A2: produc410756839_state,B2: produc410756839_state] : ( P @ ( produc2065881943_state @ A2 @ B2 ) )
% 0.20/0.45 => ( P @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases
% 0.20/0.45 thf(fact_130_Pair__inject,axiom,
% 0.20/0.45 ! [A: list_com,B: state,A5: list_com,B4: state] :
% 0.20/0.45 ( ( ( produc1204172211_state @ A @ B )
% 0.20/0.45 = ( produc1204172211_state @ A5 @ B4 ) )
% 0.20/0.45 => ~ ( ( A = A5 )
% 0.20/0.45 => ( B != B4 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Pair_inject
% 0.20/0.45 thf(fact_131_Pair__inject,axiom,
% 0.20/0.45 ! [A: produc2041926651_state,B: produc2041926651_state,A5: produc2041926651_state,B4: produc2041926651_state] :
% 0.20/0.45 ( ( ( produc1909270103_state @ A @ B )
% 0.20/0.45 = ( produc1909270103_state @ A5 @ B4 ) )
% 0.20/0.45 => ~ ( ( A = A5 )
% 0.20/0.45 => ( B != B4 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Pair_inject
% 0.20/0.45 thf(fact_132_Pair__inject,axiom,
% 0.20/0.45 ! [A: produc410756839_state,B: produc410756839_state,A5: produc410756839_state,B4: produc410756839_state] :
% 0.20/0.45 ( ( ( produc2065881943_state @ A @ B )
% 0.20/0.45 = ( produc2065881943_state @ A5 @ B4 ) )
% 0.20/0.45 => ~ ( ( A = A5 )
% 0.20/0.45 => ( B != B4 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Pair_inject
% 0.20/0.45 thf(fact_133_old_Oprod_Oexhaust,axiom,
% 0.20/0.45 ! [Y: produc2041926651_state] :
% 0.20/0.45 ~ ! [A2: list_com,B2: state] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc1204172211_state @ A2 @ B2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.exhaust
% 0.20/0.45 thf(fact_134_old_Oprod_Oexhaust,axiom,
% 0.20/0.45 ! [Y: produc410756839_state] :
% 0.20/0.45 ~ ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc1909270103_state @ A2 @ B2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.exhaust
% 0.20/0.45 thf(fact_135_old_Oprod_Oexhaust,axiom,
% 0.20/0.45 ! [Y: produc186437863_state] :
% 0.20/0.45 ~ ! [A2: produc410756839_state,B2: produc410756839_state] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc2065881943_state @ A2 @ B2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.exhaust
% 0.20/0.45 thf(fact_136_old_Oprod_Oinducts,axiom,
% 0.20/0.45 ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 0.20/0.45 ( ! [A2: list_com,B2: state] : ( P @ ( produc1204172211_state @ A2 @ B2 ) )
% 0.20/0.45 => ( P @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inducts
% 0.20/0.45 thf(fact_137_old_Oprod_Oinducts,axiom,
% 0.20/0.45 ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 0.20/0.45 ( ! [A2: produc2041926651_state,B2: produc2041926651_state] : ( P @ ( produc1909270103_state @ A2 @ B2 ) )
% 0.20/0.45 => ( P @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inducts
% 0.20/0.45 thf(fact_138_old_Oprod_Oinducts,axiom,
% 0.20/0.45 ! [P: produc186437863_state > $o,Prod: produc186437863_state] :
% 0.20/0.45 ( ! [A2: produc410756839_state,B2: produc410756839_state] : ( P @ ( produc2065881943_state @ A2 @ B2 ) )
% 0.20/0.45 => ( P @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inducts
% 0.20/0.45 thf(fact_139_not__Cons__self2,axiom,
% 0.20/0.45 ! [X: com,Xs: list_com] :
% 0.20/0.45 ( ( cons_com @ X @ Xs )
% 0.20/0.45 != Xs ) ).
% 0.20/0.45
% 0.20/0.45 % not_Cons_self2
% 0.20/0.45 thf(fact_140_Suc__inject,axiom,
% 0.20/0.45 ! [X: nat,Y: nat] :
% 0.20/0.45 ( ( ( suc @ X )
% 0.20/0.45 = ( suc @ Y ) )
% 0.20/0.45 => ( X = Y ) ) ).
% 0.20/0.45
% 0.20/0.45 % Suc_inject
% 0.20/0.45 thf(fact_141_n__not__Suc__n,axiom,
% 0.20/0.45 ! [N: nat] :
% 0.20/0.45 ( N
% 0.20/0.45 != ( suc @ N ) ) ).
% 0.20/0.45
% 0.20/0.45 % n_not_Suc_n
% 0.20/0.45 thf(fact_142_inf__cases,axiom,
% 0.20/0.45 ! [C: com,Cs3: list_com,S: state] :
% 0.20/0.45 ( ( pHoare2126160787le_inf @ ( cons_com @ C @ Cs3 ) @ S )
% 0.20/0.45 => ( ( pHoare2126160787le_inf @ ( cons_com @ C @ nil_com ) @ S )
% 0.20/0.45 | ? [T2: state] :
% 0.20/0.45 ( ( exec @ S @ C @ T2 )
% 0.20/0.45 & ( pHoare2126160787le_inf @ Cs3 @ T2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % inf_cases
% 0.20/0.45 thf(fact_143_nat_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [X2: nat] :
% 0.20/0.45 ( zero_zero_nat
% 0.20/0.45 != ( suc @ X2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % nat.distinct(1)
% 0.20/0.45 thf(fact_144_old_Onat_Odistinct_I2_J,axiom,
% 0.20/0.45 ! [Nat2: nat] :
% 0.20/0.45 ( ( suc @ Nat2 )
% 0.20/0.45 != zero_zero_nat ) ).
% 0.20/0.45
% 0.20/0.45 % old.nat.distinct(2)
% 0.20/0.45 thf(fact_145_old_Onat_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [Nat2: nat] :
% 0.20/0.45 ( zero_zero_nat
% 0.20/0.45 != ( suc @ Nat2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.nat.distinct(1)
% 0.20/0.45 thf(fact_146_nat_OdiscI,axiom,
% 0.20/0.45 ! [Nat: nat,X2: nat] :
% 0.20/0.45 ( ( Nat
% 0.20/0.45 = ( suc @ X2 ) )
% 0.20/0.45 => ( Nat != zero_zero_nat ) ) ).
% 0.20/0.45
% 0.20/0.45 % nat.discI
% 0.20/0.45 thf(fact_147_nat__induct,axiom,
% 0.20/0.45 ! [P: nat > $o,N: nat] :
% 0.20/0.45 ( ( P @ zero_zero_nat )
% 0.20/0.45 => ( ! [N2: nat] :
% 0.20/0.45 ( ( P @ N2 )
% 0.20/0.45 => ( P @ ( suc @ N2 ) ) )
% 0.20/0.45 => ( P @ N ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % nat_induct
% 0.20/0.45 thf(fact_148_diff__induct,axiom,
% 0.20/0.45 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.20/0.45 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.20/0.45 => ( ! [Y2: nat] : ( P @ zero_zero_nat @ ( suc @ Y2 ) )
% 0.20/0.45 => ( ! [X3: nat,Y2: nat] :
% 0.20/0.45 ( ( P @ X3 @ Y2 )
% 0.20/0.45 => ( P @ ( suc @ X3 ) @ ( suc @ Y2 ) ) )
% 0.20/0.45 => ( P @ M @ N ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % diff_induct
% 0.20/0.45 thf(fact_149_zero__induct,axiom,
% 0.20/0.45 ! [P: nat > $o,K: nat] :
% 0.20/0.45 ( ( P @ K )
% 0.20/0.45 => ( ! [N2: nat] :
% 0.20/0.45 ( ( P @ ( suc @ N2 ) )
% 0.20/0.45 => ( P @ N2 ) )
% 0.20/0.45 => ( P @ zero_zero_nat ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % zero_induct
% 0.20/0.45 thf(fact_150_Suc__neq__Zero,axiom,
% 0.20/0.45 ! [M: nat] :
% 0.20/0.45 ( ( suc @ M )
% 0.20/0.45 != zero_zero_nat ) ).
% 0.20/0.45
% 0.20/0.45 % Suc_neq_Zero
% 0.20/0.45 thf(fact_151_Zero__neq__Suc,axiom,
% 0.20/0.45 ! [M: nat] :
% 0.20/0.45 ( zero_zero_nat
% 0.20/0.45 != ( suc @ M ) ) ).
% 0.20/0.45
% 0.20/0.45 % Zero_neq_Suc
% 0.20/0.45 thf(fact_152_Zero__not__Suc,axiom,
% 0.20/0.45 ! [M: nat] :
% 0.20/0.45 ( zero_zero_nat
% 0.20/0.45 != ( suc @ M ) ) ).
% 0.20/0.45
% 0.20/0.45 % Zero_not_Suc
% 0.20/0.45 thf(fact_153_old_Onat_Oexhaust,axiom,
% 0.20/0.45 ! [Y: nat] :
% 0.20/0.45 ( ( Y != zero_zero_nat )
% 0.20/0.45 => ~ ! [Nat3: nat] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( suc @ Nat3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.nat.exhaust
% 0.20/0.45 thf(fact_154_old_Onat_Oinducts,axiom,
% 0.20/0.45 ! [P: nat > $o,Nat: nat] :
% 0.20/0.45 ( ( P @ zero_zero_nat )
% 0.20/0.45 => ( ! [Nat3: nat] :
% 0.20/0.45 ( ( P @ Nat3 )
% 0.20/0.45 => ( P @ ( suc @ Nat3 ) ) )
% 0.20/0.45 => ( P @ Nat ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.nat.inducts
% 0.20/0.45 thf(fact_155_not0__implies__Suc,axiom,
% 0.20/0.45 ! [N: nat] :
% 0.20/0.45 ( ( N != zero_zero_nat )
% 0.20/0.45 => ? [M2: nat] :
% 0.20/0.45 ( N
% 0.20/0.45 = ( suc @ M2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % not0_implies_Suc
% 0.20/0.45 thf(fact_156_list_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [X21: com,X22: list_com] :
% 0.20/0.45 ( nil_com
% 0.20/0.45 != ( cons_com @ X21 @ X22 ) ) ).
% 0.20/0.45
% 0.20/0.45 % list.distinct(1)
% 0.20/0.45 thf(fact_157_list_OdiscI,axiom,
% 0.20/0.45 ! [List: list_com,X21: com,X22: list_com] :
% 0.20/0.45 ( ( List
% 0.20/0.45 = ( cons_com @ X21 @ X22 ) )
% 0.20/0.45 => ( List != nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % list.discI
% 0.20/0.45 thf(fact_158_list_Oexhaust,axiom,
% 0.20/0.45 ! [Y: list_com] :
% 0.20/0.45 ( ( Y != nil_com )
% 0.20/0.45 => ~ ! [X212: com,X222: list_com] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( cons_com @ X212 @ X222 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % list.exhaust
% 0.20/0.45 thf(fact_159_list_Oinducts,axiom,
% 0.20/0.45 ! [P: list_com > $o,List: list_com] :
% 0.20/0.45 ( ( P @ nil_com )
% 0.20/0.45 => ( ! [X12: com,X23: list_com] :
% 0.20/0.45 ( ( P @ X23 )
% 0.20/0.45 => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 0.20/0.45 => ( P @ List ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % list.inducts
% 0.20/0.45 thf(fact_160_neq__Nil__conv,axiom,
% 0.20/0.45 ! [Xs: list_com] :
% 0.20/0.45 ( ( Xs != nil_com )
% 0.20/0.45 = ( ? [Y3: com,Ys: list_com] :
% 0.20/0.45 ( Xs
% 0.20/0.45 = ( cons_com @ Y3 @ Ys ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % neq_Nil_conv
% 0.20/0.45 thf(fact_161_list__induct2_H,axiom,
% 0.20/0.45 ! [P: list_com > list_com > $o,Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( P @ nil_com @ nil_com )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com] : ( P @ ( cons_com @ X3 @ Xs2 ) @ nil_com )
% 0.20/0.45 => ( ! [Y2: com,Ys3: list_com] : ( P @ nil_com @ ( cons_com @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com,Y2: com,Ys3: list_com] :
% 0.20/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) )
% 0.20/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % list_induct2'
% 0.20/0.45 thf(fact_162_splice_Oinduct,axiom,
% 0.20/0.45 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.20/0.45 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 0.20/0.45 ( ( P @ Ys3 @ Xs2 )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) )
% 0.20/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % splice.induct
% 0.20/0.45 thf(fact_163_induct__list012,axiom,
% 0.20/0.45 ! [P: list_com > $o,Xs: list_com] :
% 0.20/0.45 ( ( P @ nil_com )
% 0.20/0.45 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.20/0.45 => ( ! [X3: com,Y2: com,Zs: list_com] :
% 0.20/0.45 ( ( P @ Zs )
% 0.20/0.45 => ( ( P @ ( cons_com @ Y2 @ Zs ) )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Zs ) ) ) ) )
% 0.20/0.45 => ( P @ Xs ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % induct_list012
% 0.20/0.45 thf(fact_164_shuffles_Oinduct,axiom,
% 0.20/0.45 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.20/0.45 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.20/0.45 => ( ! [Xs2: list_com] : ( P @ Xs2 @ nil_com )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com,Y2: com,Ys3: list_com] :
% 0.20/0.45 ( ( P @ Xs2 @ ( cons_com @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) ) )
% 0.20/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % shuffles.induct
% 0.20/0.45 thf(fact_165_transpose_Ocases,axiom,
% 0.20/0.45 ! [X: list_list_com] :
% 0.20/0.45 ( ( X != nil_list_com )
% 0.20/0.45 => ( ! [Xss: list_list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( cons_list_com @ nil_com @ Xss ) )
% 0.20/0.45 => ~ ! [X3: com,Xs2: list_com,Xss: list_list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( cons_list_com @ ( cons_com @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % transpose.cases
% 0.20/0.45 thf(fact_166_remdups__adj_Ocases,axiom,
% 0.20/0.45 ! [X: list_com] :
% 0.20/0.45 ( ( X != nil_com )
% 0.20/0.45 => ( ! [X3: com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( cons_com @ X3 @ nil_com ) )
% 0.20/0.45 => ~ ! [X3: com,Y2: com,Xs2: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % remdups_adj.cases
% 0.20/0.45 thf(fact_167_sorted__wrt_Oinduct,axiom,
% 0.20/0.45 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.20/0.45 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.20/0.45 => ( ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 0.20/0.45 ( ( P @ P3 @ Ys3 )
% 0.20/0.45 => ( P @ P3 @ ( cons_com @ X3 @ Ys3 ) ) )
% 0.20/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % sorted_wrt.induct
% 0.20/0.45 thf(fact_168_remdups__adj_Oinduct,axiom,
% 0.20/0.45 ! [P: list_com > $o,A0: list_com] :
% 0.20/0.45 ( ( P @ nil_com )
% 0.20/0.45 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.20/0.45 => ( ! [X3: com,Y2: com,Xs2: list_com] :
% 0.20/0.45 ( ( ( X3 = Y2 )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ Xs2 ) ) )
% 0.20/0.45 => ( ( ( X3 != Y2 )
% 0.20/0.45 => ( P @ ( cons_com @ Y2 @ Xs2 ) ) )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) ) )
% 0.20/0.45 => ( P @ A0 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % remdups_adj.induct
% 0.20/0.45 thf(fact_169_successively_Oinduct,axiom,
% 0.20/0.45 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.20/0.45 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.20/0.45 => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 0.20/0.45 => ( ! [P3: com > com > $o,X3: com,Y2: com,Xs2: list_com] :
% 0.20/0.45 ( ( P @ P3 @ ( cons_com @ Y2 @ Xs2 ) )
% 0.20/0.45 => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) )
% 0.20/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % successively.induct
% 0.20/0.45 thf(fact_170_list__nonempty__induct,axiom,
% 0.20/0.45 ! [Xs: list_com,P: list_com > $o] :
% 0.20/0.45 ( ( Xs != nil_com )
% 0.20/0.45 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com] :
% 0.20/0.45 ( ( Xs2 != nil_com )
% 0.20/0.45 => ( ( P @ Xs2 )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ Xs2 ) ) ) )
% 0.20/0.45 => ( P @ Xs ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % list_nonempty_induct
% 0.20/0.45 thf(fact_171_map__tailrec__rev_Oinduct,axiom,
% 0.20/0.45 ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 0.20/0.45 ( ! [F2: com > com,X_1: list_com] : ( P @ F2 @ nil_com @ X_1 )
% 0.20/0.45 => ( ! [F2: com > com,A2: com,As: list_com,Bs: list_com] :
% 0.20/0.45 ( ( P @ F2 @ As @ ( cons_com @ ( F2 @ A2 ) @ Bs ) )
% 0.20/0.45 => ( P @ F2 @ ( cons_com @ A2 @ As ) @ Bs ) )
% 0.20/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % map_tailrec_rev.induct
% 0.20/0.45 thf(fact_172_splice_Ocases,axiom,
% 0.20/0.45 ! [X: produc258871771st_com] :
% 0.20/0.45 ( ! [Ys3: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 0.20/0.45 => ~ ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % splice.cases
% 0.20/0.45 thf(fact_173_shuffles_Ocases,axiom,
% 0.20/0.45 ! [X: produc258871771st_com] :
% 0.20/0.45 ( ! [Ys3: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 0.20/0.45 => ( ! [Xs2: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1307105171st_com @ Xs2 @ nil_com ) )
% 0.20/0.45 => ~ ! [X3: com,Xs2: list_com,Y2: com,Ys3: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % shuffles.cases
% 0.20/0.45 thf(fact_174_sorted__wrt_Ocases,axiom,
% 0.20/0.45 ! [X: produc2058209240st_com] :
% 0.20/0.45 ( ! [P3: com > com > $o] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.20/0.45 => ~ ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % sorted_wrt.cases
% 0.20/0.45 thf(fact_175_successively_Ocases,axiom,
% 0.20/0.45 ! [X: produc2058209240st_com] :
% 0.20/0.45 ( ! [P3: com > com > $o] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.20/0.45 => ( ! [P3: com > com > $o,X3: com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 0.20/0.45 => ~ ! [P3: com > com > $o,X3: com,Y2: com,Xs2: list_com] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % successively.cases
% 0.20/0.45 thf(fact_176_exec__impl__execs,axiom,
% 0.20/0.45 ! [S: state,C: com,S2: state,Cs3: list_com] :
% 0.20/0.45 ( ( exec @ S @ C @ S2 )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs3 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec_impl_execs
% 0.20/0.45 thf(fact_177_prod__cases3,axiom,
% 0.20/0.45 ! [Y: produc410756839_state] :
% 0.20/0.45 ~ ! [A2: produc2041926651_state,B2: list_com,C3: state] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc1909270103_state @ A2 @ ( produc1204172211_state @ B2 @ C3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases3
% 0.20/0.45 thf(fact_178_prod__cases3,axiom,
% 0.20/0.45 ! [Y: produc186437863_state] :
% 0.20/0.45 ~ ! [A2: produc410756839_state,B2: produc2041926651_state,C3: produc2041926651_state] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ C3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases3
% 0.20/0.45 thf(fact_179_prod__cases4,axiom,
% 0.20/0.45 ! [Y: produc186437863_state] :
% 0.20/0.45 ~ ! [A2: produc410756839_state,B2: produc2041926651_state,C3: list_com,D: state] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ ( produc1204172211_state @ C3 @ D ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases4
% 0.20/0.45 thf(fact_180_prod__induct3,axiom,
% 0.20/0.45 ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 0.20/0.45 ( ! [A2: produc2041926651_state,B2: list_com,C3: state] : ( P @ ( produc1909270103_state @ A2 @ ( produc1204172211_state @ B2 @ C3 ) ) )
% 0.20/0.45 => ( P @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_induct3
% 0.20/0.45 thf(fact_181_prod__induct3,axiom,
% 0.20/0.45 ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 0.20/0.45 ( ! [A2: produc410756839_state,B2: produc2041926651_state,C3: produc2041926651_state] : ( P @ ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ C3 ) ) )
% 0.20/0.45 => ( P @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_induct3
% 0.20/0.45 thf(fact_182_prod__induct4,axiom,
% 0.20/0.45 ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 0.20/0.45 ( ! [A2: produc410756839_state,B2: produc2041926651_state,C3: list_com,D: state] : ( P @ ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ ( produc1204172211_state @ C3 @ D ) ) ) )
% 0.20/0.45 => ( P @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_induct4
% 0.20/0.45 thf(fact_183_exec1__pres__termis,axiom,
% 0.20/0.45 ! [Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ( ( pHoare806997636termis @ Cs3 @ S )
% 0.20/0.45 => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1_pres_termis
% 0.20/0.45 thf(fact_184_exec1E_I3_J,axiom,
% 0.20/0.45 ! [C1: com,C22: com,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ~ ( ( Cs
% 0.20/0.45 = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs3 ) ) )
% 0.20/0.45 => ( S2 != S ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1E(3)
% 0.20/0.45 thf(fact_185_exec1_OSemi,axiom,
% 0.20/0.45 ! [C1: com,C22: com,Cs3: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs3 ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 0.20/0.45
% 0.20/0.45 % exec1.Semi
% 0.20/0.45 thf(fact_186_n__lists__Nil,axiom,
% 0.20/0.45 ! [N: nat] :
% 0.20/0.45 ( ( ( N = zero_zero_nat )
% 0.20/0.45 => ( ( n_lists_com @ N @ nil_com )
% 0.20/0.45 = ( cons_list_com @ nil_com @ nil_list_com ) ) )
% 0.20/0.45 & ( ( N != zero_zero_nat )
% 0.20/0.45 => ( ( n_lists_com @ N @ nil_com )
% 0.20/0.45 = nil_list_com ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % n_lists_Nil
% 0.20/0.45 thf(fact_187_exec1E_I2_J,axiom,
% 0.20/0.45 ! [F: state > set_state,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ~ ( ( Cs = Cs3 )
% 0.20/0.45 => ~ ( member_state @ S2 @ ( F @ S ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1E(2)
% 0.20/0.45 thf(fact_188_exec1_ODo,axiom,
% 0.20/0.45 ! [T: state,F: state > set_state,S: state,Cs3: list_com] :
% 0.20/0.45 ( ( member_state @ T @ ( F @ S ) )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs3 @ T ) ) @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1.Do
% 0.20/0.45 thf(fact_189_n__lists_Osimps_I1_J,axiom,
% 0.20/0.45 ! [Xs: list_com] :
% 0.20/0.45 ( ( n_lists_com @ zero_zero_nat @ Xs )
% 0.20/0.45 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % n_lists.simps(1)
% 0.20/0.45 thf(fact_190_termi_OSemi,axiom,
% 0.20/0.45 ! [C1: com,S0: state,C22: com] :
% 0.20/0.45 ( ( termi @ C1 @ S0 )
% 0.20/0.45 => ( ! [S1: state] :
% 0.20/0.45 ( ( exec @ S0 @ C1 @ S1 )
% 0.20/0.45 => ( termi @ C22 @ S1 ) )
% 0.20/0.45 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi.Semi
% 0.20/0.45 thf(fact_191_com_Oinject_I2_J,axiom,
% 0.20/0.45 ! [X21: com,X22: com,Y21: com,Y222: com] :
% 0.20/0.45 ( ( ( semi @ X21 @ X22 )
% 0.20/0.45 = ( semi @ Y21 @ Y222 ) )
% 0.20/0.45 = ( ( X21 = Y21 )
% 0.20/0.45 & ( X22 = Y222 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.inject(2)
% 0.20/0.45 thf(fact_192_com_Oinject_I1_J,axiom,
% 0.20/0.45 ! [X1: state > set_state,Y1: state > set_state] :
% 0.20/0.45 ( ( ( do @ X1 )
% 0.20/0.45 = ( do @ Y1 ) )
% 0.20/0.45 = ( X1 = Y1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.inject(1)
% 0.20/0.45 thf(fact_193_com_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [X1: state > set_state,X21: com,X22: com] :
% 0.20/0.45 ( ( do @ X1 )
% 0.20/0.45 != ( semi @ X21 @ X22 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.distinct(1)
% 0.20/0.45 thf(fact_194_exec_ODo,axiom,
% 0.20/0.45 ! [T: state,F: state > set_state,S: state] :
% 0.20/0.45 ( ( member_state @ T @ ( F @ S ) )
% 0.20/0.45 => ( exec @ S @ ( do @ F ) @ T ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec.Do
% 0.20/0.45 thf(fact_195_exec_OSemi,axiom,
% 0.20/0.45 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 0.20/0.45 ( ( exec @ S0 @ C1 @ S12 )
% 0.20/0.45 => ( ( exec @ S12 @ C22 @ S22 )
% 0.20/0.45 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec.Semi
% 0.20/0.45 thf(fact_196_product__lists_Osimps_I1_J,axiom,
% 0.20/0.45 ( ( product_lists_com @ nil_list_com )
% 0.20/0.45 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % product_lists.simps(1)
% 0.20/0.45 thf(fact_197_subseqs_Osimps_I1_J,axiom,
% 0.20/0.45 ( ( subseqs_com @ nil_com )
% 0.20/0.45 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % subseqs.simps(1)
% 0.20/0.45 thf(fact_198_exec1E_I4_J,axiom,
% 0.20/0.45 ! [B: state > $o,C1: com,C22: com,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ( ( ( Cs
% 0.20/0.45 = ( cons_com @ C1 @ Cs3 ) )
% 0.20/0.45 => ( ( S2 = S )
% 0.20/0.45 => ~ ( B @ S ) ) )
% 0.20/0.45 => ~ ( ( Cs
% 0.20/0.45 = ( cons_com @ C22 @ Cs3 ) )
% 0.20/0.45 => ( ( S2 = S )
% 0.20/0.45 => ( B @ S ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1E(4)
% 0.20/0.45 thf(fact_199_com_Oinject_I3_J,axiom,
% 0.20/0.45 ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 0.20/0.45 ( ( ( cond @ X31 @ X322 @ X33 )
% 0.20/0.45 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 0.20/0.45 = ( ( X31 = Y31 )
% 0.20/0.45 & ( X322 = Y32 )
% 0.20/0.45 & ( X33 = Y33 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.inject(3)
% 0.20/0.45 thf(fact_200_exec_OIfTrue,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C1: com,T: state,C22: com] :
% 0.20/0.45 ( ( B @ S )
% 0.20/0.45 => ( ( exec @ S @ C1 @ T )
% 0.20/0.45 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec.IfTrue
% 0.20/0.45 thf(fact_201_exec_OIfFalse,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C22: com,T: state,C1: com] :
% 0.20/0.45 ( ~ ( B @ S )
% 0.20/0.45 => ( ( exec @ S @ C22 @ T )
% 0.20/0.45 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec.IfFalse
% 0.20/0.45 thf(fact_202_termi_OIfTrue,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C1: com,C22: com] :
% 0.20/0.45 ( ( B @ S )
% 0.20/0.45 => ( ( termi @ C1 @ S )
% 0.20/0.45 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi.IfTrue
% 0.20/0.45 thf(fact_203_termi_OIfFalse,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C22: com,C1: com] :
% 0.20/0.45 ( ~ ( B @ S )
% 0.20/0.45 => ( ( termi @ C22 @ S )
% 0.20/0.45 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi.IfFalse
% 0.20/0.45 thf(fact_204_com_Odistinct_I3_J,axiom,
% 0.20/0.45 ! [X1: state > set_state,X31: state > $o,X322: com,X33: com] :
% 0.20/0.45 ( ( do @ X1 )
% 0.20/0.45 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.distinct(3)
% 0.20/0.45 thf(fact_205_com_Odistinct_I11_J,axiom,
% 0.20/0.45 ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 0.20/0.45 ( ( semi @ X21 @ X22 )
% 0.20/0.45 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.distinct(11)
% 0.20/0.45 thf(fact_206_exec1_OIfFalse,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C1: com,C22: com,Cs3: list_com] :
% 0.20/0.45 ( ~ ( B @ S )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs3 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1.IfFalse
% 0.20/0.45 thf(fact_207_exec1_OIfTrue,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C1: com,C22: com,Cs3: list_com] :
% 0.20/0.45 ( ( B @ S )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs3 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1.IfTrue
% 0.20/0.45 thf(fact_208_gen__length__code_I2_J,axiom,
% 0.20/0.45 ! [N: nat,X: com,Xs: list_com] :
% 0.20/0.45 ( ( gen_length_com @ N @ ( cons_com @ X @ Xs ) )
% 0.20/0.45 = ( gen_length_com @ ( suc @ N ) @ Xs ) ) ).
% 0.20/0.45
% 0.20/0.45 % gen_length_code(2)
% 0.20/0.45 thf(fact_209_insert__Nil,axiom,
% 0.20/0.45 ! [X: com] :
% 0.20/0.45 ( ( insert_com @ X @ nil_com )
% 0.20/0.45 = ( cons_com @ X @ nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % insert_Nil
% 0.20/0.45 thf(fact_210_exec1_OWhileFalse,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C: com,Cs3: list_com] :
% 0.20/0.45 ( ~ ( B @ S )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs3 @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1.WhileFalse
% 0.20/0.45 thf(fact_211_com_Oinject_I4_J,axiom,
% 0.20/0.45 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.20/0.45 ( ( ( while @ X41 @ X42 )
% 0.20/0.45 = ( while @ Y41 @ Y42 ) )
% 0.20/0.45 = ( ( X41 = Y41 )
% 0.20/0.45 & ( X42 = Y42 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.inject(4)
% 0.20/0.45 thf(fact_212_com_Odistinct_I19_J,axiom,
% 0.20/0.45 ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 0.20/0.45 ( ( cond @ X31 @ X322 @ X33 )
% 0.20/0.45 != ( while @ X41 @ X42 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.distinct(19)
% 0.20/0.45 thf(fact_213_while__termiE,axiom,
% 0.20/0.45 ! [B: state > $o,C: com,S: state] :
% 0.20/0.45 ( ( termi @ ( while @ B @ C ) @ S )
% 0.20/0.45 => ( ( B @ S )
% 0.20/0.45 => ( termi @ C @ S ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % while_termiE
% 0.20/0.45 thf(fact_214_exec_OWhileFalse,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C: com] :
% 0.20/0.45 ( ~ ( B @ S )
% 0.20/0.45 => ( exec @ S @ ( while @ B @ C ) @ S ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec.WhileFalse
% 0.20/0.45 thf(fact_215_exec_OWhileTrue,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C: com,T: state,U: state] :
% 0.20/0.45 ( ( B @ S )
% 0.20/0.45 => ( ( exec @ S @ C @ T )
% 0.20/0.45 => ( ( exec @ T @ ( while @ B @ C ) @ U )
% 0.20/0.45 => ( exec @ S @ ( while @ B @ C ) @ U ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec.WhileTrue
% 0.20/0.45 thf(fact_216_termi_OWhileFalse,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C: com] :
% 0.20/0.45 ( ~ ( B @ S )
% 0.20/0.45 => ( termi @ ( while @ B @ C ) @ S ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi.WhileFalse
% 0.20/0.45 thf(fact_217_com_Odistinct_I5_J,axiom,
% 0.20/0.45 ! [X1: state > set_state,X41: state > $o,X42: com] :
% 0.20/0.45 ( ( do @ X1 )
% 0.20/0.45 != ( while @ X41 @ X42 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.distinct(5)
% 0.20/0.45 thf(fact_218_com_Odistinct_I13_J,axiom,
% 0.20/0.45 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 0.20/0.45 ( ( semi @ X21 @ X22 )
% 0.20/0.45 != ( while @ X41 @ X42 ) ) ).
% 0.20/0.45
% 0.20/0.45 % com.distinct(13)
% 0.20/0.45 thf(fact_219_termi_OWhileTrue,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C: com] :
% 0.20/0.45 ( ( B @ S )
% 0.20/0.45 => ( ( termi @ C @ S )
% 0.20/0.45 => ( ! [T2: state] :
% 0.20/0.45 ( ( exec @ S @ C @ T2 )
% 0.20/0.45 => ( termi @ ( while @ B @ C ) @ T2 ) )
% 0.20/0.45 => ( termi @ ( while @ B @ C ) @ S ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi.WhileTrue
% 0.20/0.45 thf(fact_220_while__termiE2,axiom,
% 0.20/0.45 ! [B: state > $o,C: com,S: state,T: state] :
% 0.20/0.45 ( ( termi @ ( while @ B @ C ) @ S )
% 0.20/0.45 => ( ( B @ S )
% 0.20/0.45 => ( ( exec @ S @ C @ T )
% 0.20/0.45 => ( termi @ ( while @ B @ C ) @ T ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % while_termiE2
% 0.20/0.45 thf(fact_221_gen__length__code_I1_J,axiom,
% 0.20/0.45 ! [N: nat] :
% 0.20/0.45 ( ( gen_length_com @ N @ nil_com )
% 0.20/0.45 = N ) ).
% 0.20/0.45
% 0.20/0.45 % gen_length_code(1)
% 0.20/0.45 thf(fact_222_termi__while,axiom,
% 0.20/0.45 ! [B: state > $o,C: com,F: nat > state,K: nat] :
% 0.20/0.45 ( ( termi @ ( while @ B @ C ) @ ( F @ K ) )
% 0.20/0.45 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) )
% 0.20/0.45 => ? [I: nat] :
% 0.20/0.45 ~ ( B @ ( F @ I ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi_while
% 0.20/0.45 thf(fact_223_termi__while__lemma,axiom,
% 0.20/0.45 ! [W: com,Fk: state,F: nat > state,K: nat,B: state > $o,C: com] :
% 0.20/0.45 ( ( termi @ W @ Fk )
% 0.20/0.45 => ( ( ( Fk
% 0.20/0.45 = ( F @ K ) )
% 0.20/0.45 & ( W
% 0.20/0.45 = ( while @ B @ C ) )
% 0.20/0.45 & ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) ) )
% 0.20/0.45 => ? [I: nat] :
% 0.20/0.45 ~ ( B @ ( F @ I ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % termi_while_lemma
% 0.20/0.45 thf(fact_224_exec1E_I5_J,axiom,
% 0.20/0.45 ! [B: state > $o,C: com,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ( ( ( Cs = Cs3 )
% 0.20/0.45 => ( ( S2 = S )
% 0.20/0.45 => ( B @ S ) ) )
% 0.20/0.45 => ~ ( ( Cs
% 0.20/0.45 = ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) ) )
% 0.20/0.45 => ( ( S2 = S )
% 0.20/0.45 => ~ ( B @ S ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1E(5)
% 0.20/0.45 thf(fact_225_exec1_OWhileTrue,axiom,
% 0.20/0.45 ! [B: state > $o,S: state,C: com,Cs3: list_com] :
% 0.20/0.45 ( ( B @ S )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1.WhileTrue
% 0.20/0.45 thf(fact_226_nths__singleton,axiom,
% 0.20/0.45 ! [A4: set_nat,X: com] :
% 0.20/0.45 ( ( ( member_nat @ zero_zero_nat @ A4 )
% 0.20/0.45 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 0.20/0.45 = ( cons_com @ X @ nil_com ) ) )
% 0.20/0.45 & ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.20/0.45 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 0.20/0.45 = nil_com ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % nths_singleton
% 0.20/0.45 thf(fact_227_app__execs,axiom,
% 0.20/0.45 ! [Cs3: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs3 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % app_execs
% 0.20/0.45 thf(fact_228_listrel_Ocases,axiom,
% 0.20/0.45 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ( ( ( A1 = nil_com )
% 0.20/0.45 => ( A22 != nil_com ) )
% 0.20/0.45 => ~ ! [X3: com,Y2: com,Xs2: list_com] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_com @ X3 @ Xs2 ) )
% 0.20/0.45 => ! [Ys3: list_com] :
% 0.20/0.45 ( ( A22
% 0.20/0.45 = ( cons_com @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.cases
% 0.20/0.45 thf(fact_229_listrel_Ocases,axiom,
% 0.20/0.45 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.20/0.45 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 => ( ( ( A1 = nil_list_com )
% 0.20/0.45 => ( A22 != nil_state ) )
% 0.20/0.45 => ~ ! [X3: list_com,Y2: state,Xs2: list_list_com] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_list_com @ X3 @ Xs2 ) )
% 0.20/0.45 => ! [Ys3: list_state] :
% 0.20/0.45 ( ( A22
% 0.20/0.45 = ( cons_state @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.cases
% 0.20/0.45 thf(fact_230_listrel_Ocases,axiom,
% 0.20/0.45 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 => ( ( ( A1 = nil_Pr1844458753_state )
% 0.20/0.45 => ( A22 != nil_Pr1844458753_state ) )
% 0.20/0.45 => ~ ! [X3: produc2041926651_state,Y2: produc2041926651_state,Xs2: list_P1040014977_state] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 0.20/0.45 => ! [Ys3: list_P1040014977_state] :
% 0.20/0.45 ( ( A22
% 0.20/0.45 = ( cons_P465369265_state @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.cases
% 0.20/0.45 thf(fact_231_listrel_Ocases,axiom,
% 0.20/0.45 ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 => ( ( ( A1 = nil_Pr1347322605_state )
% 0.20/0.45 => ( A22 != nil_Pr1347322605_state ) )
% 0.20/0.45 => ~ ! [X3: produc410756839_state,Y2: produc410756839_state,Xs2: list_P890094829_state] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_P438230685_state @ X3 @ Xs2 ) )
% 0.20/0.45 => ! [Ys3: list_P890094829_state] :
% 0.20/0.45 ( ( A22
% 0.20/0.45 = ( cons_P438230685_state @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.cases
% 0.20/0.45 thf(fact_232_same__append__eq,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ Ys2 )
% 0.20/0.45 = ( append_com @ Xs @ Zs2 ) )
% 0.20/0.45 = ( Ys2 = Zs2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % same_append_eq
% 0.20/0.45 thf(fact_233_append__same__eq,axiom,
% 0.20/0.45 ! [Ys2: list_com,Xs: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( ( append_com @ Ys2 @ Xs )
% 0.20/0.45 = ( append_com @ Zs2 @ Xs ) )
% 0.20/0.45 = ( Ys2 = Zs2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_same_eq
% 0.20/0.45 thf(fact_234_append__assoc,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( append_com @ ( append_com @ Xs @ Ys2 ) @ Zs2 )
% 0.20/0.45 = ( append_com @ Xs @ ( append_com @ Ys2 @ Zs2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_assoc
% 0.20/0.45 thf(fact_235_append_Oassoc,axiom,
% 0.20/0.45 ! [A: list_com,B: list_com,C: list_com] :
% 0.20/0.45 ( ( append_com @ ( append_com @ A @ B ) @ C )
% 0.20/0.45 = ( append_com @ A @ ( append_com @ B @ C ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append.assoc
% 0.20/0.45 thf(fact_236_append__Nil2,axiom,
% 0.20/0.45 ! [Xs: list_com] :
% 0.20/0.45 ( ( append_com @ Xs @ nil_com )
% 0.20/0.45 = Xs ) ).
% 0.20/0.45
% 0.20/0.45 % append_Nil2
% 0.20/0.45 thf(fact_237_append__self__conv,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ Ys2 )
% 0.20/0.45 = Xs )
% 0.20/0.45 = ( Ys2 = nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_self_conv
% 0.20/0.45 thf(fact_238_self__append__conv,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( append_com @ Xs @ Ys2 ) )
% 0.20/0.45 = ( Ys2 = nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % self_append_conv
% 0.20/0.45 thf(fact_239_append__self__conv2,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ Ys2 )
% 0.20/0.45 = Ys2 )
% 0.20/0.45 = ( Xs = nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_self_conv2
% 0.20/0.45 thf(fact_240_self__append__conv2,axiom,
% 0.20/0.45 ! [Ys2: list_com,Xs: list_com] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( append_com @ Xs @ Ys2 ) )
% 0.20/0.45 = ( Xs = nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % self_append_conv2
% 0.20/0.45 thf(fact_241_Nil__is__append__conv,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( nil_com
% 0.20/0.45 = ( append_com @ Xs @ Ys2 ) )
% 0.20/0.45 = ( ( Xs = nil_com )
% 0.20/0.45 & ( Ys2 = nil_com ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Nil_is_append_conv
% 0.20/0.45 thf(fact_242_append__is__Nil__conv,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ Ys2 )
% 0.20/0.45 = nil_com )
% 0.20/0.45 = ( ( Xs = nil_com )
% 0.20/0.45 & ( Ys2 = nil_com ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_is_Nil_conv
% 0.20/0.45 thf(fact_243_append_Oright__neutral,axiom,
% 0.20/0.45 ! [A: list_com] :
% 0.20/0.45 ( ( append_com @ A @ nil_com )
% 0.20/0.45 = A ) ).
% 0.20/0.45
% 0.20/0.45 % append.right_neutral
% 0.20/0.45 thf(fact_244_nths__nil,axiom,
% 0.20/0.45 ! [A4: set_nat] :
% 0.20/0.45 ( ( nths_com @ nil_com @ A4 )
% 0.20/0.45 = nil_com ) ).
% 0.20/0.45
% 0.20/0.45 % nths_nil
% 0.20/0.45 thf(fact_245_append1__eq__conv,axiom,
% 0.20/0.45 ! [Xs: list_com,X: com,Ys2: list_com,Y: com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ ( cons_com @ X @ nil_com ) )
% 0.20/0.45 = ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) )
% 0.20/0.45 = ( ( Xs = Ys2 )
% 0.20/0.45 & ( X = Y ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append1_eq_conv
% 0.20/0.45 thf(fact_246_listrel__rtrancl__refl,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_rtrancl_refl
% 0.20/0.45 thf(fact_247_listrel__rtrancl__refl,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,R: set_Pr2096893127_state] : ( member423306384_state @ ( produc1354769367_state @ Xs @ Xs ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_rtrancl_refl
% 0.20/0.45 thf(fact_248_append__eq__append__conv2,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,Zs2: list_com,Ts: list_com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ Ys2 )
% 0.20/0.45 = ( append_com @ Zs2 @ Ts ) )
% 0.20/0.45 = ( ? [Us: list_com] :
% 0.20/0.45 ( ( ( Xs
% 0.20/0.45 = ( append_com @ Zs2 @ Us ) )
% 0.20/0.45 & ( ( append_com @ Us @ Ys2 )
% 0.20/0.45 = Ts ) )
% 0.20/0.45 | ( ( ( append_com @ Xs @ Us )
% 0.20/0.45 = Zs2 )
% 0.20/0.45 & ( Ys2
% 0.20/0.45 = ( append_com @ Us @ Ts ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_eq_append_conv2
% 0.20/0.45 thf(fact_249_append__eq__appendI,axiom,
% 0.20/0.45 ! [Xs: list_com,Xs1: list_com,Zs2: list_com,Ys2: list_com,Us2: list_com] :
% 0.20/0.45 ( ( ( append_com @ Xs @ Xs1 )
% 0.20/0.45 = Zs2 )
% 0.20/0.45 => ( ( Ys2
% 0.20/0.45 = ( append_com @ Xs1 @ Us2 ) )
% 0.20/0.45 => ( ( append_com @ Xs @ Ys2 )
% 0.20/0.45 = ( append_com @ Zs2 @ Us2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_eq_appendI
% 0.20/0.45 thf(fact_250_eq__Nil__appendI,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( Xs = Ys2 )
% 0.20/0.45 => ( Xs
% 0.20/0.45 = ( append_com @ nil_com @ Ys2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_Nil_appendI
% 0.20/0.45 thf(fact_251_append__Nil,axiom,
% 0.20/0.45 ! [Ys2: list_com] :
% 0.20/0.45 ( ( append_com @ nil_com @ Ys2 )
% 0.20/0.45 = Ys2 ) ).
% 0.20/0.45
% 0.20/0.45 % append_Nil
% 0.20/0.45 thf(fact_252_append_Oleft__neutral,axiom,
% 0.20/0.45 ! [A: list_com] :
% 0.20/0.45 ( ( append_com @ nil_com @ A )
% 0.20/0.45 = A ) ).
% 0.20/0.45
% 0.20/0.45 % append.left_neutral
% 0.20/0.45 thf(fact_253_Cons__eq__appendI,axiom,
% 0.20/0.45 ! [X: com,Xs1: list_com,Ys2: list_com,Xs: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( ( cons_com @ X @ Xs1 )
% 0.20/0.45 = Ys2 )
% 0.20/0.45 => ( ( Xs
% 0.20/0.45 = ( append_com @ Xs1 @ Zs2 ) )
% 0.20/0.45 => ( ( cons_com @ X @ Xs )
% 0.20/0.45 = ( append_com @ Ys2 @ Zs2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_eq_appendI
% 0.20/0.45 thf(fact_254_append__Cons,axiom,
% 0.20/0.45 ! [X: com,Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( append_com @ ( cons_com @ X @ Xs ) @ Ys2 )
% 0.20/0.45 = ( cons_com @ X @ ( append_com @ Xs @ Ys2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_Cons
% 0.20/0.45 thf(fact_255_rev__nonempty__induct,axiom,
% 0.20/0.45 ! [Xs: list_com,P: list_com > $o] :
% 0.20/0.45 ( ( Xs != nil_com )
% 0.20/0.45 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com] :
% 0.20/0.45 ( ( Xs2 != nil_com )
% 0.20/0.45 => ( ( P @ Xs2 )
% 0.20/0.45 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 0.20/0.45 => ( P @ Xs ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rev_nonempty_induct
% 0.20/0.45 thf(fact_256_append__eq__Cons__conv,axiom,
% 0.20/0.45 ! [Ys2: list_com,Zs2: list_com,X: com,Xs: list_com] :
% 0.20/0.45 ( ( ( append_com @ Ys2 @ Zs2 )
% 0.20/0.45 = ( cons_com @ X @ Xs ) )
% 0.20/0.45 = ( ( ( Ys2 = nil_com )
% 0.20/0.45 & ( Zs2
% 0.20/0.45 = ( cons_com @ X @ Xs ) ) )
% 0.20/0.45 | ? [Ys4: list_com] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_com @ X @ Ys4 ) )
% 0.20/0.45 & ( ( append_com @ Ys4 @ Zs2 )
% 0.20/0.45 = Xs ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_eq_Cons_conv
% 0.20/0.45 thf(fact_257_Cons__eq__append__conv,axiom,
% 0.20/0.45 ! [X: com,Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( ( cons_com @ X @ Xs )
% 0.20/0.45 = ( append_com @ Ys2 @ Zs2 ) )
% 0.20/0.45 = ( ( ( Ys2 = nil_com )
% 0.20/0.45 & ( ( cons_com @ X @ Xs )
% 0.20/0.45 = Zs2 ) )
% 0.20/0.45 | ? [Ys4: list_com] :
% 0.20/0.45 ( ( ( cons_com @ X @ Ys4 )
% 0.20/0.45 = Ys2 )
% 0.20/0.45 & ( Xs
% 0.20/0.45 = ( append_com @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_eq_append_conv
% 0.20/0.45 thf(fact_258_rev__exhaust,axiom,
% 0.20/0.45 ! [Xs: list_com] :
% 0.20/0.45 ( ( Xs != nil_com )
% 0.20/0.45 => ~ ! [Ys3: list_com,Y2: com] :
% 0.20/0.45 ( Xs
% 0.20/0.45 != ( append_com @ Ys3 @ ( cons_com @ Y2 @ nil_com ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rev_exhaust
% 0.20/0.45 thf(fact_259_rev__induct,axiom,
% 0.20/0.45 ! [P: list_com > $o,Xs: list_com] :
% 0.20/0.45 ( ( P @ nil_com )
% 0.20/0.45 => ( ! [X3: com,Xs2: list_com] :
% 0.20/0.45 ( ( P @ Xs2 )
% 0.20/0.45 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) )
% 0.20/0.45 => ( P @ Xs ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rev_induct
% 0.20/0.45 thf(fact_260_listrel_ONil,axiom,
% 0.20/0.45 ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.Nil
% 0.20/0.45 thf(fact_261_listrel__Nil1,axiom,
% 0.20/0.45 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ( Xs = nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Nil1
% 0.20/0.45 thf(fact_262_listrel__Nil2,axiom,
% 0.20/0.45 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ( Xs = nil_com ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Nil2
% 0.20/0.45 thf(fact_263_listrel__rtrancl__trans,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state,Zs2: list_P1040014977_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.20/0.45 => ( ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_rtrancl_trans
% 0.20/0.45 thf(fact_264_listrel__rtrancl__trans,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state,Zs2: list_P890094829_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 0.20/0.45 => ( ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ Xs @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_rtrancl_trans
% 0.20/0.45 thf(fact_265_app__exec,axiom,
% 0.20/0.45 ! [Cs3: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs3 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 % app_exec
% 0.20/0.45 thf(fact_266_listrel__Cons2,axiom,
% 0.20/0.45 ! [Xs: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ~ ! [X3: com,Xs2: list_com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_com @ X3 @ Xs2 ) )
% 0.20/0.45 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 0.20/0.45 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons2
% 0.20/0.45 thf(fact_267_listrel__Cons2,axiom,
% 0.20/0.45 ! [Xs: list_list_com,Y: state,Ys2: list_state,R: set_Pr849496667_state] :
% 0.20/0.45 ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 => ~ ! [X3: list_com,Xs2: list_list_com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_list_com @ X3 @ Xs2 ) )
% 0.20/0.45 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 0.20/0.45 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons2
% 0.20/0.45 thf(fact_268_listrel__Cons2,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 => ~ ! [X3: produc2041926651_state,Xs2: list_P1040014977_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 0.20/0.45 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 0.20/0.45 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons2
% 0.20/0.45 thf(fact_269_listrel__Cons2,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 => ~ ! [X3: produc410756839_state,Xs2: list_P890094829_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P438230685_state @ X3 @ Xs2 ) )
% 0.20/0.45 => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R )
% 0.20/0.45 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons2
% 0.20/0.45 thf(fact_270_listrel__Cons1,axiom,
% 0.20/0.45 ! [Y: com,Ys2: list_com,Xs: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys2 ) @ Xs ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ~ ! [Y2: com,Ys3: list_com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_com @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons1
% 0.20/0.45 thf(fact_271_listrel__Cons1,axiom,
% 0.20/0.45 ! [Y: list_com,Ys2: list_list_com,Xs: list_state,R: set_Pr849496667_state] :
% 0.20/0.45 ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys2 ) @ Xs ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 => ~ ! [Y2: state,Ys3: list_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_state @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys2 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons1
% 0.20/0.45 thf(fact_272_listrel__Cons1,axiom,
% 0.20/0.45 ! [Y: produc2041926651_state,Ys2: list_P1040014977_state,Xs: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys2 ) @ Xs ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 => ~ ! [Y2: produc2041926651_state,Ys3: list_P1040014977_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P465369265_state @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons1
% 0.20/0.45 thf(fact_273_listrel__Cons1,axiom,
% 0.20/0.45 ! [Y: produc410756839_state,Ys2: list_P890094829_state,Xs: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ Y @ Ys2 ) @ Xs ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 => ~ ! [Y2: produc410756839_state,Ys3: list_P890094829_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P438230685_state @ Y2 @ Ys3 ) )
% 0.20/0.45 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Y2 ) @ R )
% 0.20/0.45 => ~ ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_Cons1
% 0.20/0.45 thf(fact_274_listrel_OCons,axiom,
% 0.20/0.45 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.20/0.45 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.Cons
% 0.20/0.45 thf(fact_275_listrel_OCons,axiom,
% 0.20/0.45 ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs: list_list_com,Ys2: list_state] :
% 0.20/0.45 ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 0.20/0.45 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs ) @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.Cons
% 0.20/0.45 thf(fact_276_listrel_OCons,axiom,
% 0.20/0.45 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.20/0.45 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.Cons
% 0.20/0.45 thf(fact_277_listrel_OCons,axiom,
% 0.20/0.45 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.20/0.45 => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.Cons
% 0.20/0.45 thf(fact_278_exec1__only1__aux,axiom,
% 0.20/0.45 ! [Ccs: list_com,S: state,Cs: list_com,T: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ccs @ S ) @ ( produc1204172211_state @ Cs @ T ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ! [C5: com,Cs5: list_com] :
% 0.20/0.45 ( ( Ccs
% 0.20/0.45 = ( cons_com @ C5 @ Cs5 ) )
% 0.20/0.45 => ? [Cs1: list_com] :
% 0.20/0.45 ( Cs
% 0.20/0.45 = ( append_com @ Cs1 @ Cs5 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1_only1_aux
% 0.20/0.45 thf(fact_279_exec1__only1,axiom,
% 0.20/0.45 ! [C: com,Cs3: list_com,S: state,Cs: list_com,T: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ T ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ? [Cs1: list_com] :
% 0.20/0.45 ( Cs
% 0.20/0.45 = ( append_com @ Cs1 @ Cs3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1_only1
% 0.20/0.45 thf(fact_280_exec1__drop__suffix__aux,axiom,
% 0.20/0.45 ! [Cs12: list_com,S: state,Cs1_2: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs12 @ S ) @ ( produc1204172211_state @ Cs1_2 @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ! [Cs13: list_com,Cs23: list_com,Cs14: list_com] :
% 0.20/0.45 ( ( ( Cs12
% 0.20/0.45 = ( append_com @ Cs13 @ Cs23 ) )
% 0.20/0.45 & ( Cs1_2
% 0.20/0.45 = ( append_com @ Cs14 @ Cs23 ) )
% 0.20/0.45 & ( Cs13 != nil_com ) )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs13 @ S ) @ ( produc1204172211_state @ Cs14 @ S2 ) ) @ pHoare259243666_exec1 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1_drop_suffix_aux
% 0.20/0.45 thf(fact_281_exec1__drop__suffix,axiom,
% 0.20/0.45 ! [Cs15: list_com,Cs22: list_com,S: state,Cs16: list_com,S2: state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs15 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs16 @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 )
% 0.20/0.45 => ( ( Cs15 != nil_com )
% 0.20/0.45 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs15 @ S ) @ ( produc1204172211_state @ Cs16 @ S2 ) ) @ pHoare259243666_exec1 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exec1_drop_suffix
% 0.20/0.45 thf(fact_282_listrel_Oinducts,axiom,
% 0.20/0.45 ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ( ( P @ nil_com @ nil_com )
% 0.20/0.45 => ( ! [X3: com,Y2: com,Xs2: list_com,Ys3: list_com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.45 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) ) ) )
% 0.20/0.45 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.inducts
% 0.20/0.45 thf(fact_283_listrel_Oinducts,axiom,
% 0.20/0.45 ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 0.20/0.45 ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 => ( ( P @ nil_list_com @ nil_state )
% 0.20/0.45 => ( ! [X3: list_com,Y2: state,Xs2: list_list_com,Ys3: list_state] :
% 0.20/0.45 ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.45 => ( P @ ( cons_list_com @ X3 @ Xs2 ) @ ( cons_state @ Y2 @ Ys3 ) ) ) ) )
% 0.20/0.45 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.inducts
% 0.20/0.45 thf(fact_284_listrel_Oinducts,axiom,
% 0.20/0.45 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 0.20/0.45 => ( ! [X3: produc2041926651_state,Y2: produc2041926651_state,Xs2: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.45 => ( P @ ( cons_P465369265_state @ X3 @ Xs2 ) @ ( cons_P465369265_state @ Y2 @ Ys3 ) ) ) ) )
% 0.20/0.45 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.inducts
% 0.20/0.45 thf(fact_285_listrel_Oinducts,axiom,
% 0.20/0.45 ! [X1: list_P890094829_state,X2: list_P890094829_state,R: set_Pr2096893127_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ X1 @ X2 ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 => ( ( P @ nil_Pr1347322605_state @ nil_Pr1347322605_state )
% 0.20/0.45 => ( ! [X3: produc410756839_state,Y2: produc410756839_state,Xs2: list_P890094829_state,Ys3: list_P890094829_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys3 ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.45 => ( P @ ( cons_P438230685_state @ X3 @ Xs2 ) @ ( cons_P438230685_state @ Y2 @ Ys3 ) ) ) ) )
% 0.20/0.45 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.inducts
% 0.20/0.45 thf(fact_286_listrel_Osimps,axiom,
% 0.20/0.45 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.20/0.45 = ( ( ( A1 = nil_com )
% 0.20/0.45 & ( A22 = nil_com ) )
% 0.20/0.45 | ? [X4: com,Y3: com,Xs3: list_com,Ys: list_com] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_com @ X4 @ Xs3 ) )
% 0.20/0.45 & ( A22
% 0.20/0.45 = ( cons_com @ Y3 @ Ys ) )
% 0.20/0.45 & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y3 ) @ R )
% 0.20/0.45 & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.simps
% 0.20/0.45 thf(fact_287_listrel_Osimps,axiom,
% 0.20/0.45 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.20/0.45 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.20/0.45 = ( ( ( A1 = nil_list_com )
% 0.20/0.45 & ( A22 = nil_state ) )
% 0.20/0.45 | ? [X4: list_com,Y3: state,Xs3: list_list_com,Ys: list_state] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_list_com @ X4 @ Xs3 ) )
% 0.20/0.45 & ( A22
% 0.20/0.45 = ( cons_state @ Y3 @ Ys ) )
% 0.20/0.45 & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y3 ) @ R )
% 0.20/0.45 & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.simps
% 0.20/0.45 thf(fact_288_listrel_Osimps,axiom,
% 0.20/0.45 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.20/0.45 = ( ( ( A1 = nil_Pr1844458753_state )
% 0.20/0.45 & ( A22 = nil_Pr1844458753_state ) )
% 0.20/0.45 | ? [X4: produc2041926651_state,Y3: produc2041926651_state,Xs3: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 0.20/0.45 & ( A22
% 0.20/0.45 = ( cons_P465369265_state @ Y3 @ Ys ) )
% 0.20/0.45 & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y3 ) @ R )
% 0.20/0.45 & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.simps
% 0.20/0.45 thf(fact_289_listrel_Osimps,axiom,
% 0.20/0.45 ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 0.20/0.45 = ( ( ( A1 = nil_Pr1347322605_state )
% 0.20/0.45 & ( A22 = nil_Pr1347322605_state ) )
% 0.20/0.45 | ? [X4: produc410756839_state,Y3: produc410756839_state,Xs3: list_P890094829_state,Ys: list_P890094829_state] :
% 0.20/0.45 ( ( A1
% 0.20/0.45 = ( cons_P438230685_state @ X4 @ Xs3 ) )
% 0.20/0.45 & ( A22
% 0.20/0.45 = ( cons_P438230685_state @ Y3 @ Ys ) )
% 0.20/0.45 & ( member512523024_state @ ( produc2065881943_state @ X4 @ Y3 ) @ R )
% 0.20/0.45 & ( member423306384_state @ ( produc1354769367_state @ Xs3 @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel.simps
% 0.20/0.45 thf(fact_290_bind__simps_I2_J,axiom,
% 0.20/0.45 ! [X: com,Xs: list_com,F: com > list_com] :
% 0.20/0.45 ( ( bind_com_com @ ( cons_com @ X @ Xs ) @ F )
% 0.20/0.45 = ( append_com @ ( F @ X ) @ ( bind_com_com @ Xs @ F ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % bind_simps(2)
% 0.20/0.45 thf(fact_291_snoc__listrel1__snoc__iff,axiom,
% 0.20/0.45 ! [Xs: list_com,X: com,Ys2: list_com,Y: com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 0.20/0.45 = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.20/0.45 & ( X = Y ) )
% 0.20/0.45 | ( ( Xs = Ys2 )
% 0.20/0.45 & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % snoc_listrel1_snoc_iff
% 0.20/0.45 thf(fact_292_snoc__listrel1__snoc__iff,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,X: produc2041926651_state,Ys2: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys2 @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 & ( X = Y ) )
% 0.20/0.45 | ( ( Xs = Ys2 )
% 0.20/0.45 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % snoc_listrel1_snoc_iff
% 0.20/0.45 thf(fact_293_snoc__listrel1__snoc__iff,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,X: produc410756839_state,Ys2: list_P890094829_state,Y: produc410756839_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs @ ( cons_P438230685_state @ X @ nil_Pr1347322605_state ) ) @ ( append221843330_state @ Ys2 @ ( cons_P438230685_state @ Y @ nil_Pr1347322605_state ) ) ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 = ( ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 & ( X = Y ) )
% 0.20/0.45 | ( ( Xs = Ys2 )
% 0.20/0.45 & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % snoc_listrel1_snoc_iff
% 0.20/0.45 thf(fact_294_maps__simps_I1_J,axiom,
% 0.20/0.45 ! [F: com > list_com,X: com,Xs: list_com] :
% 0.20/0.45 ( ( maps_com_com @ F @ ( cons_com @ X @ Xs ) )
% 0.20/0.45 = ( append_com @ ( F @ X ) @ ( maps_com_com @ F @ Xs ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % maps_simps(1)
% 0.20/0.45 thf(fact_295_bind__simps_I1_J,axiom,
% 0.20/0.45 ! [F: com > list_com] :
% 0.20/0.45 ( ( bind_com_com @ nil_com @ F )
% 0.20/0.45 = nil_com ) ).
% 0.20/0.45
% 0.20/0.45 % bind_simps(1)
% 0.20/0.45 thf(fact_296_Cons__listrel1__Cons,axiom,
% 0.20/0.45 ! [X: com,Xs: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 0.20/0.45 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.20/0.45 & ( Xs = Ys2 ) )
% 0.20/0.45 | ( ( X = Y )
% 0.20/0.45 & ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1_Cons
% 0.20/0.45 thf(fact_297_Cons__listrel1__Cons,axiom,
% 0.20/0.45 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.20/0.45 & ( Xs = Ys2 ) )
% 0.20/0.45 | ( ( X = Y )
% 0.20/0.45 & ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1_Cons
% 0.20/0.45 thf(fact_298_Cons__listrel1__Cons,axiom,
% 0.20/0.45 ! [X: produc410756839_state,Xs: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.20/0.45 & ( Xs = Ys2 ) )
% 0.20/0.45 | ( ( X = Y )
% 0.20/0.45 & ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1_Cons
% 0.20/0.45 thf(fact_299_rtrancl__listrel1__ConsI1,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rtrancl_listrel1_ConsI1
% 0.20/0.45 thf(fact_300_listrel1I2,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I2
% 0.20/0.45 thf(fact_301_not__listrel1__Nil,axiom,
% 0.20/0.45 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 0.20/0.45
% 0.20/0.45 % not_listrel1_Nil
% 0.20/0.45 thf(fact_302_not__Nil__listrel1,axiom,
% 0.20/0.45 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel1_com @ R ) ) ).
% 0.20/0.45
% 0.20/0.45 % not_Nil_listrel1
% 0.20/0.45 thf(fact_303_append__listrel1I,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Us2: list_com,Vs: list_com] :
% 0.20/0.45 ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.20/0.45 & ( Us2 = Vs ) )
% 0.20/0.45 | ( ( Xs = Ys2 )
% 0.20/0.45 & ( member32358020st_com @ ( produc1307105171st_com @ Us2 @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Us2 ) @ ( append_com @ Ys2 @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % append_listrel1I
% 0.20/0.45 thf(fact_304_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.20/0.45 ! [R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 0.20/0.45 = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_rtrancl_eq_rtrancl_listrel1
% 0.20/0.45 thf(fact_305_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.20/0.45 ! [R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( listre1244407729_state @ ( transi463013610_state @ R ) )
% 0.20/0.45 = ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_rtrancl_eq_rtrancl_listrel1
% 0.20/0.45 thf(fact_306_maps__simps_I2_J,axiom,
% 0.20/0.45 ! [F: com > list_com] :
% 0.20/0.45 ( ( maps_com_com @ F @ nil_com )
% 0.20/0.45 = nil_com ) ).
% 0.20/0.45
% 0.20/0.45 % maps_simps(2)
% 0.20/0.45 thf(fact_307_listrel1I1,axiom,
% 0.20/0.45 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Xs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I1
% 0.20/0.45 thf(fact_308_listrel1I1,axiom,
% 0.20/0.45 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Xs ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I1
% 0.20/0.45 thf(fact_309_listrel1I1,axiom,
% 0.20/0.45 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Xs ) ) @ ( listre1725776070_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I1
% 0.20/0.45 thf(fact_310_Cons__listrel1E1,axiom,
% 0.20/0.45 ! [X: com,Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.20/0.45 => ( ! [Y2: com] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_com @ Y2 @ Xs ) )
% 0.20/0.45 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y2 ) @ R ) )
% 0.20/0.45 => ~ ! [Zs: list_com] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_com @ X @ Zs ) )
% 0.20/0.45 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Zs ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1E1
% 0.20/0.45 thf(fact_311_Cons__listrel1E1,axiom,
% 0.20/0.45 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 => ( ! [Y2: produc2041926651_state] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_P465369265_state @ Y2 @ Xs ) )
% 0.20/0.45 => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y2 ) @ R ) )
% 0.20/0.45 => ~ ! [Zs: list_P1040014977_state] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_P465369265_state @ X @ Zs ) )
% 0.20/0.45 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1E1
% 0.20/0.45 thf(fact_312_Cons__listrel1E1,axiom,
% 0.20/0.45 ! [X: produc410756839_state,Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 => ( ! [Y2: produc410756839_state] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_P438230685_state @ Y2 @ Xs ) )
% 0.20/0.45 => ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y2 ) @ R ) )
% 0.20/0.45 => ~ ! [Zs: list_P890094829_state] :
% 0.20/0.45 ( ( Ys2
% 0.20/0.45 = ( cons_P438230685_state @ X @ Zs ) )
% 0.20/0.45 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Zs ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1E1
% 0.20/0.45 thf(fact_313_Cons__listrel1E2,axiom,
% 0.20/0.45 ! [Xs: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 0.20/0.45 => ( ! [X3: com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_com @ X3 @ Ys2 ) )
% 0.20/0.45 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 0.20/0.45 => ~ ! [Zs: list_com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_com @ Y @ Zs ) )
% 0.20/0.45 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1E2
% 0.20/0.45 thf(fact_314_Cons__listrel1E2,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 => ( ! [X3: produc2041926651_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P465369265_state @ X3 @ Ys2 ) )
% 0.20/0.45 => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 0.20/0.45 => ~ ! [Zs: list_P1040014977_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P465369265_state @ Y @ Zs ) )
% 0.20/0.45 => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1E2
% 0.20/0.45 thf(fact_315_Cons__listrel1E2,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 => ( ! [X3: produc410756839_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P438230685_state @ X3 @ Ys2 ) )
% 0.20/0.45 => ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R ) )
% 0.20/0.45 => ~ ! [Zs: list_P890094829_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( cons_P438230685_state @ Y @ Zs ) )
% 0.20/0.45 => ~ ( member423306384_state @ ( produc1354769367_state @ Zs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Cons_listrel1E2
% 0.20/0.45 thf(fact_316_listrel__reflcl__if__listrel1,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_reflcl_if_listrel1
% 0.20/0.45 thf(fact_317_listrel__reflcl__if__listrel1,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel_reflcl_if_listrel1
% 0.20/0.45 thf(fact_318_listrel1I,axiom,
% 0.20/0.45 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Us2: list_com,Vs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.20/0.45 => ( ( Xs
% 0.20/0.45 = ( append_com @ Us2 @ ( cons_com @ X @ Vs ) ) )
% 0.20/0.45 => ( ( Ys2
% 0.20/0.45 = ( append_com @ Us2 @ ( cons_com @ Y @ Vs ) ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I
% 0.20/0.45 thf(fact_319_listrel1I,axiom,
% 0.20/0.45 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Us2: list_P1040014977_state,Vs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.20/0.45 => ( ( Xs
% 0.20/0.45 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ X @ Vs ) ) )
% 0.20/0.45 => ( ( Ys2
% 0.20/0.45 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I
% 0.20/0.45 thf(fact_320_listrel1I,axiom,
% 0.20/0.45 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state,Us2: list_P890094829_state,Vs: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.20/0.45 => ( ( Xs
% 0.20/0.45 = ( append221843330_state @ Us2 @ ( cons_P438230685_state @ X @ Vs ) ) )
% 0.20/0.45 => ( ( Ys2
% 0.20/0.45 = ( append221843330_state @ Us2 @ ( cons_P438230685_state @ Y @ Vs ) ) )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1I
% 0.20/0.45 thf(fact_321_listrel1E,axiom,
% 0.20/0.45 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.20/0.45 => ~ ! [X3: com,Y2: com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ! [Us3: list_com,Vs2: list_com] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 0.20/0.45 => ( Ys2
% 0.20/0.45 != ( append_com @ Us3 @ ( cons_com @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1E
% 0.20/0.45 thf(fact_322_listrel1E,axiom,
% 0.20/0.45 ! [Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.20/0.45 => ~ ! [X3: produc2041926651_state,Y2: produc2041926651_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 0.20/0.45 => ( Ys2
% 0.20/0.45 != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1E
% 0.20/0.45 thf(fact_323_listrel1E,axiom,
% 0.20/0.45 ! [Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.20/0.45 => ~ ! [X3: produc410756839_state,Y2: produc410756839_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 0.20/0.45 => ! [Us3: list_P890094829_state,Vs2: list_P890094829_state] :
% 0.20/0.45 ( ( Xs
% 0.20/0.45 = ( append221843330_state @ Us3 @ ( cons_P438230685_state @ X3 @ Vs2 ) ) )
% 0.20/0.45 => ( Ys2
% 0.20/0.45 != ( append221843330_state @ Us3 @ ( cons_P438230685_state @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % listrel1E
% 0.20/0.45 thf(fact_324_rtrancl__listrel1__ConsI2,axiom,
% 0.20/0.45 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys2: list_com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 0.20/0.45 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rtrancl_listrel1_ConsI2
% 0.20/0.45 thf(fact_325_rtrancl__listrel1__ConsI2,axiom,
% 0.20/0.45 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.20/0.45 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rtrancl_listrel1_ConsI2
% 0.20/0.45 thf(fact_326_rtrancl__listrel1__ConsI2,axiom,
% 0.20/0.45 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.20/0.45 => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % rtrancl_listrel1_ConsI2
% 0.20/0.45 thf(fact_327_concat__eq__append__conv,axiom,
% 0.20/0.45 ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( ( concat_com @ Xss2 )
% 0.20/0.45 = ( append_com @ Ys2 @ Zs2 ) )
% 0.20/0.45 = ( ( ( Xss2 = nil_list_com )
% 0.20/0.45 => ( ( Ys2 = nil_com )
% 0.20/0.45 & ( Zs2 = nil_com ) ) )
% 0.20/0.45 & ( ( Xss2 != nil_list_com )
% 0.20/0.45 => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 0.20/0.45 ( ( Xss2
% 0.20/0.45 = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.20/0.45 & ( Ys2
% 0.20/0.45 = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 0.20/0.45 & ( Zs2
% 0.20/0.45 = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % concat_eq_append_conv
% 0.20/0.45 thf(fact_328_lexord__append__left__rightI,axiom,
% 0.20/0.45 ! [A: com,B: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 0.20/0.45 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A @ X ) ) @ ( append_com @ U @ ( cons_com @ B @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_left_rightI
% 0.20/0.45 thf(fact_329_lexord__append__left__rightI,axiom,
% 0.20/0.45 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_left_rightI
% 0.20/0.45 thf(fact_330_lexord__append__left__rightI,axiom,
% 0.20/0.45 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,U: list_P890094829_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ U @ ( cons_P438230685_state @ A @ X ) ) @ ( append221843330_state @ U @ ( cons_P438230685_state @ B @ Y ) ) ) @ ( lexord1893203674_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_left_rightI
% 0.20/0.45 thf(fact_331_concat__append,axiom,
% 0.20/0.45 ! [Xs: list_list_com,Ys2: list_list_com] :
% 0.20/0.45 ( ( concat_com @ ( append_list_com @ Xs @ Ys2 ) )
% 0.20/0.45 = ( append_com @ ( concat_com @ Xs ) @ ( concat_com @ Ys2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % concat_append
% 0.20/0.45 thf(fact_332_lexord__cons__cons,axiom,
% 0.20/0.45 ! [A: com,X: list_com,B: com,Y: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A @ X ) @ ( cons_com @ B @ Y ) ) @ ( lexord_com @ R ) )
% 0.20/0.45 = ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 0.20/0.45 | ( ( A = B )
% 0.20/0.45 & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_cons_cons
% 0.20/0.45 thf(fact_333_lexord__cons__cons,axiom,
% 0.20/0.45 ! [A: produc2041926651_state,X: list_P1040014977_state,B: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A @ X ) @ ( cons_P465369265_state @ B @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 0.20/0.45 = ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.20/0.45 | ( ( A = B )
% 0.20/0.45 & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_cons_cons
% 0.20/0.45 thf(fact_334_lexord__cons__cons,axiom,
% 0.20/0.45 ! [A: produc410756839_state,X: list_P890094829_state,B: produc410756839_state,Y: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ A @ X ) @ ( cons_P438230685_state @ B @ Y ) ) @ ( lexord1893203674_state @ R ) )
% 0.20/0.45 = ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.20/0.45 | ( ( A = B )
% 0.20/0.45 & ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_cons_cons
% 0.20/0.45 thf(fact_335_lexord__Nil__left,axiom,
% 0.20/0.45 ! [Y: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 0.20/0.45 = ( ? [A3: com,X4: list_com] :
% 0.20/0.45 ( Y
% 0.20/0.45 = ( cons_com @ A3 @ X4 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_Nil_left
% 0.20/0.45 thf(fact_336_lexord__linear,axiom,
% 0.20/0.45 ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.20/0.45 ( ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 0.20/0.45 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.20/0.45 | ( A2 = B2 )
% 0.20/0.45 | ( member1069318160_state @ ( produc1909270103_state @ B2 @ A2 ) @ R ) )
% 0.20/0.45 => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 0.20/0.45 | ( X = Y )
% 0.20/0.45 | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_linear
% 0.20/0.45 thf(fact_337_lexord__linear,axiom,
% 0.20/0.45 ! [R: set_Pr2096893127_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 0.20/0.45 ( ! [A2: produc410756839_state,B2: produc410756839_state] :
% 0.20/0.45 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.20/0.45 | ( A2 = B2 )
% 0.20/0.45 | ( member512523024_state @ ( produc2065881943_state @ B2 @ A2 ) @ R ) )
% 0.20/0.45 => ( ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) )
% 0.20/0.45 | ( X = Y )
% 0.20/0.45 | ( member423306384_state @ ( produc1354769367_state @ Y @ X ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_linear
% 0.20/0.45 thf(fact_338_lexord__irreflexive,axiom,
% 0.20/0.45 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 0.20/0.45 ( ! [X3: produc2041926651_state] :
% 0.20/0.45 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.20/0.45 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_irreflexive
% 0.20/0.45 thf(fact_339_lexord__irreflexive,axiom,
% 0.20/0.45 ! [R: set_Pr2096893127_state,Xs: list_P890094829_state] :
% 0.20/0.45 ( ! [X3: produc410756839_state] :
% 0.20/0.45 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.20/0.45 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Xs ) @ ( lexord1893203674_state @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_irreflexive
% 0.20/0.45 thf(fact_340_concat_Osimps_I1_J,axiom,
% 0.20/0.45 ( ( concat_com @ nil_list_com )
% 0.20/0.45 = nil_com ) ).
% 0.20/0.45
% 0.20/0.45 % concat.simps(1)
% 0.20/0.45 thf(fact_341_lexord__Nil__right,axiom,
% 0.20/0.45 ! [X: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_Nil_right
% 0.20/0.45 thf(fact_342_concat_Osimps_I2_J,axiom,
% 0.20/0.45 ! [X: list_com,Xs: list_list_com] :
% 0.20/0.45 ( ( concat_com @ ( cons_list_com @ X @ Xs ) )
% 0.20/0.45 = ( append_com @ X @ ( concat_com @ Xs ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % concat.simps(2)
% 0.20/0.45 thf(fact_343_lexord__append__leftI,axiom,
% 0.20/0.45 ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_leftI
% 0.20/0.45 thf(fact_344_lexord__append__leftD,axiom,
% 0.20/0.45 ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 0.20/0.45 => ( ! [A2: com] :
% 0.20/0.45 ~ ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ A2 ) @ R )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_leftD
% 0.20/0.45 thf(fact_345_lexord__append__leftD,axiom,
% 0.20/0.45 ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.20/0.45 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 0.20/0.45 => ( ! [A2: produc2041926651_state] :
% 0.20/0.45 ~ ( member1069318160_state @ ( produc1909270103_state @ A2 @ A2 ) @ R )
% 0.20/0.45 => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_leftD
% 0.20/0.45 thf(fact_346_lexord__append__leftD,axiom,
% 0.20/0.45 ! [X: list_P890094829_state,U: list_P890094829_state,V: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.20/0.45 ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ X @ U ) @ ( append221843330_state @ X @ V ) ) @ ( lexord1893203674_state @ R ) )
% 0.20/0.45 => ( ! [A2: produc410756839_state] :
% 0.20/0.45 ~ ( member512523024_state @ ( produc2065881943_state @ A2 @ A2 ) @ R )
% 0.20/0.45 => ( member423306384_state @ ( produc1354769367_state @ U @ V ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_leftD
% 0.20/0.45 thf(fact_347_lexord__append__rightI,axiom,
% 0.20/0.45 ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 0.20/0.45 ( ? [B5: com,Z3: list_com] :
% 0.20/0.45 ( Y
% 0.20/0.45 = ( cons_com @ B5 @ Z3 ) )
% 0.20/0.45 => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_append_rightI
% 0.20/0.45 thf(fact_348_concat__eq__appendD,axiom,
% 0.20/0.45 ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( ( concat_com @ Xss2 )
% 0.20/0.45 = ( append_com @ Ys2 @ Zs2 ) )
% 0.20/0.45 => ( ( Xss2 != nil_list_com )
% 0.20/0.45 => ? [Xss12: list_list_com,Xs2: list_com,Xs5: list_com,Xss23: list_list_com] :
% 0.20/0.45 ( ( Xss2
% 0.20/0.45 = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.20/0.45 & ( Ys2
% 0.20/0.45 = ( append_com @ ( concat_com @ Xss12 ) @ Xs2 ) )
% 0.20/0.45 & ( Zs2
% 0.20/0.45 = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % concat_eq_appendD
% 0.20/0.45 thf(fact_349_lexord__same__pref__if__irrefl,axiom,
% 0.20/0.45 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 0.20/0.45 ( ( irrefl_com @ R )
% 0.20/0.45 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys2 ) @ ( append_com @ Xs @ Zs2 ) ) @ ( lexord_com @ R ) )
% 0.20/0.45 = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lexord_com @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % lexord_same_pref_if_irrefl
% 0.20/0.45
% 0.20/0.45 % Conjectures (5)
% 0.20/0.45 thf(conj_0,hypothesis,
% 0.20/0.45 termi @ c @ s ).
% 0.20/0.45
% 0.20/0.45 thf(conj_1,hypothesis,
% 0.20/0.45 ( ( f @ zero_zero_nat )
% 0.20/0.45 = ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(conj_2,hypothesis,
% 0.20/0.45 ! [I2: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ I2 ) @ ( f @ ( suc @ I2 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(conj_3,hypothesis,
% 0.20/0.45 member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 0.20/0.45
% 0.20/0.45 thf(conj_4,conjecture,
% 0.20/0.45 member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 2.71/1.54 ---- Embedded in THF ---
% 2.71/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.71/1.55 %%% Generated on Tue Feb 24 08:27:42 EST 2026
% 2.71/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.71/1.55 %%% Logic specification used:
% 2.71/1.55 %%% thf(spec, logic, $$dhol).
% 2.71/1.55
% 2.71/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2DTF26179.p
% See solution above
% 2.71/1.55 ------------------------
% 2.71/1.58 ---- Cleaned THF ---
% 2.71/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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_Mt__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_J,type,
% 2.71/1.58 set_Pr541394119_state: $tType ).
% 2.71/1.58
% 2.71/1.58 thf(ty_n_t__Product____Type__Oprod_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_Mt__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,
% 2.71/1.58 produc2046512871_state: $tType ).
% 2.71/1.58
% 2.71/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_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_Mt__List__Olist_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_J_J,type,
% 2.71/1.58 set_Pr1325664839_state: $tType ).
% 2.71/1.58
% 2.71/1.58 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_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_Mt__List__Olist_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_J,type,
% 2.71/1.58 produc1586269031_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 set_Pr2096893127_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 produc186437863_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 set_Pr1142642759_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 produc1225889383_state: $tType ).
% 2.71/1.58
% 2.71/1.58 thf(ty_n_t__List__Olist_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,
% 2.71/1.58 list_P890094829_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 set_Pr1165141447_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 produc410756839_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 set_Pr391631483_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
% 2.71/1.58 produc1393453339_state: $tType ).
% 2.71/1.58
% 2.71/1.58 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,
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% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__Nat__Onat,type,
% 2.71/1.59 member_nat: nat > set_nat > $o ).
% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__PLang__Ostate,type,
% 2.71/1.59 member_state: state > set_state > $o ).
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% 2.71/1.59 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,
% 2.71/1.59 member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 2.71/1.59 member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 2.71/1.59 member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
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% 2.71/1.59 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,
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% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_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_Mt__List__Olist_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_J,type,
% 2.71/1.59 member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o ).
% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 2.71/1.59 member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
% 2.71/1.59
% 2.71/1.59 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,
% 2.71/1.59 member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
% 2.71/1.59
% 2.71/1.59 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,
% 2.71/1.59 member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
% 2.71/1.59
% 2.71/1.59 thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__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,
% 2.71/1.59 member284400400_state: produc2046512871_state > set_Pr541394119_state > $o ).
% 2.71/1.59
% 2.71/1.59 thf(sy_v_c,type,
% 2.71/1.59 c: com ).
% 2.71/1.59
% 2.71/1.59 thf(sy_v_f,type,
% 2.71/1.59 f: nat > produc2041926651_state ).
% 2.71/1.59
% 2.71/1.59 thf(sy_v_n,type,
% 2.71/1.59 n: nat ).
% 2.71/1.59
% 2.71/1.59 thf(sy_v_s,type,
% 2.71/1.59 s: state ).
% 2.71/1.59
% 2.71/1.59 thf(fact_0_exec1E_I1_J,axiom,
% 2.71/1.59 ! [S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ nil_com @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_1_renumber,axiom,
% 2.71/1.59 ! [A: produc410756839_state,F: nat > produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ! [I: nat] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F @ I ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 2.71/1.59 => ? [F2: nat > produc410756839_state] :
% 2.71/1.59 ( ( ( F2 @ zero_zero_nat )
% 2.71/1.59 = A )
% 2.71/1.59 & ! [I2: nat] : ( member512523024_state @ ( produc2065881943_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_2_renumber,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,F: nat > produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ! [I: nat] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ ( F @ I ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 2.71/1.59 => ? [F2: nat > produc2041926651_state] :
% 2.71/1.59 ( ( ( F2 @ zero_zero_nat )
% 2.71/1.59 = A )
% 2.71/1.59 & ! [I2: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_3_renumber__aux,axiom,
% 2.71/1.59 ! [A: produc410756839_state,F: nat > produc410756839_state,R: set_Pr2096893127_state,B: produc410756839_state] :
% 2.71/1.59 ( ! [I: nat] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ ( F @ I ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( B
% 2.71/1.59 = ( F @ zero_zero_nat ) )
% 2.71/1.59 => ? [F2: nat > produc410756839_state] :
% 2.71/1.59 ( ( ( F2 @ zero_zero_nat )
% 2.71/1.59 = A )
% 2.71/1.59 & ! [I2: nat] : ( member512523024_state @ ( produc2065881943_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_4_renumber__aux,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,F: nat > produc2041926651_state,R: set_Pr1165141447_state,B: produc2041926651_state] :
% 2.71/1.59 ( ! [I: nat] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ ( F @ I ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( B
% 2.71/1.59 = ( F @ zero_zero_nat ) )
% 2.71/1.59 => ? [F2: nat > produc2041926651_state] :
% 2.71/1.59 ( ( ( F2 @ zero_zero_nat )
% 2.71/1.59 = A )
% 2.71/1.59 & ! [I2: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_5_execs__pres__termi,axiom,
% 2.71/1.59 ! [C: com,S: state,C2: com,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C2 @ Cs ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 2.71/1.59 => ( ( termi @ C @ S )
% 2.71/1.59 => ( termi @ C2 @ S2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_6_rtrancl__trancl__absorb,axiom,
% 2.71/1.59 ! [R2: set_Pr2096893127_state] :
% 2.71/1.59 ( ( transi1666849160_state @ ( transi463013610_state @ R2 ) )
% 2.71/1.59 = ( transi463013610_state @ R2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_7_rtrancl__trancl__absorb,axiom,
% 2.71/1.59 ! [R2: set_Pr1165141447_state] :
% 2.71/1.59 ( ( transi1726587420_state @ ( transi1302705790_state @ R2 ) )
% 2.71/1.59 = ( transi1302705790_state @ R2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_8_trancl__rtrancl__absorb,axiom,
% 2.71/1.59 ! [R2: set_Pr2096893127_state] :
% 2.71/1.59 ( ( transi463013610_state @ ( transi1666849160_state @ R2 ) )
% 2.71/1.59 = ( transi463013610_state @ R2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_9_trancl__rtrancl__absorb,axiom,
% 2.71/1.59 ! [R2: set_Pr1165141447_state] :
% 2.71/1.59 ( ( transi1302705790_state @ ( transi1726587420_state @ R2 ) )
% 2.71/1.59 = ( transi1302705790_state @ R2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_10_trancl__induct2,axiom,
% 2.71/1.59 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi1995721864_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ R )
% 2.71/1.59 => ( P @ A2 @ B2 ) )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ ( transi1995721864_state @ R ) )
% 2.71/1.59 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( P @ Aa @ Ba ) ) ) )
% 2.71/1.59 => ( P @ Bx @ By ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_11_trancl__induct2,axiom,
% 2.71/1.59 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ R )
% 2.71/1.59 => ( P @ A2 @ B2 ) )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( P @ Aa @ Ba ) ) ) )
% 2.71/1.59 => ( P @ Bx @ By ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_12_trancl__induct2,axiom,
% 2.71/1.59 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ! [A2: list_com,B2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ R )
% 2.71/1.59 => ( P @ A2 @ B2 ) )
% 2.71/1.59 => ( ! [A2: list_com,B2: state,Aa: list_com,Ba: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( P @ Aa @ Ba ) ) ) )
% 2.71/1.59 => ( P @ Bx @ By ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_13_inf__def,axiom,
% 2.71/1.59 ( pHoare2126160787le_inf
% 2.71/1.59 = ( ^ [Cs2: list_com,S3: state] :
% 2.71/1.59 ? [F3: nat > produc2041926651_state] :
% 2.71/1.59 ( ( ( F3 @ zero_zero_nat )
% 2.71/1.59 = ( produc1204172211_state @ Cs2 @ S3 ) )
% 2.71/1.59 & ! [I3: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ pHoare259243666_exec1 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_14_rtrancl__induct2,axiom,
% 2.71/1.59 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 2.71/1.59 => ( ( P @ Ax @ Ay )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ ( transi152726506_state @ R ) )
% 2.71/1.59 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( P @ Aa @ Ba ) ) ) )
% 2.71/1.59 => ( P @ Bx @ By ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_15_rtrancl__induct2,axiom,
% 2.71/1.59 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ Ax @ Ay )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( P @ Aa @ Ba ) ) ) )
% 2.71/1.59 => ( P @ Bx @ By ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_16_rtrancl__induct2,axiom,
% 2.71/1.59 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ Ax @ Ay )
% 2.71/1.59 => ( ! [A2: list_com,B2: state,Aa: list_com,Ba: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( P @ Aa @ Ba ) ) ) )
% 2.71/1.59 => ( P @ Bx @ By ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_17_converse__rtranclE2,axiom,
% 2.71/1.59 ! [Xa: produc410756839_state,Xb: produc410756839_state,Za: produc410756839_state,Zb: produc410756839_state,R: set_Pr541394119_state] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) )
% 2.71/1.59 => ( ( ( produc2065881943_state @ Xa @ Xb )
% 2.71/1.59 != ( produc2065881943_state @ Za @ Zb ) )
% 2.71/1.59 => ~ ! [A2: produc410756839_state,B2: produc410756839_state] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ A2 @ B2 ) ) @ R )
% 2.71/1.59 => ~ ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_18_converse__rtranclE2,axiom,
% 2.71/1.59 ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( ( produc1909270103_state @ Xa @ Xb )
% 2.71/1.59 != ( produc1909270103_state @ Za @ Zb ) )
% 2.71/1.59 => ~ ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A2 @ B2 ) ) @ R )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_19_converse__rtranclE2,axiom,
% 2.71/1.59 ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( ( produc1204172211_state @ Xa @ Xb )
% 2.71/1.59 != ( produc1204172211_state @ Za @ Zb ) )
% 2.71/1.59 => ~ ! [A2: list_com,B2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A2 @ B2 ) ) @ R )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_20_converse__rtrancl__induct2,axiom,
% 2.71/1.59 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 2.71/1.59 => ( ( P @ Bx @ By )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 2.71/1.59 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Aa @ Ba ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 2.71/1.59 => ( ( P @ Aa @ Ba )
% 2.71/1.59 => ( P @ A2 @ B2 ) ) ) )
% 2.71/1.59 => ( P @ Ax @ Ay ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_21_converse__rtrancl__induct2,axiom,
% 2.71/1.59 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ Bx @ By )
% 2.71/1.59 => ( ! [A2: list_com,B2: state,Aa: list_com,Ba: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A2 @ B2 ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ Aa @ Ba )
% 2.71/1.59 => ( P @ A2 @ B2 ) ) ) )
% 2.71/1.59 => ( P @ Ax @ Ay ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_22_converse__rtrancl__induct2,axiom,
% 2.71/1.59 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ Bx @ By )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ Aa @ Ba )
% 2.71/1.59 => ( P @ A2 @ B2 ) ) ) )
% 2.71/1.59 => ( P @ Ax @ Ay ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_23_tranclD,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R2: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R2 ) )
% 2.71/1.59 => ? [Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z ) @ R2 )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ Z @ Y ) @ ( transi1302705790_state @ R2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_24_tranclD,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R2: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R2 ) )
% 2.71/1.59 => ? [Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z ) @ R2 )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ Z @ Y ) @ ( transi463013610_state @ R2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_25_rtranclD,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R2: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R2 ) )
% 2.71/1.59 => ( ( A = B )
% 2.71/1.59 | ( ( A != B )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_26_rtranclD,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R2: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R2 ) )
% 2.71/1.59 => ( ( A = B )
% 2.71/1.59 | ( ( A != B )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_27_tranclD2,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R2: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R2 ) )
% 2.71/1.59 => ? [Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z ) @ ( transi1302705790_state @ R2 ) )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ Z @ Y ) @ R2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_28_tranclD2,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R2: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R2 ) )
% 2.71/1.59 => ? [Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z ) @ ( transi463013610_state @ R2 ) )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ Z @ Y ) @ R2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_29_trancl__into__rtrancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_30_trancl__into__rtrancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_31_rtrancl__eq__or__trancl,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R2: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R2 ) )
% 2.71/1.59 = ( ( X = Y )
% 2.71/1.59 | ( ( X != Y )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_32_rtrancl__eq__or__trancl,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R2: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R2 ) )
% 2.71/1.59 = ( ( X = Y )
% 2.71/1.59 | ( ( X != Y )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_33_r__into__rtrancl,axiom,
% 2.71/1.59 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ P2 @ R )
% 2.71/1.59 => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_34_r__into__rtrancl,axiom,
% 2.71/1.59 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ P2 @ R )
% 2.71/1.59 => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_35_rtrancl__idemp,axiom,
% 2.71/1.59 ! [R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 2.71/1.59 = ( transi1302705790_state @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_36_rtrancl__idemp,axiom,
% 2.71/1.59 ! [R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 2.71/1.59 = ( transi463013610_state @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_37_r__into__trancl_H,axiom,
% 2.71/1.59 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ P2 @ R )
% 2.71/1.59 => ( member1069318160_state @ P2 @ ( transi1726587420_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_38_r__into__trancl_H,axiom,
% 2.71/1.59 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ P2 @ R )
% 2.71/1.59 => ( member512523024_state @ P2 @ ( transi1666849160_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_39_converse__rtrancl__into__rtrancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_40_converse__rtrancl__into__rtrancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_41_rtrancl_Ortrancl__into__rtrancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_42_rtrancl_Ortrancl__into__rtrancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_43_converse__rtrancl__induct,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ B )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ Z )
% 2.71/1.59 => ( P @ Y2 ) ) ) )
% 2.71/1.59 => ( P @ A ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_44_converse__rtrancl__induct,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ B )
% 2.71/1.59 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ Z )
% 2.71/1.59 => ( P @ Y2 ) ) ) )
% 2.71/1.59 => ( P @ A ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_45_rtrancl_Ortrancl__refl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ ( transi1302705790_state @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_46_rtrancl_Ortrancl__refl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,R: set_Pr2096893127_state] : ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ ( transi463013610_state @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_47_converse__rtranclE,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( X != Z2 )
% 2.71/1.59 => ~ ! [Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_48_converse__rtranclE,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( X != Z2 )
% 2.71/1.59 => ~ ! [Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_49_rtrancl_Oinducts,axiom,
% 2.71/1.59 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc2041926651_state] : ( P @ A2 @ A2 )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,C3: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C3 ) @ R )
% 2.71/1.59 => ( P @ A2 @ C3 ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_50_rtrancl_Oinducts,axiom,
% 2.71/1.59 ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc410756839_state] : ( P @ A2 @ A2 )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state,C3: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C3 ) @ R )
% 2.71/1.59 => ( P @ A2 @ C3 ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_51_rtrancl__induct,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( P @ A )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( P @ Y2 )
% 2.71/1.59 => ( P @ Z ) ) ) )
% 2.71/1.59 => ( P @ B ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_52_rtrancl__induct,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( P @ A )
% 2.71/1.59 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( P @ Y2 )
% 2.71/1.59 => ( P @ Z ) ) ) )
% 2.71/1.59 => ( P @ B ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_53_rtrancl__trans,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_54_rtrancl__trans,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_55_rtrancl_Osimps,axiom,
% 2.71/1.59 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 = ( ? [A3: produc2041926651_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = A3 ) )
% 2.71/1.59 | ? [A3: produc2041926651_state,B3: produc2041926651_state,C4: produc2041926651_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = C4 )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_56_rtrancl_Osimps,axiom,
% 2.71/1.59 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 = ( ? [A3: produc410756839_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = A3 ) )
% 2.71/1.59 | ? [A3: produc410756839_state,B3: produc410756839_state,C4: produc410756839_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = C4 )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ A3 @ B3 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_57_rtrancl_Ocases,axiom,
% 2.71/1.59 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( A22 != A1 )
% 2.71/1.59 => ~ ! [B2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_58_rtrancl_Ocases,axiom,
% 2.71/1.59 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( A22 != A1 )
% 2.71/1.59 => ~ ! [B2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_59_rtranclE,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( A != B )
% 2.71/1.59 => ~ ! [Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y2 @ B ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_60_rtranclE,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( A != B )
% 2.71/1.59 => ~ ! [Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ Y2 @ B ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_61_trancl_Otrancl__into__trancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_62_trancl_Otrancl__into__trancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_63_converse__trancl__induct,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ B ) @ R )
% 2.71/1.59 => ( P @ Y2 ) )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( P @ Z )
% 2.71/1.59 => ( P @ Y2 ) ) ) )
% 2.71/1.59 => ( P @ A ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_64_converse__trancl__induct,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ! [Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ B ) @ R )
% 2.71/1.59 => ( P @ Y2 ) )
% 2.71/1.59 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( P @ Z )
% 2.71/1.59 => ( P @ Y2 ) ) ) )
% 2.71/1.59 => ( P @ A ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_65_trancl_Or__into__trancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_66_trancl_Or__into__trancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_67_trancl__trans__induct,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ! [X3: produc2041926651_state,Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ( P @ X3 @ Y2 ) )
% 2.71/1.59 => ( ! [X3: produc2041926651_state,Y2: produc2041926651_state,Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( P @ X3 @ Y2 )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( P @ Y2 @ Z )
% 2.71/1.59 => ( P @ X3 @ Z ) ) ) ) )
% 2.71/1.59 => ( P @ X @ Y ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_68_trancl__trans__induct,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ! [X3: produc410756839_state,Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ( P @ X3 @ Y2 ) )
% 2.71/1.59 => ( ! [X3: produc410756839_state,Y2: produc410756839_state,Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( P @ X3 @ Y2 )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( P @ Y2 @ Z )
% 2.71/1.59 => ( P @ X3 @ Z ) ) ) ) )
% 2.71/1.59 => ( P @ X @ Y ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_69_trancl__into__trancl2,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_70_trancl__into__trancl2,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_71_irrefl__trancl__rD,axiom,
% 2.71/1.59 ! [R: set_Pr1165141447_state,X: produc2041926651_state,Y: produc2041926651_state] :
% 2.71/1.59 ( ! [X3: produc2041926651_state] :
% 2.71/1.59 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 2.71/1.59 => ( X != Y ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_72_irrefl__trancl__rD,axiom,
% 2.71/1.59 ! [R: set_Pr2096893127_state,X: produc410756839_state,Y: produc410756839_state] :
% 2.71/1.59 ( ! [X3: produc410756839_state] :
% 2.71/1.59 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 2.71/1.59 => ( X != Y ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_73_converse__tranclE,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ R )
% 2.71/1.59 => ~ ! [Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z2 ) @ ( transi1726587420_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_74_converse__tranclE,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ~ ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ R )
% 2.71/1.59 => ~ ! [Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z2 ) @ ( transi1666849160_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_75_r__r__into__trancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R2: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R2 )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R2 )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_76_r__r__into__trancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R2: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R2 )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R2 )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_77_trancl_Oinducts,axiom,
% 2.71/1.59 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 2.71/1.59 => ( P @ A2 @ B2 ) )
% 2.71/1.59 => ( ! [A2: produc2041926651_state,B2: produc2041926651_state,C3: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C3 ) @ R )
% 2.71/1.59 => ( P @ A2 @ C3 ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_78_trancl_Oinducts,axiom,
% 2.71/1.59 ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 2.71/1.59 => ( P @ A2 @ B2 ) )
% 2.71/1.59 => ( ! [A2: produc410756839_state,B2: produc410756839_state,C3: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( P @ A2 @ B2 )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C3 ) @ R )
% 2.71/1.59 => ( P @ A2 @ C3 ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_79_trancl__induct,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ R )
% 2.71/1.59 => ( P @ Y2 ) )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state,Z: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ Y2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( P @ Y2 )
% 2.71/1.59 => ( P @ Z ) ) ) )
% 2.71/1.59 => ( P @ B ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_80_trancl__induct,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ! [Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ R )
% 2.71/1.59 => ( P @ Y2 ) )
% 2.71/1.59 => ( ! [Y2: produc410756839_state,Z: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ Y2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y2 @ Z ) @ R )
% 2.71/1.59 => ( ( P @ Y2 )
% 2.71/1.59 => ( P @ Z ) ) ) )
% 2.71/1.59 => ( P @ B ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_81_trancl__trans,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_82_trancl__trans,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_83_trancl_Osimps,axiom,
% 2.71/1.59 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 = ( ? [A3: produc2041926651_state,B3: produc2041926651_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = B3 )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ R ) )
% 2.71/1.59 | ? [A3: produc2041926651_state,B3: produc2041926651_state,C4: produc2041926651_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = C4 )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ A3 @ B3 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_84_trancl_Osimps,axiom,
% 2.71/1.59 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 = ( ? [A3: produc410756839_state,B3: produc410756839_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = B3 )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ A3 @ B3 ) @ R ) )
% 2.71/1.59 | ? [A3: produc410756839_state,B3: produc410756839_state,C4: produc410756839_state] :
% 2.71/1.59 ( ( A1 = A3 )
% 2.71/1.59 & ( A22 = C4 )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ A3 @ B3 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ B3 @ C4 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_85_trancl_Ocases,axiom,
% 2.71/1.59 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ~ ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ R )
% 2.71/1.59 => ~ ! [B2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_86_trancl_Ocases,axiom,
% 2.71/1.59 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ~ ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ R )
% 2.71/1.59 => ~ ! [B2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ B2 @ A22 ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_87_tranclE,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ~ ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 => ~ ! [C3: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ C3 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ C3 @ B ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_88_tranclE,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ~ ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 => ~ ! [C3: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ C3 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ C3 @ B ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_89_termi__impl__not__inf,axiom,
% 2.71/1.59 ! [C: com,S: state] :
% 2.71/1.59 ( ( termi @ C @ S )
% 2.71/1.59 => ~ ( pHoare2126160787le_inf @ ( cons_com @ C @ nil_com ) @ S ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_90_mem__Collect__eq,axiom,
% 2.71/1.59 ! [A: produc410756839_state,P: produc410756839_state > $o] :
% 2.71/1.59 ( ( member1069318160_state @ A @ ( collec300063826_state @ P ) )
% 2.71/1.59 = ( P @ A ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_91_mem__Collect__eq,axiom,
% 2.71/1.59 ! [A: state,P: state > $o] :
% 2.71/1.59 ( ( member_state @ A @ ( collect_state @ P ) )
% 2.71/1.59 = ( P @ A ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_92_mem__Collect__eq,axiom,
% 2.71/1.59 ! [A: produc186437863_state,P: produc186437863_state > $o] :
% 2.71/1.59 ( ( member512523024_state @ A @ ( collec489924946_state @ P ) )
% 2.71/1.59 = ( P @ A ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_93_Collect__mem__eq,axiom,
% 2.71/1.59 ! [A4: set_Pr1165141447_state] :
% 2.71/1.59 ( ( collec300063826_state
% 2.71/1.59 @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 2.71/1.59 = A4 ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_94_Collect__mem__eq,axiom,
% 2.71/1.59 ! [A4: set_state] :
% 2.71/1.59 ( ( collect_state
% 2.71/1.59 @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 2.71/1.59 = A4 ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_95_Collect__mem__eq,axiom,
% 2.71/1.59 ! [A4: set_Pr2096893127_state] :
% 2.71/1.59 ( ( collec489924946_state
% 2.71/1.59 @ ^ [X4: produc186437863_state] : ( member512523024_state @ X4 @ A4 ) )
% 2.71/1.59 = A4 ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_96_trancl__rtrancl__trancl,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_97_trancl__rtrancl__trancl,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_98_rtrancl__trancl__trancl,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1726587420_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_99_rtrancl__trancl__trancl,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi1666849160_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_100_rtrancl__into__trancl2,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_101_rtrancl__into__trancl2,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_102_rtrancl__into__trancl1,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C ) @ R )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ A @ C ) @ ( transi1726587420_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_103_rtrancl__into__trancl1,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C ) @ R )
% 2.71/1.59 => ( member512523024_state @ ( produc2065881943_state @ A @ C ) @ ( transi1666849160_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_104_exec1s__impl__execs,axiom,
% 2.71/1.59 ! [Cs3: list_com,S: state,T: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 2.71/1.59 => ( pHoare259243732_execs @ S @ Cs3 @ T ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_105_execs__pres__termis,axiom,
% 2.71/1.59 ! [Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 2.71/1.59 => ( ( pHoare806997636termis @ Cs3 @ S )
% 2.71/1.59 => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_106_old_Onat_Oinject,axiom,
% 2.71/1.59 ! [Nat: nat,Nat2: nat] :
% 2.71/1.59 ( ( ( suc @ Nat )
% 2.71/1.59 = ( suc @ Nat2 ) )
% 2.71/1.59 = ( Nat = Nat2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_107_nat_Oinject,axiom,
% 2.71/1.59 ! [X2: nat,Y22: nat] :
% 2.71/1.59 ( ( ( suc @ X2 )
% 2.71/1.59 = ( suc @ Y22 ) )
% 2.71/1.59 = ( X2 = Y22 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_108_list_Oinject,axiom,
% 2.71/1.59 ! [X21: com,X22: list_com,Y21: com,Y222: list_com] :
% 2.71/1.59 ( ( ( cons_com @ X21 @ X22 )
% 2.71/1.59 = ( cons_com @ Y21 @ Y222 ) )
% 2.71/1.59 = ( ( X21 = Y21 )
% 2.71/1.59 & ( X22 = Y222 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_109_exec1s__impl__exec,axiom,
% 2.71/1.59 ! [C: com,S: state,T: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 2.71/1.59 => ( exec @ S @ C @ T ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_110_old_Oprod_Oinject,axiom,
% 2.71/1.59 ! [A: list_com,B: state,A5: list_com,B4: state] :
% 2.71/1.59 ( ( ( produc1204172211_state @ A @ B )
% 2.71/1.59 = ( produc1204172211_state @ A5 @ B4 ) )
% 2.71/1.59 = ( ( A = A5 )
% 2.71/1.59 & ( B = B4 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_111_old_Oprod_Oinject,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,A5: produc2041926651_state,B4: produc2041926651_state] :
% 2.71/1.59 ( ( ( produc1909270103_state @ A @ B )
% 2.71/1.59 = ( produc1909270103_state @ A5 @ B4 ) )
% 2.71/1.59 = ( ( A = A5 )
% 2.71/1.59 & ( B = B4 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_112_old_Oprod_Oinject,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,A5: produc410756839_state,B4: produc410756839_state] :
% 2.71/1.59 ( ( ( produc2065881943_state @ A @ B )
% 2.71/1.59 = ( produc2065881943_state @ A5 @ B4 ) )
% 2.71/1.59 = ( ( A = A5 )
% 2.71/1.59 & ( B = B4 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_113_prod_Oinject,axiom,
% 2.71/1.59 ! [X1: list_com,X2: state,Y1: list_com,Y22: state] :
% 2.71/1.59 ( ( ( produc1204172211_state @ X1 @ X2 )
% 2.71/1.59 = ( produc1204172211_state @ Y1 @ Y22 ) )
% 2.71/1.59 = ( ( X1 = Y1 )
% 2.71/1.59 & ( X2 = Y22 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_114_prod_Oinject,axiom,
% 2.71/1.59 ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y22: produc2041926651_state] :
% 2.71/1.59 ( ( ( produc1909270103_state @ X1 @ X2 )
% 2.71/1.59 = ( produc1909270103_state @ Y1 @ Y22 ) )
% 2.71/1.59 = ( ( X1 = Y1 )
% 2.71/1.59 & ( X2 = Y22 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_115_prod_Oinject,axiom,
% 2.71/1.59 ! [X1: produc410756839_state,X2: produc410756839_state,Y1: produc410756839_state,Y22: produc410756839_state] :
% 2.71/1.59 ( ( ( produc2065881943_state @ X1 @ X2 )
% 2.71/1.59 = ( produc2065881943_state @ Y1 @ Y22 ) )
% 2.71/1.59 = ( ( X1 = Y1 )
% 2.71/1.59 & ( X2 = Y22 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_116_execs_Ointros_I2_J,axiom,
% 2.71/1.59 ! [S: state,C: com,T: state,Cs3: list_com,U: state] :
% 2.71/1.59 ( ( exec @ S @ C @ T )
% 2.71/1.59 => ( ( pHoare259243732_execs @ T @ Cs3 @ U )
% 2.71/1.59 => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs3 ) @ U ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_117_execs_Ocases,axiom,
% 2.71/1.59 ! [A1: state,A22: list_com,A32: state] :
% 2.71/1.59 ( ( pHoare259243732_execs @ A1 @ A22 @ A32 )
% 2.71/1.59 => ( ( ( A22 = nil_com )
% 2.71/1.59 => ( A32 != A1 ) )
% 2.71/1.59 => ~ ! [C3: com,T2: state,Cs4: list_com] :
% 2.71/1.59 ( ( A22
% 2.71/1.59 = ( cons_com @ C3 @ Cs4 ) )
% 2.71/1.59 => ( ( exec @ A1 @ C3 @ T2 )
% 2.71/1.59 => ~ ( pHoare259243732_execs @ T2 @ Cs4 @ A32 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_118_execs_Osimps,axiom,
% 2.71/1.59 ( pHoare259243732_execs
% 2.71/1.59 = ( ^ [A12: state,A23: list_com,A33: state] :
% 2.71/1.59 ( ? [S3: state] :
% 2.71/1.59 ( ( A12 = S3 )
% 2.71/1.59 & ( A23 = nil_com )
% 2.71/1.59 & ( A33 = S3 ) )
% 2.71/1.59 | ? [S3: state,C4: com,T3: state,Cs2: list_com,U2: state] :
% 2.71/1.59 ( ( A12 = S3 )
% 2.71/1.59 & ( A23
% 2.71/1.59 = ( cons_com @ C4 @ Cs2 ) )
% 2.71/1.59 & ( A33 = U2 )
% 2.71/1.59 & ( exec @ S3 @ C4 @ T3 )
% 2.71/1.59 & ( pHoare259243732_execs @ T3 @ Cs2 @ U2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_119_execs_Oinducts,axiom,
% 2.71/1.59 ! [X1: state,X2: list_com,X32: state,P: state > list_com > state > $o] :
% 2.71/1.59 ( ( pHoare259243732_execs @ X1 @ X2 @ X32 )
% 2.71/1.59 => ( ! [S4: state] : ( P @ S4 @ nil_com @ S4 )
% 2.71/1.59 => ( ! [S4: state,C3: com,T2: state,Cs4: list_com,U3: state] :
% 2.71/1.59 ( ( exec @ S4 @ C3 @ T2 )
% 2.71/1.59 => ( ( pHoare259243732_execs @ T2 @ Cs4 @ U3 )
% 2.71/1.59 => ( ( P @ T2 @ Cs4 @ U3 )
% 2.71/1.59 => ( P @ S4 @ ( cons_com @ C3 @ Cs4 ) @ U3 ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_120_termis_Osimps_I2_J,axiom,
% 2.71/1.59 ! [C: com,Cs3: list_com,S: state] :
% 2.71/1.59 ( ( pHoare806997636termis @ ( cons_com @ C @ Cs3 ) @ S )
% 2.71/1.59 = ( ( termi @ C @ S )
% 2.71/1.59 & ! [T3: state] :
% 2.71/1.59 ( ( exec @ S @ C @ T3 )
% 2.71/1.59 => ( pHoare806997636termis @ Cs3 @ T3 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_121_execs_Ointros_I1_J,axiom,
% 2.71/1.59 ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_122_termis_Osimps_I1_J,axiom,
% 2.71/1.59 ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_123_zero__reorient,axiom,
% 2.71/1.59 ! [X: nat] :
% 2.71/1.59 ( ( zero_zero_nat = X )
% 2.71/1.59 = ( X = zero_zero_nat ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_124_surj__pair,axiom,
% 2.71/1.59 ! [P2: produc2041926651_state] :
% 2.71/1.59 ? [X3: list_com,Y2: state] :
% 2.71/1.59 ( P2
% 2.71/1.59 = ( produc1204172211_state @ X3 @ Y2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_125_surj__pair,axiom,
% 2.71/1.59 ! [P2: produc410756839_state] :
% 2.71/1.59 ? [X3: produc2041926651_state,Y2: produc2041926651_state] :
% 2.71/1.59 ( P2
% 2.71/1.59 = ( produc1909270103_state @ X3 @ Y2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_126_surj__pair,axiom,
% 2.71/1.59 ! [P2: produc186437863_state] :
% 2.71/1.59 ? [X3: produc410756839_state,Y2: produc410756839_state] :
% 2.71/1.59 ( P2
% 2.71/1.59 = ( produc2065881943_state @ X3 @ Y2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_127_prod__cases,axiom,
% 2.71/1.59 ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 2.71/1.59 ( ! [A2: list_com,B2: state] : ( P @ ( produc1204172211_state @ A2 @ B2 ) )
% 2.71/1.59 => ( P @ P2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_128_prod__cases,axiom,
% 2.71/1.59 ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 2.71/1.59 ( ! [A2: produc2041926651_state,B2: produc2041926651_state] : ( P @ ( produc1909270103_state @ A2 @ B2 ) )
% 2.71/1.59 => ( P @ P2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_129_prod__cases,axiom,
% 2.71/1.59 ! [P: produc186437863_state > $o,P2: produc186437863_state] :
% 2.71/1.59 ( ! [A2: produc410756839_state,B2: produc410756839_state] : ( P @ ( produc2065881943_state @ A2 @ B2 ) )
% 2.71/1.59 => ( P @ P2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_130_Pair__inject,axiom,
% 2.71/1.59 ! [A: list_com,B: state,A5: list_com,B4: state] :
% 2.71/1.59 ( ( ( produc1204172211_state @ A @ B )
% 2.71/1.59 = ( produc1204172211_state @ A5 @ B4 ) )
% 2.71/1.59 => ~ ( ( A = A5 )
% 2.71/1.59 => ( B != B4 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_131_Pair__inject,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,A5: produc2041926651_state,B4: produc2041926651_state] :
% 2.71/1.59 ( ( ( produc1909270103_state @ A @ B )
% 2.71/1.59 = ( produc1909270103_state @ A5 @ B4 ) )
% 2.71/1.59 => ~ ( ( A = A5 )
% 2.71/1.59 => ( B != B4 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_132_Pair__inject,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,A5: produc410756839_state,B4: produc410756839_state] :
% 2.71/1.59 ( ( ( produc2065881943_state @ A @ B )
% 2.71/1.59 = ( produc2065881943_state @ A5 @ B4 ) )
% 2.71/1.59 => ~ ( ( A = A5 )
% 2.71/1.59 => ( B != B4 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_133_old_Oprod_Oexhaust,axiom,
% 2.71/1.59 ! [Y: produc2041926651_state] :
% 2.71/1.59 ~ ! [A2: list_com,B2: state] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( produc1204172211_state @ A2 @ B2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_134_old_Oprod_Oexhaust,axiom,
% 2.71/1.59 ! [Y: produc410756839_state] :
% 2.71/1.59 ~ ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( produc1909270103_state @ A2 @ B2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_135_old_Oprod_Oexhaust,axiom,
% 2.71/1.59 ! [Y: produc186437863_state] :
% 2.71/1.59 ~ ! [A2: produc410756839_state,B2: produc410756839_state] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( produc2065881943_state @ A2 @ B2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_136_old_Oprod_Oinducts,axiom,
% 2.71/1.59 ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 2.71/1.59 ( ! [A2: list_com,B2: state] : ( P @ ( produc1204172211_state @ A2 @ B2 ) )
% 2.71/1.59 => ( P @ Prod ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_137_old_Oprod_Oinducts,axiom,
% 2.71/1.59 ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 2.71/1.59 ( ! [A2: produc2041926651_state,B2: produc2041926651_state] : ( P @ ( produc1909270103_state @ A2 @ B2 ) )
% 2.71/1.59 => ( P @ Prod ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_138_old_Oprod_Oinducts,axiom,
% 2.71/1.59 ! [P: produc186437863_state > $o,Prod: produc186437863_state] :
% 2.71/1.59 ( ! [A2: produc410756839_state,B2: produc410756839_state] : ( P @ ( produc2065881943_state @ A2 @ B2 ) )
% 2.71/1.59 => ( P @ Prod ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_139_not__Cons__self2,axiom,
% 2.71/1.59 ! [X: com,Xs: list_com] :
% 2.71/1.59 ( ( cons_com @ X @ Xs )
% 2.71/1.59 != Xs ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_140_Suc__inject,axiom,
% 2.71/1.59 ! [X: nat,Y: nat] :
% 2.71/1.59 ( ( ( suc @ X )
% 2.71/1.59 = ( suc @ Y ) )
% 2.71/1.59 => ( X = Y ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_141_n__not__Suc__n,axiom,
% 2.71/1.59 ! [N: nat] :
% 2.71/1.59 ( N
% 2.71/1.59 != ( suc @ N ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_142_inf__cases,axiom,
% 2.71/1.59 ! [C: com,Cs3: list_com,S: state] :
% 2.71/1.59 ( ( pHoare2126160787le_inf @ ( cons_com @ C @ Cs3 ) @ S )
% 2.71/1.59 => ( ( pHoare2126160787le_inf @ ( cons_com @ C @ nil_com ) @ S )
% 2.71/1.59 | ? [T2: state] :
% 2.71/1.59 ( ( exec @ S @ C @ T2 )
% 2.71/1.59 & ( pHoare2126160787le_inf @ Cs3 @ T2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_143_nat_Odistinct_I1_J,axiom,
% 2.71/1.59 ! [X2: nat] :
% 2.71/1.59 ( zero_zero_nat
% 2.71/1.59 != ( suc @ X2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_144_old_Onat_Odistinct_I2_J,axiom,
% 2.71/1.59 ! [Nat2: nat] :
% 2.71/1.59 ( ( suc @ Nat2 )
% 2.71/1.59 != zero_zero_nat ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_145_old_Onat_Odistinct_I1_J,axiom,
% 2.71/1.59 ! [Nat2: nat] :
% 2.71/1.59 ( zero_zero_nat
% 2.71/1.59 != ( suc @ Nat2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_146_nat_OdiscI,axiom,
% 2.71/1.59 ! [Nat: nat,X2: nat] :
% 2.71/1.59 ( ( Nat
% 2.71/1.59 = ( suc @ X2 ) )
% 2.71/1.59 => ( Nat != zero_zero_nat ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_147_nat__induct,axiom,
% 2.71/1.59 ! [P: nat > $o,N: nat] :
% 2.71/1.59 ( ( P @ zero_zero_nat )
% 2.71/1.59 => ( ! [N2: nat] :
% 2.71/1.59 ( ( P @ N2 )
% 2.71/1.59 => ( P @ ( suc @ N2 ) ) )
% 2.71/1.59 => ( P @ N ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_148_diff__induct,axiom,
% 2.71/1.59 ! [P: nat > nat > $o,M: nat,N: nat] :
% 2.71/1.59 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 2.71/1.59 => ( ! [Y2: nat] : ( P @ zero_zero_nat @ ( suc @ Y2 ) )
% 2.71/1.59 => ( ! [X3: nat,Y2: nat] :
% 2.71/1.59 ( ( P @ X3 @ Y2 )
% 2.71/1.59 => ( P @ ( suc @ X3 ) @ ( suc @ Y2 ) ) )
% 2.71/1.59 => ( P @ M @ N ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_149_zero__induct,axiom,
% 2.71/1.59 ! [P: nat > $o,K: nat] :
% 2.71/1.59 ( ( P @ K )
% 2.71/1.59 => ( ! [N2: nat] :
% 2.71/1.59 ( ( P @ ( suc @ N2 ) )
% 2.71/1.59 => ( P @ N2 ) )
% 2.71/1.59 => ( P @ zero_zero_nat ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_150_Suc__neq__Zero,axiom,
% 2.71/1.59 ! [M: nat] :
% 2.71/1.59 ( ( suc @ M )
% 2.71/1.59 != zero_zero_nat ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_151_Zero__neq__Suc,axiom,
% 2.71/1.59 ! [M: nat] :
% 2.71/1.59 ( zero_zero_nat
% 2.71/1.59 != ( suc @ M ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_152_Zero__not__Suc,axiom,
% 2.71/1.59 ! [M: nat] :
% 2.71/1.59 ( zero_zero_nat
% 2.71/1.59 != ( suc @ M ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_153_old_Onat_Oexhaust,axiom,
% 2.71/1.59 ! [Y: nat] :
% 2.71/1.59 ( ( Y != zero_zero_nat )
% 2.71/1.59 => ~ ! [Nat3: nat] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( suc @ Nat3 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_154_old_Onat_Oinducts,axiom,
% 2.71/1.59 ! [P: nat > $o,Nat: nat] :
% 2.71/1.59 ( ( P @ zero_zero_nat )
% 2.71/1.59 => ( ! [Nat3: nat] :
% 2.71/1.59 ( ( P @ Nat3 )
% 2.71/1.59 => ( P @ ( suc @ Nat3 ) ) )
% 2.71/1.59 => ( P @ Nat ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_155_not0__implies__Suc,axiom,
% 2.71/1.59 ! [N: nat] :
% 2.71/1.59 ( ( N != zero_zero_nat )
% 2.71/1.59 => ? [M2: nat] :
% 2.71/1.59 ( N
% 2.71/1.59 = ( suc @ M2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_156_list_Odistinct_I1_J,axiom,
% 2.71/1.59 ! [X21: com,X22: list_com] :
% 2.71/1.59 ( nil_com
% 2.71/1.59 != ( cons_com @ X21 @ X22 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_157_list_OdiscI,axiom,
% 2.71/1.59 ! [List: list_com,X21: com,X22: list_com] :
% 2.71/1.59 ( ( List
% 2.71/1.59 = ( cons_com @ X21 @ X22 ) )
% 2.71/1.59 => ( List != nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_158_list_Oexhaust,axiom,
% 2.71/1.59 ! [Y: list_com] :
% 2.71/1.59 ( ( Y != nil_com )
% 2.71/1.59 => ~ ! [X212: com,X222: list_com] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( cons_com @ X212 @ X222 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_159_list_Oinducts,axiom,
% 2.71/1.59 ! [P: list_com > $o,List: list_com] :
% 2.71/1.59 ( ( P @ nil_com )
% 2.71/1.59 => ( ! [X12: com,X23: list_com] :
% 2.71/1.59 ( ( P @ X23 )
% 2.71/1.59 => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 2.71/1.59 => ( P @ List ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_160_neq__Nil__conv,axiom,
% 2.71/1.59 ! [Xs: list_com] :
% 2.71/1.59 ( ( Xs != nil_com )
% 2.71/1.59 = ( ? [Y3: com,Ys: list_com] :
% 2.71/1.59 ( Xs
% 2.71/1.59 = ( cons_com @ Y3 @ Ys ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_161_list__induct2_H,axiom,
% 2.71/1.59 ! [P: list_com > list_com > $o,Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( P @ nil_com @ nil_com )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com] : ( P @ ( cons_com @ X3 @ Xs2 ) @ nil_com )
% 2.71/1.59 => ( ! [Y2: com,Ys3: list_com] : ( P @ nil_com @ ( cons_com @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com,Y2: com,Ys3: list_com] :
% 2.71/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) )
% 2.71/1.59 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_162_splice_Oinduct,axiom,
% 2.71/1.59 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 2.71/1.59 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 2.71/1.59 ( ( P @ Ys3 @ Xs2 )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) )
% 2.71/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_163_induct__list012,axiom,
% 2.71/1.59 ! [P: list_com > $o,Xs: list_com] :
% 2.71/1.59 ( ( P @ nil_com )
% 2.71/1.59 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 2.71/1.59 => ( ! [X3: com,Y2: com,Zs: list_com] :
% 2.71/1.59 ( ( P @ Zs )
% 2.71/1.59 => ( ( P @ ( cons_com @ Y2 @ Zs ) )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Zs ) ) ) ) )
% 2.71/1.59 => ( P @ Xs ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_164_shuffles_Oinduct,axiom,
% 2.71/1.59 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 2.71/1.59 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 2.71/1.59 => ( ! [Xs2: list_com] : ( P @ Xs2 @ nil_com )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com,Y2: com,Ys3: list_com] :
% 2.71/1.59 ( ( P @ Xs2 @ ( cons_com @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( P @ ( cons_com @ X3 @ Xs2 ) @ Ys3 )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) ) )
% 2.71/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_165_transpose_Ocases,axiom,
% 2.71/1.59 ! [X: list_list_com] :
% 2.71/1.59 ( ( X != nil_list_com )
% 2.71/1.59 => ( ! [Xss: list_list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( cons_list_com @ nil_com @ Xss ) )
% 2.71/1.59 => ~ ! [X3: com,Xs2: list_com,Xss: list_list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( cons_list_com @ ( cons_com @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_166_remdups__adj_Ocases,axiom,
% 2.71/1.59 ! [X: list_com] :
% 2.71/1.59 ( ( X != nil_com )
% 2.71/1.59 => ( ! [X3: com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( cons_com @ X3 @ nil_com ) )
% 2.71/1.59 => ~ ! [X3: com,Y2: com,Xs2: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_167_sorted__wrt_Oinduct,axiom,
% 2.71/1.59 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 2.71/1.59 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 2.71/1.59 => ( ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 2.71/1.59 ( ( P @ P3 @ Ys3 )
% 2.71/1.59 => ( P @ P3 @ ( cons_com @ X3 @ Ys3 ) ) )
% 2.71/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_168_remdups__adj_Oinduct,axiom,
% 2.71/1.59 ! [P: list_com > $o,A0: list_com] :
% 2.71/1.59 ( ( P @ nil_com )
% 2.71/1.59 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 2.71/1.59 => ( ! [X3: com,Y2: com,Xs2: list_com] :
% 2.71/1.59 ( ( ( X3 = Y2 )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ Xs2 ) ) )
% 2.71/1.59 => ( ( ( X3 != Y2 )
% 2.71/1.59 => ( P @ ( cons_com @ Y2 @ Xs2 ) ) )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) ) )
% 2.71/1.59 => ( P @ A0 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_169_successively_Oinduct,axiom,
% 2.71/1.59 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 2.71/1.59 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 2.71/1.59 => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 2.71/1.59 => ( ! [P3: com > com > $o,X3: com,Y2: com,Xs2: list_com] :
% 2.71/1.59 ( ( P @ P3 @ ( cons_com @ Y2 @ Xs2 ) )
% 2.71/1.59 => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) )
% 2.71/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_170_list__nonempty__induct,axiom,
% 2.71/1.59 ! [Xs: list_com,P: list_com > $o] :
% 2.71/1.59 ( ( Xs != nil_com )
% 2.71/1.59 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com] :
% 2.71/1.59 ( ( Xs2 != nil_com )
% 2.71/1.59 => ( ( P @ Xs2 )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ Xs2 ) ) ) )
% 2.71/1.59 => ( P @ Xs ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_171_map__tailrec__rev_Oinduct,axiom,
% 2.71/1.59 ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 2.71/1.59 ( ! [F2: com > com,X_1: list_com] : ( P @ F2 @ nil_com @ X_1 )
% 2.71/1.59 => ( ! [F2: com > com,A2: com,As: list_com,Bs: list_com] :
% 2.71/1.59 ( ( P @ F2 @ As @ ( cons_com @ ( F2 @ A2 ) @ Bs ) )
% 2.71/1.59 => ( P @ F2 @ ( cons_com @ A2 @ As ) @ Bs ) )
% 2.71/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_172_splice_Ocases,axiom,
% 2.71/1.59 ! [X: produc258871771st_com] :
% 2.71/1.59 ( ! [Ys3: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 2.71/1.59 => ~ ! [X3: com,Xs2: list_com,Ys3: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_173_shuffles_Ocases,axiom,
% 2.71/1.59 ! [X: produc258871771st_com] :
% 2.71/1.59 ( ! [Ys3: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1307105171st_com @ nil_com @ Ys3 ) )
% 2.71/1.59 => ( ! [Xs2: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1307105171st_com @ Xs2 @ nil_com ) )
% 2.71/1.59 => ~ ! [X3: com,Xs2: list_com,Y2: com,Ys3: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_174_sorted__wrt_Ocases,axiom,
% 2.71/1.59 ! [X: produc2058209240st_com] :
% 2.71/1.59 ( ! [P3: com > com > $o] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 2.71/1.59 => ~ ! [P3: com > com > $o,X3: com,Ys3: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys3 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_175_successively_Ocases,axiom,
% 2.71/1.59 ! [X: produc2058209240st_com] :
% 2.71/1.59 ( ! [P3: com > com > $o] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 2.71/1.59 => ( ! [P3: com > com > $o,X3: com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 2.71/1.59 => ~ ! [P3: com > com > $o,X3: com,Y2: com,Xs2: list_com] :
% 2.71/1.59 ( X
% 2.71/1.59 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_176_exec__impl__execs,axiom,
% 2.71/1.59 ! [S: state,C: com,S2: state,Cs3: list_com] :
% 2.71/1.59 ( ( exec @ S @ C @ S2 )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs3 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_177_prod__cases3,axiom,
% 2.71/1.59 ! [Y: produc410756839_state] :
% 2.71/1.59 ~ ! [A2: produc2041926651_state,B2: list_com,C3: state] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( produc1909270103_state @ A2 @ ( produc1204172211_state @ B2 @ C3 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_178_prod__cases3,axiom,
% 2.71/1.59 ! [Y: produc186437863_state] :
% 2.71/1.59 ~ ! [A2: produc410756839_state,B2: produc2041926651_state,C3: produc2041926651_state] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ C3 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_179_prod__cases4,axiom,
% 2.71/1.59 ! [Y: produc186437863_state] :
% 2.71/1.59 ~ ! [A2: produc410756839_state,B2: produc2041926651_state,C3: list_com,D: state] :
% 2.71/1.59 ( Y
% 2.71/1.59 != ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ ( produc1204172211_state @ C3 @ D ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_180_prod__induct3,axiom,
% 2.71/1.59 ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 2.71/1.59 ( ! [A2: produc2041926651_state,B2: list_com,C3: state] : ( P @ ( produc1909270103_state @ A2 @ ( produc1204172211_state @ B2 @ C3 ) ) )
% 2.71/1.59 => ( P @ X ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_181_prod__induct3,axiom,
% 2.71/1.59 ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 2.71/1.59 ( ! [A2: produc410756839_state,B2: produc2041926651_state,C3: produc2041926651_state] : ( P @ ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ C3 ) ) )
% 2.71/1.59 => ( P @ X ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_182_prod__induct4,axiom,
% 2.71/1.59 ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 2.71/1.59 ( ! [A2: produc410756839_state,B2: produc2041926651_state,C3: list_com,D: state] : ( P @ ( produc2065881943_state @ A2 @ ( produc1909270103_state @ B2 @ ( produc1204172211_state @ C3 @ D ) ) ) )
% 2.71/1.59 => ( P @ X ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_183_exec1__pres__termis,axiom,
% 2.71/1.59 ! [Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ( ( pHoare806997636termis @ Cs3 @ S )
% 2.71/1.59 => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_184_exec1E_I3_J,axiom,
% 2.71/1.59 ! [C1: com,C22: com,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ~ ( ( Cs
% 2.71/1.59 = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs3 ) ) )
% 2.71/1.59 => ( S2 != S ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_185_exec1_OSemi,axiom,
% 2.71/1.59 ! [C1: com,C22: com,Cs3: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs3 ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_186_n__lists__Nil,axiom,
% 2.71/1.59 ! [N: nat] :
% 2.71/1.59 ( ( ( N = zero_zero_nat )
% 2.71/1.59 => ( ( n_lists_com @ N @ nil_com )
% 2.71/1.59 = ( cons_list_com @ nil_com @ nil_list_com ) ) )
% 2.71/1.59 & ( ( N != zero_zero_nat )
% 2.71/1.59 => ( ( n_lists_com @ N @ nil_com )
% 2.71/1.59 = nil_list_com ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_187_exec1E_I2_J,axiom,
% 2.71/1.59 ! [F: state > set_state,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ~ ( ( Cs = Cs3 )
% 2.71/1.59 => ~ ( member_state @ S2 @ ( F @ S ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_188_exec1_ODo,axiom,
% 2.71/1.59 ! [T: state,F: state > set_state,S: state,Cs3: list_com] :
% 2.71/1.59 ( ( member_state @ T @ ( F @ S ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs3 @ T ) ) @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_189_n__lists_Osimps_I1_J,axiom,
% 2.71/1.59 ! [Xs: list_com] :
% 2.71/1.59 ( ( n_lists_com @ zero_zero_nat @ Xs )
% 2.71/1.59 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_190_termi_OSemi,axiom,
% 2.71/1.59 ! [C1: com,S0: state,C22: com] :
% 2.71/1.59 ( ( termi @ C1 @ S0 )
% 2.71/1.59 => ( ! [S1: state] :
% 2.71/1.59 ( ( exec @ S0 @ C1 @ S1 )
% 2.71/1.59 => ( termi @ C22 @ S1 ) )
% 2.71/1.59 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_191_com_Oinject_I2_J,axiom,
% 2.71/1.59 ! [X21: com,X22: com,Y21: com,Y222: com] :
% 2.71/1.59 ( ( ( semi @ X21 @ X22 )
% 2.71/1.59 = ( semi @ Y21 @ Y222 ) )
% 2.71/1.59 = ( ( X21 = Y21 )
% 2.71/1.59 & ( X22 = Y222 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_192_com_Oinject_I1_J,axiom,
% 2.71/1.59 ! [X1: state > set_state,Y1: state > set_state] :
% 2.71/1.59 ( ( ( do @ X1 )
% 2.71/1.59 = ( do @ Y1 ) )
% 2.71/1.59 = ( X1 = Y1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_193_com_Odistinct_I1_J,axiom,
% 2.71/1.59 ! [X1: state > set_state,X21: com,X22: com] :
% 2.71/1.59 ( ( do @ X1 )
% 2.71/1.59 != ( semi @ X21 @ X22 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_194_exec_ODo,axiom,
% 2.71/1.59 ! [T: state,F: state > set_state,S: state] :
% 2.71/1.59 ( ( member_state @ T @ ( F @ S ) )
% 2.71/1.59 => ( exec @ S @ ( do @ F ) @ T ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_195_exec_OSemi,axiom,
% 2.71/1.59 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 2.71/1.59 ( ( exec @ S0 @ C1 @ S12 )
% 2.71/1.59 => ( ( exec @ S12 @ C22 @ S22 )
% 2.71/1.59 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_196_product__lists_Osimps_I1_J,axiom,
% 2.71/1.59 ( ( product_lists_com @ nil_list_com )
% 2.71/1.59 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_197_subseqs_Osimps_I1_J,axiom,
% 2.71/1.59 ( ( subseqs_com @ nil_com )
% 2.71/1.59 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_198_exec1E_I4_J,axiom,
% 2.71/1.59 ! [B: state > $o,C1: com,C22: com,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ( ( ( Cs
% 2.71/1.59 = ( cons_com @ C1 @ Cs3 ) )
% 2.71/1.59 => ( ( S2 = S )
% 2.71/1.59 => ~ ( B @ S ) ) )
% 2.71/1.59 => ~ ( ( Cs
% 2.71/1.59 = ( cons_com @ C22 @ Cs3 ) )
% 2.71/1.59 => ( ( S2 = S )
% 2.71/1.59 => ( B @ S ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_199_com_Oinject_I3_J,axiom,
% 2.71/1.59 ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 2.71/1.59 ( ( ( cond @ X31 @ X322 @ X33 )
% 2.71/1.59 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 2.71/1.59 = ( ( X31 = Y31 )
% 2.71/1.59 & ( X322 = Y32 )
% 2.71/1.59 & ( X33 = Y33 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_200_exec_OIfTrue,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C1: com,T: state,C22: com] :
% 2.71/1.59 ( ( B @ S )
% 2.71/1.59 => ( ( exec @ S @ C1 @ T )
% 2.71/1.59 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_201_exec_OIfFalse,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C22: com,T: state,C1: com] :
% 2.71/1.59 ( ~ ( B @ S )
% 2.71/1.59 => ( ( exec @ S @ C22 @ T )
% 2.71/1.59 => ( exec @ S @ ( cond @ B @ C1 @ C22 ) @ T ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_202_termi_OIfTrue,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C1: com,C22: com] :
% 2.71/1.59 ( ( B @ S )
% 2.71/1.59 => ( ( termi @ C1 @ S )
% 2.71/1.59 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_203_termi_OIfFalse,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C22: com,C1: com] :
% 2.71/1.59 ( ~ ( B @ S )
% 2.71/1.59 => ( ( termi @ C22 @ S )
% 2.71/1.59 => ( termi @ ( cond @ B @ C1 @ C22 ) @ S ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_204_com_Odistinct_I3_J,axiom,
% 2.71/1.59 ! [X1: state > set_state,X31: state > $o,X322: com,X33: com] :
% 2.71/1.59 ( ( do @ X1 )
% 2.71/1.59 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_205_com_Odistinct_I11_J,axiom,
% 2.71/1.59 ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 2.71/1.59 ( ( semi @ X21 @ X22 )
% 2.71/1.59 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_206_exec1_OIfFalse,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C1: com,C22: com,Cs3: list_com] :
% 2.71/1.59 ( ~ ( B @ S )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs3 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_207_exec1_OIfTrue,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C1: com,C22: com,Cs3: list_com] :
% 2.71/1.59 ( ( B @ S )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs3 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_208_gen__length__code_I2_J,axiom,
% 2.71/1.59 ! [N: nat,X: com,Xs: list_com] :
% 2.71/1.59 ( ( gen_length_com @ N @ ( cons_com @ X @ Xs ) )
% 2.71/1.59 = ( gen_length_com @ ( suc @ N ) @ Xs ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_209_insert__Nil,axiom,
% 2.71/1.59 ! [X: com] :
% 2.71/1.59 ( ( insert_com @ X @ nil_com )
% 2.71/1.59 = ( cons_com @ X @ nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_210_exec1_OWhileFalse,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C: com,Cs3: list_com] :
% 2.71/1.59 ( ~ ( B @ S )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs3 @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_211_com_Oinject_I4_J,axiom,
% 2.71/1.59 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 2.71/1.59 ( ( ( while @ X41 @ X42 )
% 2.71/1.59 = ( while @ Y41 @ Y42 ) )
% 2.71/1.59 = ( ( X41 = Y41 )
% 2.71/1.59 & ( X42 = Y42 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_212_com_Odistinct_I19_J,axiom,
% 2.71/1.59 ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 2.71/1.59 ( ( cond @ X31 @ X322 @ X33 )
% 2.71/1.59 != ( while @ X41 @ X42 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_213_while__termiE,axiom,
% 2.71/1.59 ! [B: state > $o,C: com,S: state] :
% 2.71/1.59 ( ( termi @ ( while @ B @ C ) @ S )
% 2.71/1.59 => ( ( B @ S )
% 2.71/1.59 => ( termi @ C @ S ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_214_exec_OWhileFalse,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C: com] :
% 2.71/1.59 ( ~ ( B @ S )
% 2.71/1.59 => ( exec @ S @ ( while @ B @ C ) @ S ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_215_exec_OWhileTrue,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C: com,T: state,U: state] :
% 2.71/1.59 ( ( B @ S )
% 2.71/1.59 => ( ( exec @ S @ C @ T )
% 2.71/1.59 => ( ( exec @ T @ ( while @ B @ C ) @ U )
% 2.71/1.59 => ( exec @ S @ ( while @ B @ C ) @ U ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_216_termi_OWhileFalse,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C: com] :
% 2.71/1.59 ( ~ ( B @ S )
% 2.71/1.59 => ( termi @ ( while @ B @ C ) @ S ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_217_com_Odistinct_I5_J,axiom,
% 2.71/1.59 ! [X1: state > set_state,X41: state > $o,X42: com] :
% 2.71/1.59 ( ( do @ X1 )
% 2.71/1.59 != ( while @ X41 @ X42 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_218_com_Odistinct_I13_J,axiom,
% 2.71/1.59 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 2.71/1.59 ( ( semi @ X21 @ X22 )
% 2.71/1.59 != ( while @ X41 @ X42 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_219_termi_OWhileTrue,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C: com] :
% 2.71/1.59 ( ( B @ S )
% 2.71/1.59 => ( ( termi @ C @ S )
% 2.71/1.59 => ( ! [T2: state] :
% 2.71/1.59 ( ( exec @ S @ C @ T2 )
% 2.71/1.59 => ( termi @ ( while @ B @ C ) @ T2 ) )
% 2.71/1.59 => ( termi @ ( while @ B @ C ) @ S ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_220_while__termiE2,axiom,
% 2.71/1.59 ! [B: state > $o,C: com,S: state,T: state] :
% 2.71/1.59 ( ( termi @ ( while @ B @ C ) @ S )
% 2.71/1.59 => ( ( B @ S )
% 2.71/1.59 => ( ( exec @ S @ C @ T )
% 2.71/1.59 => ( termi @ ( while @ B @ C ) @ T ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_221_gen__length__code_I1_J,axiom,
% 2.71/1.59 ! [N: nat] :
% 2.71/1.59 ( ( gen_length_com @ N @ nil_com )
% 2.71/1.59 = N ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_222_termi__while,axiom,
% 2.71/1.59 ! [B: state > $o,C: com,F: nat > state,K: nat] :
% 2.71/1.59 ( ( termi @ ( while @ B @ C ) @ ( F @ K ) )
% 2.71/1.59 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) )
% 2.71/1.59 => ? [I: nat] :
% 2.71/1.59 ~ ( B @ ( F @ I ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_223_termi__while__lemma,axiom,
% 2.71/1.59 ! [W: com,Fk: state,F: nat > state,K: nat,B: state > $o,C: com] :
% 2.71/1.59 ( ( termi @ W @ Fk )
% 2.71/1.59 => ( ( ( Fk
% 2.71/1.59 = ( F @ K ) )
% 2.71/1.59 & ( W
% 2.71/1.59 = ( while @ B @ C ) )
% 2.71/1.59 & ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) ) )
% 2.71/1.59 => ? [I: nat] :
% 2.71/1.59 ~ ( B @ ( F @ I ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_224_exec1E_I5_J,axiom,
% 2.71/1.59 ! [B: state > $o,C: com,Cs3: list_com,S: state,Cs: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ( ( ( Cs = Cs3 )
% 2.71/1.59 => ( ( S2 = S )
% 2.71/1.59 => ( B @ S ) ) )
% 2.71/1.59 => ~ ( ( Cs
% 2.71/1.59 = ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) ) )
% 2.71/1.59 => ( ( S2 = S )
% 2.71/1.59 => ~ ( B @ S ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_225_exec1_OWhileTrue,axiom,
% 2.71/1.59 ! [B: state > $o,S: state,C: com,Cs3: list_com] :
% 2.71/1.59 ( ( B @ S )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B @ C ) @ Cs3 ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_226_nths__singleton,axiom,
% 2.71/1.59 ! [A4: set_nat,X: com] :
% 2.71/1.59 ( ( ( member_nat @ zero_zero_nat @ A4 )
% 2.71/1.59 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 2.71/1.59 = ( cons_com @ X @ nil_com ) ) )
% 2.71/1.59 & ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 2.71/1.59 => ( ( nths_com @ ( cons_com @ X @ nil_com ) @ A4 )
% 2.71/1.59 = nil_com ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_227_app__execs,axiom,
% 2.71/1.59 ! [Cs3: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs3 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_228_listrel_Ocases,axiom,
% 2.71/1.59 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ( ( ( A1 = nil_com )
% 2.71/1.59 => ( A22 != nil_com ) )
% 2.71/1.59 => ~ ! [X3: com,Y2: com,Xs2: list_com] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_com @ X3 @ Xs2 ) )
% 2.71/1.59 => ! [Ys3: list_com] :
% 2.71/1.59 ( ( A22
% 2.71/1.59 = ( cons_com @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_229_listrel_Ocases,axiom,
% 2.71/1.59 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 2.71/1.59 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 => ( ( ( A1 = nil_list_com )
% 2.71/1.59 => ( A22 != nil_state ) )
% 2.71/1.59 => ~ ! [X3: list_com,Y2: state,Xs2: list_list_com] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_list_com @ X3 @ Xs2 ) )
% 2.71/1.59 => ! [Ys3: list_state] :
% 2.71/1.59 ( ( A22
% 2.71/1.59 = ( cons_state @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_230_listrel_Ocases,axiom,
% 2.71/1.59 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 => ( ( ( A1 = nil_Pr1844458753_state )
% 2.71/1.59 => ( A22 != nil_Pr1844458753_state ) )
% 2.71/1.59 => ~ ! [X3: produc2041926651_state,Y2: produc2041926651_state,Xs2: list_P1040014977_state] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 2.71/1.59 => ! [Ys3: list_P1040014977_state] :
% 2.71/1.59 ( ( A22
% 2.71/1.59 = ( cons_P465369265_state @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_231_listrel_Ocases,axiom,
% 2.71/1.59 ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 => ( ( ( A1 = nil_Pr1347322605_state )
% 2.71/1.59 => ( A22 != nil_Pr1347322605_state ) )
% 2.71/1.59 => ~ ! [X3: produc410756839_state,Y2: produc410756839_state,Xs2: list_P890094829_state] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_P438230685_state @ X3 @ Xs2 ) )
% 2.71/1.59 => ! [Ys3: list_P890094829_state] :
% 2.71/1.59 ( ( A22
% 2.71/1.59 = ( cons_P438230685_state @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_232_same__append__eq,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ Ys2 )
% 2.71/1.59 = ( append_com @ Xs @ Zs2 ) )
% 2.71/1.59 = ( Ys2 = Zs2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_233_append__same__eq,axiom,
% 2.71/1.59 ! [Ys2: list_com,Xs: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( ( append_com @ Ys2 @ Xs )
% 2.71/1.59 = ( append_com @ Zs2 @ Xs ) )
% 2.71/1.59 = ( Ys2 = Zs2 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_234_append__assoc,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( append_com @ ( append_com @ Xs @ Ys2 ) @ Zs2 )
% 2.71/1.59 = ( append_com @ Xs @ ( append_com @ Ys2 @ Zs2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_235_append_Oassoc,axiom,
% 2.71/1.59 ! [A: list_com,B: list_com,C: list_com] :
% 2.71/1.59 ( ( append_com @ ( append_com @ A @ B ) @ C )
% 2.71/1.59 = ( append_com @ A @ ( append_com @ B @ C ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_236_append__Nil2,axiom,
% 2.71/1.59 ! [Xs: list_com] :
% 2.71/1.59 ( ( append_com @ Xs @ nil_com )
% 2.71/1.59 = Xs ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_237_append__self__conv,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ Ys2 )
% 2.71/1.59 = Xs )
% 2.71/1.59 = ( Ys2 = nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_238_self__append__conv,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( append_com @ Xs @ Ys2 ) )
% 2.71/1.59 = ( Ys2 = nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_239_append__self__conv2,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ Ys2 )
% 2.71/1.59 = Ys2 )
% 2.71/1.59 = ( Xs = nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_240_self__append__conv2,axiom,
% 2.71/1.59 ! [Ys2: list_com,Xs: list_com] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( append_com @ Xs @ Ys2 ) )
% 2.71/1.59 = ( Xs = nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_241_Nil__is__append__conv,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( nil_com
% 2.71/1.59 = ( append_com @ Xs @ Ys2 ) )
% 2.71/1.59 = ( ( Xs = nil_com )
% 2.71/1.59 & ( Ys2 = nil_com ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_242_append__is__Nil__conv,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ Ys2 )
% 2.71/1.59 = nil_com )
% 2.71/1.59 = ( ( Xs = nil_com )
% 2.71/1.59 & ( Ys2 = nil_com ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_243_append_Oright__neutral,axiom,
% 2.71/1.59 ! [A: list_com] :
% 2.71/1.59 ( ( append_com @ A @ nil_com )
% 2.71/1.59 = A ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_244_nths__nil,axiom,
% 2.71/1.59 ! [A4: set_nat] :
% 2.71/1.59 ( ( nths_com @ nil_com @ A4 )
% 2.71/1.59 = nil_com ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_245_append1__eq__conv,axiom,
% 2.71/1.59 ! [Xs: list_com,X: com,Ys2: list_com,Y: com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ ( cons_com @ X @ nil_com ) )
% 2.71/1.59 = ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) )
% 2.71/1.59 = ( ( Xs = Ys2 )
% 2.71/1.59 & ( X = Y ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_246_listrel__rtrancl__refl,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_247_listrel__rtrancl__refl,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,R: set_Pr2096893127_state] : ( member423306384_state @ ( produc1354769367_state @ Xs @ Xs ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_248_append__eq__append__conv2,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,Zs2: list_com,Ts: list_com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ Ys2 )
% 2.71/1.59 = ( append_com @ Zs2 @ Ts ) )
% 2.71/1.59 = ( ? [Us: list_com] :
% 2.71/1.59 ( ( ( Xs
% 2.71/1.59 = ( append_com @ Zs2 @ Us ) )
% 2.71/1.59 & ( ( append_com @ Us @ Ys2 )
% 2.71/1.59 = Ts ) )
% 2.71/1.59 | ( ( ( append_com @ Xs @ Us )
% 2.71/1.59 = Zs2 )
% 2.71/1.59 & ( Ys2
% 2.71/1.59 = ( append_com @ Us @ Ts ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_249_append__eq__appendI,axiom,
% 2.71/1.59 ! [Xs: list_com,Xs1: list_com,Zs2: list_com,Ys2: list_com,Us2: list_com] :
% 2.71/1.59 ( ( ( append_com @ Xs @ Xs1 )
% 2.71/1.59 = Zs2 )
% 2.71/1.59 => ( ( Ys2
% 2.71/1.59 = ( append_com @ Xs1 @ Us2 ) )
% 2.71/1.59 => ( ( append_com @ Xs @ Ys2 )
% 2.71/1.59 = ( append_com @ Zs2 @ Us2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_250_eq__Nil__appendI,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( Xs = Ys2 )
% 2.71/1.59 => ( Xs
% 2.71/1.59 = ( append_com @ nil_com @ Ys2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_251_append__Nil,axiom,
% 2.71/1.59 ! [Ys2: list_com] :
% 2.71/1.59 ( ( append_com @ nil_com @ Ys2 )
% 2.71/1.59 = Ys2 ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_252_append_Oleft__neutral,axiom,
% 2.71/1.59 ! [A: list_com] :
% 2.71/1.59 ( ( append_com @ nil_com @ A )
% 2.71/1.59 = A ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_253_Cons__eq__appendI,axiom,
% 2.71/1.59 ! [X: com,Xs1: list_com,Ys2: list_com,Xs: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( ( cons_com @ X @ Xs1 )
% 2.71/1.59 = Ys2 )
% 2.71/1.59 => ( ( Xs
% 2.71/1.59 = ( append_com @ Xs1 @ Zs2 ) )
% 2.71/1.59 => ( ( cons_com @ X @ Xs )
% 2.71/1.59 = ( append_com @ Ys2 @ Zs2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_254_append__Cons,axiom,
% 2.71/1.59 ! [X: com,Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( append_com @ ( cons_com @ X @ Xs ) @ Ys2 )
% 2.71/1.59 = ( cons_com @ X @ ( append_com @ Xs @ Ys2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_255_rev__nonempty__induct,axiom,
% 2.71/1.59 ! [Xs: list_com,P: list_com > $o] :
% 2.71/1.59 ( ( Xs != nil_com )
% 2.71/1.59 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com] :
% 2.71/1.59 ( ( Xs2 != nil_com )
% 2.71/1.59 => ( ( P @ Xs2 )
% 2.71/1.59 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 2.71/1.59 => ( P @ Xs ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_256_append__eq__Cons__conv,axiom,
% 2.71/1.59 ! [Ys2: list_com,Zs2: list_com,X: com,Xs: list_com] :
% 2.71/1.59 ( ( ( append_com @ Ys2 @ Zs2 )
% 2.71/1.59 = ( cons_com @ X @ Xs ) )
% 2.71/1.59 = ( ( ( Ys2 = nil_com )
% 2.71/1.59 & ( Zs2
% 2.71/1.59 = ( cons_com @ X @ Xs ) ) )
% 2.71/1.59 | ? [Ys4: list_com] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_com @ X @ Ys4 ) )
% 2.71/1.59 & ( ( append_com @ Ys4 @ Zs2 )
% 2.71/1.59 = Xs ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_257_Cons__eq__append__conv,axiom,
% 2.71/1.59 ! [X: com,Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( ( cons_com @ X @ Xs )
% 2.71/1.59 = ( append_com @ Ys2 @ Zs2 ) )
% 2.71/1.59 = ( ( ( Ys2 = nil_com )
% 2.71/1.59 & ( ( cons_com @ X @ Xs )
% 2.71/1.59 = Zs2 ) )
% 2.71/1.59 | ? [Ys4: list_com] :
% 2.71/1.59 ( ( ( cons_com @ X @ Ys4 )
% 2.71/1.59 = Ys2 )
% 2.71/1.59 & ( Xs
% 2.71/1.59 = ( append_com @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_258_rev__exhaust,axiom,
% 2.71/1.59 ! [Xs: list_com] :
% 2.71/1.59 ( ( Xs != nil_com )
% 2.71/1.59 => ~ ! [Ys3: list_com,Y2: com] :
% 2.71/1.59 ( Xs
% 2.71/1.59 != ( append_com @ Ys3 @ ( cons_com @ Y2 @ nil_com ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_259_rev__induct,axiom,
% 2.71/1.59 ! [P: list_com > $o,Xs: list_com] :
% 2.71/1.59 ( ( P @ nil_com )
% 2.71/1.59 => ( ! [X3: com,Xs2: list_com] :
% 2.71/1.59 ( ( P @ Xs2 )
% 2.71/1.59 => ( P @ ( append_com @ Xs2 @ ( cons_com @ X3 @ nil_com ) ) ) )
% 2.71/1.59 => ( P @ Xs ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_260_listrel_ONil,axiom,
% 2.71/1.59 ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_261_listrel__Nil1,axiom,
% 2.71/1.59 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ( Xs = nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_262_listrel__Nil2,axiom,
% 2.71/1.59 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ( Xs = nil_com ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_263_listrel__rtrancl__trans,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state,Zs2: list_P1040014977_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 2.71/1.59 => ( ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_264_listrel__rtrancl__trans,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state,Zs2: list_P890094829_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 2.71/1.59 => ( ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ Xs @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_265_app__exec,axiom,
% 2.71/1.59 ! [Cs3: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs3 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs3 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_266_listrel__Cons2,axiom,
% 2.71/1.59 ! [Xs: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ~ ! [X3: com,Xs2: list_com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_com @ X3 @ Xs2 ) )
% 2.71/1.59 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 2.71/1.59 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_267_listrel__Cons2,axiom,
% 2.71/1.59 ! [Xs: list_list_com,Y: state,Ys2: list_state,R: set_Pr849496667_state] :
% 2.71/1.59 ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 => ~ ! [X3: list_com,Xs2: list_list_com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_list_com @ X3 @ Xs2 ) )
% 2.71/1.59 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 2.71/1.59 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_268_listrel__Cons2,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 => ~ ! [X3: produc2041926651_state,Xs2: list_P1040014977_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P465369265_state @ X3 @ Xs2 ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 2.71/1.59 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_269_listrel__Cons2,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 => ~ ! [X3: produc410756839_state,Xs2: list_P890094829_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P438230685_state @ X3 @ Xs2 ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R )
% 2.71/1.59 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_270_listrel__Cons1,axiom,
% 2.71/1.59 ! [Y: com,Ys2: list_com,Xs: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys2 ) @ Xs ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ~ ! [Y2: com,Ys3: list_com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_com @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_271_listrel__Cons1,axiom,
% 2.71/1.59 ! [Y: list_com,Ys2: list_list_com,Xs: list_state,R: set_Pr849496667_state] :
% 2.71/1.59 ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys2 ) @ Xs ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 => ~ ! [Y2: state,Ys3: list_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_state @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys2 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_272_listrel__Cons1,axiom,
% 2.71/1.59 ! [Y: produc2041926651_state,Ys2: list_P1040014977_state,Xs: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys2 ) @ Xs ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 => ~ ! [Y2: produc2041926651_state,Ys3: list_P1040014977_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P465369265_state @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_273_listrel__Cons1,axiom,
% 2.71/1.59 ! [Y: produc410756839_state,Ys2: list_P890094829_state,Xs: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ Y @ Ys2 ) @ Xs ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 => ~ ! [Y2: produc410756839_state,Ys3: list_P890094829_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P438230685_state @ Y2 @ Ys3 ) )
% 2.71/1.59 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Y2 ) @ R )
% 2.71/1.59 => ~ ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_274_listrel_OCons,axiom,
% 2.71/1.59 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 2.71/1.59 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_275_listrel_OCons,axiom,
% 2.71/1.59 ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs: list_list_com,Ys2: list_state] :
% 2.71/1.59 ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 2.71/1.59 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs ) @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_276_listrel_OCons,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 2.71/1.59 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_277_listrel_OCons,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state,Ys2: list_P890094829_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 2.71/1.59 => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_278_exec1__only1__aux,axiom,
% 2.71/1.59 ! [Ccs: list_com,S: state,Cs: list_com,T: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ccs @ S ) @ ( produc1204172211_state @ Cs @ T ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ! [C5: com,Cs5: list_com] :
% 2.71/1.59 ( ( Ccs
% 2.71/1.59 = ( cons_com @ C5 @ Cs5 ) )
% 2.71/1.59 => ? [Cs1: list_com] :
% 2.71/1.59 ( Cs
% 2.71/1.59 = ( append_com @ Cs1 @ Cs5 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_279_exec1__only1,axiom,
% 2.71/1.59 ! [C: com,Cs3: list_com,S: state,Cs: list_com,T: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs3 ) @ S ) @ ( produc1204172211_state @ Cs @ T ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ? [Cs1: list_com] :
% 2.71/1.59 ( Cs
% 2.71/1.59 = ( append_com @ Cs1 @ Cs3 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_280_exec1__drop__suffix__aux,axiom,
% 2.71/1.59 ! [Cs12: list_com,S: state,Cs1_2: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs12 @ S ) @ ( produc1204172211_state @ Cs1_2 @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ! [Cs13: list_com,Cs23: list_com,Cs14: list_com] :
% 2.71/1.59 ( ( ( Cs12
% 2.71/1.59 = ( append_com @ Cs13 @ Cs23 ) )
% 2.71/1.59 & ( Cs1_2
% 2.71/1.59 = ( append_com @ Cs14 @ Cs23 ) )
% 2.71/1.59 & ( Cs13 != nil_com ) )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs13 @ S ) @ ( produc1204172211_state @ Cs14 @ S2 ) ) @ pHoare259243666_exec1 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_281_exec1__drop__suffix,axiom,
% 2.71/1.59 ! [Cs15: list_com,Cs22: list_com,S: state,Cs16: list_com,S2: state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs15 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs16 @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 )
% 2.71/1.59 => ( ( Cs15 != nil_com )
% 2.71/1.59 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs15 @ S ) @ ( produc1204172211_state @ Cs16 @ S2 ) ) @ pHoare259243666_exec1 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_282_listrel_Oinducts,axiom,
% 2.71/1.59 ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ( ( P @ nil_com @ nil_com )
% 2.71/1.59 => ( ! [X3: com,Y2: com,Xs2: list_com,Ys3: list_com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys3 ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 => ( ( P @ Xs2 @ Ys3 )
% 2.71/1.59 => ( P @ ( cons_com @ X3 @ Xs2 ) @ ( cons_com @ Y2 @ Ys3 ) ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_283_listrel_Oinducts,axiom,
% 2.71/1.59 ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 2.71/1.59 ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 => ( ( P @ nil_list_com @ nil_state )
% 2.71/1.59 => ( ! [X3: list_com,Y2: state,Xs2: list_list_com,Ys3: list_state] :
% 2.71/1.59 ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys3 ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 => ( ( P @ Xs2 @ Ys3 )
% 2.71/1.59 => ( P @ ( cons_list_com @ X3 @ Xs2 ) @ ( cons_state @ Y2 @ Ys3 ) ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_284_listrel_Oinducts,axiom,
% 2.71/1.59 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 2.71/1.59 => ( ! [X3: produc2041926651_state,Y2: produc2041926651_state,Xs2: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys3 ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 => ( ( P @ Xs2 @ Ys3 )
% 2.71/1.59 => ( P @ ( cons_P465369265_state @ X3 @ Xs2 ) @ ( cons_P465369265_state @ Y2 @ Ys3 ) ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_285_listrel_Oinducts,axiom,
% 2.71/1.59 ! [X1: list_P890094829_state,X2: list_P890094829_state,R: set_Pr2096893127_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ X1 @ X2 ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 => ( ( P @ nil_Pr1347322605_state @ nil_Pr1347322605_state )
% 2.71/1.59 => ( ! [X3: produc410756839_state,Y2: produc410756839_state,Xs2: list_P890094829_state,Ys3: list_P890094829_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys3 ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 => ( ( P @ Xs2 @ Ys3 )
% 2.71/1.59 => ( P @ ( cons_P438230685_state @ X3 @ Xs2 ) @ ( cons_P438230685_state @ Y2 @ Ys3 ) ) ) ) )
% 2.71/1.59 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_286_listrel_Osimps,axiom,
% 2.71/1.59 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 2.71/1.59 = ( ( ( A1 = nil_com )
% 2.71/1.59 & ( A22 = nil_com ) )
% 2.71/1.59 | ? [X4: com,Y3: com,Xs3: list_com,Ys: list_com] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_com @ X4 @ Xs3 ) )
% 2.71/1.59 & ( A22
% 2.71/1.59 = ( cons_com @ Y3 @ Ys ) )
% 2.71/1.59 & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y3 ) @ R )
% 2.71/1.59 & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_287_listrel_Osimps,axiom,
% 2.71/1.59 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 2.71/1.59 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 2.71/1.59 = ( ( ( A1 = nil_list_com )
% 2.71/1.59 & ( A22 = nil_state ) )
% 2.71/1.59 | ? [X4: list_com,Y3: state,Xs3: list_list_com,Ys: list_state] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_list_com @ X4 @ Xs3 ) )
% 2.71/1.59 & ( A22
% 2.71/1.59 = ( cons_state @ Y3 @ Ys ) )
% 2.71/1.59 & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y3 ) @ R )
% 2.71/1.59 & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_288_listrel_Osimps,axiom,
% 2.71/1.59 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 2.71/1.59 = ( ( ( A1 = nil_Pr1844458753_state )
% 2.71/1.59 & ( A22 = nil_Pr1844458753_state ) )
% 2.71/1.59 | ? [X4: produc2041926651_state,Y3: produc2041926651_state,Xs3: list_P1040014977_state,Ys: list_P1040014977_state] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 2.71/1.59 & ( A22
% 2.71/1.59 = ( cons_P465369265_state @ Y3 @ Ys ) )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y3 ) @ R )
% 2.71/1.59 & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_289_listrel_Osimps,axiom,
% 2.71/1.59 ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 2.71/1.59 = ( ( ( A1 = nil_Pr1347322605_state )
% 2.71/1.59 & ( A22 = nil_Pr1347322605_state ) )
% 2.71/1.59 | ? [X4: produc410756839_state,Y3: produc410756839_state,Xs3: list_P890094829_state,Ys: list_P890094829_state] :
% 2.71/1.59 ( ( A1
% 2.71/1.59 = ( cons_P438230685_state @ X4 @ Xs3 ) )
% 2.71/1.59 & ( A22
% 2.71/1.59 = ( cons_P438230685_state @ Y3 @ Ys ) )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ X4 @ Y3 ) @ R )
% 2.71/1.59 & ( member423306384_state @ ( produc1354769367_state @ Xs3 @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_290_bind__simps_I2_J,axiom,
% 2.71/1.59 ! [X: com,Xs: list_com,F: com > list_com] :
% 2.71/1.59 ( ( bind_com_com @ ( cons_com @ X @ Xs ) @ F )
% 2.71/1.59 = ( append_com @ ( F @ X ) @ ( bind_com_com @ Xs @ F ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_291_snoc__listrel1__snoc__iff,axiom,
% 2.71/1.59 ! [Xs: list_com,X: com,Ys2: list_com,Y: com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 2.71/1.59 = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 2.71/1.59 & ( X = Y ) )
% 2.71/1.59 | ( ( Xs = Ys2 )
% 2.71/1.59 & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_292_snoc__listrel1__snoc__iff,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,X: produc2041926651_state,Ys2: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys2 @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 & ( X = Y ) )
% 2.71/1.59 | ( ( Xs = Ys2 )
% 2.71/1.59 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_293_snoc__listrel1__snoc__iff,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,X: produc410756839_state,Ys2: list_P890094829_state,Y: produc410756839_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs @ ( cons_P438230685_state @ X @ nil_Pr1347322605_state ) ) @ ( append221843330_state @ Ys2 @ ( cons_P438230685_state @ Y @ nil_Pr1347322605_state ) ) ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 = ( ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 & ( X = Y ) )
% 2.71/1.59 | ( ( Xs = Ys2 )
% 2.71/1.59 & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_294_maps__simps_I1_J,axiom,
% 2.71/1.59 ! [F: com > list_com,X: com,Xs: list_com] :
% 2.71/1.59 ( ( maps_com_com @ F @ ( cons_com @ X @ Xs ) )
% 2.71/1.59 = ( append_com @ ( F @ X ) @ ( maps_com_com @ F @ Xs ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_295_bind__simps_I1_J,axiom,
% 2.71/1.59 ! [F: com > list_com] :
% 2.71/1.59 ( ( bind_com_com @ nil_com @ F )
% 2.71/1.59 = nil_com ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_296_Cons__listrel1__Cons,axiom,
% 2.71/1.59 ! [X: com,Xs: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 2.71/1.59 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 2.71/1.59 & ( Xs = Ys2 ) )
% 2.71/1.59 | ( ( X = Y )
% 2.71/1.59 & ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_297_Cons__listrel1__Cons,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 2.71/1.59 & ( Xs = Ys2 ) )
% 2.71/1.59 | ( ( X = Y )
% 2.71/1.59 & ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_298_Cons__listrel1__Cons,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Xs: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 2.71/1.59 & ( Xs = Ys2 ) )
% 2.71/1.59 | ( ( X = Y )
% 2.71/1.59 & ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_299_rtrancl__listrel1__ConsI1,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_300_listrel1I2,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ X @ Ys2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_301_not__listrel1__Nil,axiom,
% 2.71/1.59 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_302_not__Nil__listrel1,axiom,
% 2.71/1.59 ! [Xs: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs ) @ ( listrel1_com @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_303_append__listrel1I,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Us2: list_com,Vs: list_com] :
% 2.71/1.59 ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 2.71/1.59 & ( Us2 = Vs ) )
% 2.71/1.59 | ( ( Xs = Ys2 )
% 2.71/1.59 & ( member32358020st_com @ ( produc1307105171st_com @ Us2 @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Us2 ) @ ( append_com @ Ys2 @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_304_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 2.71/1.59 ! [R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 2.71/1.59 = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_305_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 2.71/1.59 ! [R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( listre1244407729_state @ ( transi463013610_state @ R ) )
% 2.71/1.59 = ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_306_maps__simps_I2_J,axiom,
% 2.71/1.59 ! [F: com > list_com] :
% 2.71/1.59 ( ( maps_com_com @ F @ nil_com )
% 2.71/1.59 = nil_com ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_307_listrel1I1,axiom,
% 2.71/1.59 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Xs ) ) @ ( listrel1_com @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_308_listrel1I1,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Xs ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_309_listrel1I1,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Xs ) ) @ ( listre1725776070_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_310_Cons__listrel1E1,axiom,
% 2.71/1.59 ! [X: com,Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ Ys2 ) @ ( listrel1_com @ R ) )
% 2.71/1.59 => ( ! [Y2: com] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_com @ Y2 @ Xs ) )
% 2.71/1.59 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y2 ) @ R ) )
% 2.71/1.59 => ~ ! [Zs: list_com] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_com @ X @ Zs ) )
% 2.71/1.59 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Zs ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_311_Cons__listrel1E1,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 => ( ! [Y2: produc2041926651_state] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_P465369265_state @ Y2 @ Xs ) )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y2 ) @ R ) )
% 2.71/1.59 => ~ ! [Zs: list_P1040014977_state] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_P465369265_state @ X @ Zs ) )
% 2.71/1.59 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Zs ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_312_Cons__listrel1E1,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 => ( ! [Y2: produc410756839_state] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_P438230685_state @ Y2 @ Xs ) )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y2 ) @ R ) )
% 2.71/1.59 => ~ ! [Zs: list_P890094829_state] :
% 2.71/1.59 ( ( Ys2
% 2.71/1.59 = ( cons_P438230685_state @ X @ Zs ) )
% 2.71/1.59 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Zs ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_313_Cons__listrel1E2,axiom,
% 2.71/1.59 ! [Xs: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 2.71/1.59 => ( ! [X3: com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_com @ X3 @ Ys2 ) )
% 2.71/1.59 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 2.71/1.59 => ~ ! [Zs: list_com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_com @ Y @ Zs ) )
% 2.71/1.59 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_314_Cons__listrel1E2,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 => ( ! [X3: produc2041926651_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P465369265_state @ X3 @ Ys2 ) )
% 2.71/1.59 => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 2.71/1.59 => ~ ! [Zs: list_P1040014977_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P465369265_state @ Y @ Zs ) )
% 2.71/1.59 => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_315_Cons__listrel1E2,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 => ( ! [X3: produc410756839_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P438230685_state @ X3 @ Ys2 ) )
% 2.71/1.59 => ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R ) )
% 2.71/1.59 => ~ ! [Zs: list_P890094829_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( cons_P438230685_state @ Y @ Zs ) )
% 2.71/1.59 => ~ ( member423306384_state @ ( produc1354769367_state @ Zs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_316_listrel__reflcl__if__listrel1,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_317_listrel__reflcl__if__listrel1,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_318_listrel1I,axiom,
% 2.71/1.59 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Us2: list_com,Vs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 2.71/1.59 => ( ( Xs
% 2.71/1.59 = ( append_com @ Us2 @ ( cons_com @ X @ Vs ) ) )
% 2.71/1.59 => ( ( Ys2
% 2.71/1.59 = ( append_com @ Us2 @ ( cons_com @ Y @ Vs ) ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_319_listrel1I,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Us2: list_P1040014977_state,Vs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 2.71/1.59 => ( ( Xs
% 2.71/1.59 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ X @ Vs ) ) )
% 2.71/1.59 => ( ( Ys2
% 2.71/1.59 = ( append982487830_state @ Us2 @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_320_listrel1I,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state,Us2: list_P890094829_state,Vs: list_P890094829_state,Ys2: list_P890094829_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 2.71/1.59 => ( ( Xs
% 2.71/1.59 = ( append221843330_state @ Us2 @ ( cons_P438230685_state @ X @ Vs ) ) )
% 2.71/1.59 => ( ( Ys2
% 2.71/1.59 = ( append221843330_state @ Us2 @ ( cons_P438230685_state @ Y @ Vs ) ) )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_321_listrel1E,axiom,
% 2.71/1.59 ! [Xs: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel1_com @ R ) )
% 2.71/1.59 => ~ ! [X3: com,Y2: com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ! [Us3: list_com,Vs2: list_com] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 2.71/1.59 => ( Ys2
% 2.71/1.59 != ( append_com @ Us3 @ ( cons_com @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_322_listrel1E,axiom,
% 2.71/1.59 ! [Xs: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 2.71/1.59 => ~ ! [X3: produc2041926651_state,Y2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 2.71/1.59 => ( Ys2
% 2.71/1.59 != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_323_listrel1E,axiom,
% 2.71/1.59 ! [Xs: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 2.71/1.59 => ~ ! [X3: produc410756839_state,Y2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y2 ) @ R )
% 2.71/1.59 => ! [Us3: list_P890094829_state,Vs2: list_P890094829_state] :
% 2.71/1.59 ( ( Xs
% 2.71/1.59 = ( append221843330_state @ Us3 @ ( cons_P438230685_state @ X3 @ Vs2 ) ) )
% 2.71/1.59 => ( Ys2
% 2.71/1.59 != ( append221843330_state @ Us3 @ ( cons_P438230685_state @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_324_rtrancl__listrel1__ConsI2,axiom,
% 2.71/1.59 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs: list_com,Ys2: list_com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 2.71/1.59 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs ) @ ( cons_com @ Y @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_325_rtrancl__listrel1__ConsI2,axiom,
% 2.71/1.59 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 2.71/1.59 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_326_rtrancl__listrel1__ConsI2,axiom,
% 2.71/1.59 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs: list_P890094829_state,Ys2: list_P890094829_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 2.71/1.59 => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_327_concat__eq__append__conv,axiom,
% 2.71/1.59 ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( ( concat_com @ Xss2 )
% 2.71/1.59 = ( append_com @ Ys2 @ Zs2 ) )
% 2.71/1.59 = ( ( ( Xss2 = nil_list_com )
% 2.71/1.59 => ( ( Ys2 = nil_com )
% 2.71/1.59 & ( Zs2 = nil_com ) ) )
% 2.71/1.59 & ( ( Xss2 != nil_list_com )
% 2.71/1.59 => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 2.71/1.59 ( ( Xss2
% 2.71/1.59 = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.71/1.59 & ( Ys2
% 2.71/1.59 = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 2.71/1.59 & ( Zs2
% 2.71/1.59 = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_328_lexord__append__left__rightI,axiom,
% 2.71/1.59 ! [A: com,B: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 2.71/1.59 ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A @ X ) ) @ ( append_com @ U @ ( cons_com @ B @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_329_lexord__append__left__rightI,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,B: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_330_lexord__append__left__rightI,axiom,
% 2.71/1.59 ! [A: produc410756839_state,B: produc410756839_state,R: set_Pr2096893127_state,U: list_P890094829_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ U @ ( cons_P438230685_state @ A @ X ) ) @ ( append221843330_state @ U @ ( cons_P438230685_state @ B @ Y ) ) ) @ ( lexord1893203674_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_331_concat__append,axiom,
% 2.71/1.59 ! [Xs: list_list_com,Ys2: list_list_com] :
% 2.71/1.59 ( ( concat_com @ ( append_list_com @ Xs @ Ys2 ) )
% 2.71/1.59 = ( append_com @ ( concat_com @ Xs ) @ ( concat_com @ Ys2 ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_332_lexord__cons__cons,axiom,
% 2.71/1.59 ! [A: com,X: list_com,B: com,Y: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A @ X ) @ ( cons_com @ B @ Y ) ) @ ( lexord_com @ R ) )
% 2.71/1.59 = ( ( member1333916004om_com @ ( product_Pair_com_com @ A @ B ) @ R )
% 2.71/1.59 | ( ( A = B )
% 2.71/1.59 & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_333_lexord__cons__cons,axiom,
% 2.71/1.59 ! [A: produc2041926651_state,X: list_P1040014977_state,B: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A @ X ) @ ( cons_P465369265_state @ B @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 2.71/1.59 = ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 2.71/1.59 | ( ( A = B )
% 2.71/1.59 & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_334_lexord__cons__cons,axiom,
% 2.71/1.59 ! [A: produc410756839_state,X: list_P890094829_state,B: produc410756839_state,Y: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ A @ X ) @ ( cons_P438230685_state @ B @ Y ) ) @ ( lexord1893203674_state @ R ) )
% 2.71/1.59 = ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 2.71/1.59 | ( ( A = B )
% 2.71/1.59 & ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_335_lexord__Nil__left,axiom,
% 2.71/1.59 ! [Y: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 2.71/1.59 = ( ? [A3: com,X4: list_com] :
% 2.71/1.59 ( Y
% 2.71/1.59 = ( cons_com @ A3 @ X4 ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_336_lexord__linear,axiom,
% 2.71/1.59 ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 2.71/1.59 ( ! [A2: produc2041926651_state,B2: produc2041926651_state] :
% 2.71/1.59 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 2.71/1.59 | ( A2 = B2 )
% 2.71/1.59 | ( member1069318160_state @ ( produc1909270103_state @ B2 @ A2 ) @ R ) )
% 2.71/1.59 => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 2.71/1.59 | ( X = Y )
% 2.71/1.59 | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_337_lexord__linear,axiom,
% 2.71/1.59 ! [R: set_Pr2096893127_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 2.71/1.59 ( ! [A2: produc410756839_state,B2: produc410756839_state] :
% 2.71/1.59 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 2.71/1.59 | ( A2 = B2 )
% 2.71/1.59 | ( member512523024_state @ ( produc2065881943_state @ B2 @ A2 ) @ R ) )
% 2.71/1.59 => ( ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) )
% 2.71/1.59 | ( X = Y )
% 2.71/1.59 | ( member423306384_state @ ( produc1354769367_state @ Y @ X ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_338_lexord__irreflexive,axiom,
% 2.71/1.59 ! [R: set_Pr1165141447_state,Xs: list_P1040014977_state] :
% 2.71/1.59 ( ! [X3: produc2041926651_state] :
% 2.71/1.59 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 2.71/1.59 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Xs ) @ ( lexord1062073966_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_339_lexord__irreflexive,axiom,
% 2.71/1.59 ! [R: set_Pr2096893127_state,Xs: list_P890094829_state] :
% 2.71/1.59 ( ! [X3: produc410756839_state] :
% 2.71/1.59 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 2.71/1.59 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Xs ) @ ( lexord1893203674_state @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_340_concat_Osimps_I1_J,axiom,
% 2.71/1.59 ( ( concat_com @ nil_list_com )
% 2.71/1.59 = nil_com ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_341_lexord__Nil__right,axiom,
% 2.71/1.59 ! [X: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_342_concat_Osimps_I2_J,axiom,
% 2.71/1.59 ! [X: list_com,Xs: list_list_com] :
% 2.71/1.59 ( ( concat_com @ ( cons_list_com @ X @ Xs ) )
% 2.71/1.59 = ( append_com @ X @ ( concat_com @ Xs ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_343_lexord__append__leftI,axiom,
% 2.71/1.59 ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_344_lexord__append__leftD,axiom,
% 2.71/1.59 ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 2.71/1.59 => ( ! [A2: com] :
% 2.71/1.59 ~ ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ A2 ) @ R )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_345_lexord__append__leftD,axiom,
% 2.71/1.59 ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 2.71/1.59 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc2041926651_state] :
% 2.71/1.59 ~ ( member1069318160_state @ ( produc1909270103_state @ A2 @ A2 ) @ R )
% 2.71/1.59 => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_346_lexord__append__leftD,axiom,
% 2.71/1.59 ! [X: list_P890094829_state,U: list_P890094829_state,V: list_P890094829_state,R: set_Pr2096893127_state] :
% 2.71/1.59 ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ X @ U ) @ ( append221843330_state @ X @ V ) ) @ ( lexord1893203674_state @ R ) )
% 2.71/1.59 => ( ! [A2: produc410756839_state] :
% 2.71/1.59 ~ ( member512523024_state @ ( produc2065881943_state @ A2 @ A2 ) @ R )
% 2.71/1.59 => ( member423306384_state @ ( produc1354769367_state @ U @ V ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_347_lexord__append__rightI,axiom,
% 2.71/1.59 ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 2.71/1.59 ( ? [B5: com,Z3: list_com] :
% 2.71/1.59 ( Y
% 2.71/1.59 = ( cons_com @ B5 @ Z3 ) )
% 2.71/1.59 => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_348_concat__eq__appendD,axiom,
% 2.71/1.59 ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( ( concat_com @ Xss2 )
% 2.71/1.59 = ( append_com @ Ys2 @ Zs2 ) )
% 2.71/1.59 => ( ( Xss2 != nil_list_com )
% 2.71/1.59 => ? [Xss12: list_list_com,Xs2: list_com,Xs5: list_com,Xss23: list_list_com] :
% 2.71/1.59 ( ( Xss2
% 2.71/1.59 = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 2.71/1.59 & ( Ys2
% 2.71/1.59 = ( append_com @ ( concat_com @ Xss12 ) @ Xs2 ) )
% 2.71/1.59 & ( Zs2
% 2.71/1.59 = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(fact_349_lexord__same__pref__if__irrefl,axiom,
% 2.71/1.59 ! [R: set_Pr1822651163om_com,Xs: list_com,Ys2: list_com,Zs2: list_com] :
% 2.71/1.59 ( ( irrefl_com @ R )
% 2.71/1.59 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs @ Ys2 ) @ ( append_com @ Xs @ Zs2 ) ) @ ( lexord_com @ R ) )
% 2.71/1.59 = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lexord_com @ R ) ) ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(conj_0,hypothesis,
% 2.71/1.59 termi @ c @ s ).
% 2.71/1.59
% 2.71/1.59 thf(conj_1,hypothesis,
% 2.71/1.59 ( ( f @ zero_zero_nat )
% 2.71/1.59 = ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(conj_2,hypothesis,
% 2.71/1.59 ! [I2: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ I2 ) @ ( f @ ( suc @ I2 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ).
% 2.71/1.59
% 2.71/1.59 thf(conj_3,hypothesis,
% 2.71/1.59 member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 2.71/1.59
% 2.71/1.59 thf(conj_4,conjecture,
% 2.71/1.59 member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 2.71/1.59 ------------------------
% 2.93/1.62 % (26300)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/183Mi)
% 2.93/1.62 % (26302)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_26179 for (2999ds/27Mi)
% 2.93/1.62 % (26304)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_26179 for (2999ds/2Mi)
% 2.93/1.62 % (26304)Instruction limit reached!
% 2.93/1.62 % (26304)------------------------------
% 2.93/1.62 % (26304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (26304)Termination reason: Unknown
% 2.93/1.62 % (26304)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (26304)Memory used [KB]: 1663
% 2.93/1.62 % (26304)Time elapsed: 0.002 s
% 2.93/1.62 % (26304)Instructions burned: 2 (million)
% 2.93/1.62 % (26304)------------------------------
% 2.93/1.62 % (26304)------------------------------
% 2.93/1.62 % (26306)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/18Mi)
% 2.93/1.62 % (26301)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_26179 for (2999ds/4Mi)
% 2.93/1.62 % (26301)Instruction limit reached!
% 2.93/1.62 % (26301)------------------------------
% 2.93/1.62 % (26301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (26301)Termination reason: Unknown
% 2.93/1.62 % (26301)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (26301)Memory used [KB]: 1663
% 2.93/1.62 % (26301)Time elapsed: 0.003 s
% 2.93/1.62 % (26301)Instructions burned: 6 (million)
% 2.93/1.62 % (26301)------------------------------
% 2.93/1.62 % (26301)------------------------------
% 2.93/1.63 % (26303)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/2Mi)
% 2.93/1.63 % (26302)Instruction limit reached!
% 2.93/1.63 % (26302)------------------------------
% 2.93/1.63 % (26302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (26302)Termination reason: Unknown
% 2.93/1.63 % (26302)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (26302)Memory used [KB]: 2174
% 2.93/1.63 % (26302)Time elapsed: 0.010 s
% 2.93/1.63 % (26302)Instructions burned: 27 (million)
% 2.93/1.63 % (26302)------------------------------
% 2.93/1.63 % (26302)------------------------------
% 2.93/1.63 % (26306)Instruction limit reached!
% 2.93/1.63 % (26306)------------------------------
% 2.93/1.63 % (26306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (26306)Termination reason: Unknown
% 2.93/1.63 % (26306)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (26306)Memory used [KB]: 1918
% 2.93/1.63 % (26306)Time elapsed: 0.008 s
% 2.93/1.63 % (26306)Instructions burned: 20 (million)
% 2.93/1.63 % (26306)------------------------------
% 2.93/1.63 % (26306)------------------------------
% 2.93/1.63 % (26303)Instruction limit reached!
% 2.93/1.63 % (26303)------------------------------
% 2.93/1.63 % (26303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (26303)Termination reason: Unknown
% 2.93/1.63 % (26303)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (26303)Memory used [KB]: 1663
% 2.93/1.63 % (26303)Time elapsed: 0.004 s
% 2.93/1.63 % (26303)Instructions burned: 2 (million)
% 2.93/1.63 % (26303)------------------------------
% 2.93/1.63 % (26303)------------------------------
% 2.93/1.64 % (26305)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_26179 for (2999ds/275Mi)
% 2.93/1.64 % (26308)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_26179 for (2999ds/37Mi)
% 2.93/1.64 % (26310)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_26179 for (2999ds/3Mi)
% 2.93/1.64 % (26311)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_26179 for (2999ds/1041Mi)
% 2.93/1.64 % (26307)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/3Mi)
% 2.93/1.64 % (26307)Instruction limit reached!
% 2.93/1.64 % (26307)------------------------------
% 2.93/1.64 % (26307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (26307)Termination reason: Unknown
% 2.93/1.64 % (26307)Termination phase: shuffling
% 2.93/1.64
% 2.93/1.64 % (26307)Memory used [KB]: 1663
% 2.93/1.64 % (26307)Time elapsed: 0.003 s
% 2.93/1.64 % (26307)Instructions burned: 3 (million)
% 2.93/1.64 % (26307)------------------------------
% 2.93/1.64 % (26307)------------------------------
% 2.93/1.64 % (26310)Instruction limit reached!
% 2.93/1.64 % (26310)------------------------------
% 2.93/1.64 % (26310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (26310)Termination reason: Unknown
% 2.93/1.64 % (26310)Termination phase: shuffling
% 2.93/1.64
% 2.93/1.64 % (26310)Memory used [KB]: 1663
% 2.93/1.64 % (26310)Time elapsed: 0.003 s
% 2.93/1.64 % (26310)Instructions burned: 5 (million)
% 2.93/1.64 % (26310)------------------------------
% 2.93/1.64 % (26310)------------------------------
% 2.93/1.65 % (26309)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_26179 for (2999ds/15Mi)
% 2.93/1.65 % (26308)Instruction limit reached!
% 2.93/1.65 % (26308)------------------------------
% 2.93/1.65 % (26308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (26308)Termination reason: Unknown
% 2.93/1.65 % (26308)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (26308)Memory used [KB]: 2302
% 2.93/1.65 % (26308)Time elapsed: 0.011 s
% 2.93/1.65 % (26308)Instructions burned: 37 (million)
% 2.93/1.65 % (26308)------------------------------
% 2.93/1.65 % (26308)------------------------------
% 2.93/1.65 % (26313)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/16Mi)
% 2.93/1.65 % (26312)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/7Mi)
% 2.93/1.66 % (26312)Instruction limit reached!
% 2.93/1.66 % (26312)------------------------------
% 2.93/1.66 % (26312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (26312)Termination reason: Unknown
% 2.93/1.66 % (26312)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (26312)Memory used [KB]: 1791
% 2.93/1.66 % (26312)Time elapsed: 0.005 s
% 2.93/1.66 % (26312)Instructions burned: 9 (million)
% 2.93/1.66 % (26312)------------------------------
% 2.93/1.66 % (26312)------------------------------
% 2.93/1.66 % (26313)Instruction limit reached!
% 2.93/1.66 % (26313)------------------------------
% 2.93/1.66 % (26313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (26313)Termination reason: Unknown
% 2.93/1.66 % (26313)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (26313)Memory used [KB]: 1918
% 2.93/1.66 % (26313)Time elapsed: 0.006 s
% 2.93/1.66 % (26313)Instructions burned: 16 (million)
% 2.93/1.66 % (26313)------------------------------
% 2.93/1.66 % (26313)------------------------------
% 2.93/1.66 % (26309)Instruction limit reached!
% 2.93/1.66 % (26309)------------------------------
% 2.93/1.66 % (26309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (26309)Termination reason: Unknown
% 2.93/1.66 % (26309)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (26309)Memory used [KB]: 1918
% 2.93/1.66 % (26309)Time elapsed: 0.011 s
% 2.93/1.66 % (26309)Instructions burned: 15 (million)
% 2.93/1.66 % (26309)------------------------------
% 2.93/1.66 % (26309)------------------------------
% 2.93/1.66 % (26314)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_26179 for (2999ds/3Mi)
% 2.93/1.66 % (26314)Instruction limit reached!
% 2.93/1.66 % (26314)------------------------------
% 2.93/1.66 % (26314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (26314)Termination reason: Unknown
% 2.93/1.66 % (26314)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (26314)Memory used [KB]: 1663
% 2.93/1.66 % (26314)Time elapsed: 0.002 s
% 2.93/1.66 % (26314)Instructions burned: 3 (million)
% 2.93/1.66 % (26314)------------------------------
% 2.93/1.66 % (26314)------------------------------
% 2.93/1.67 % (26315)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_26179 for (2999ds/3Mi)
% 2.93/1.67 % (26316)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/7Mi)
% 2.93/1.67 % (26315)Instruction limit reached!
% 2.93/1.67 % (26315)------------------------------
% 2.93/1.67 % (26315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (26315)Termination reason: Unknown
% 2.93/1.67 % (26315)Termination phase: shuffling
% 2.93/1.67
% 2.93/1.67 % (26315)Memory used [KB]: 1663
% 2.93/1.67 % (26315)Time elapsed: 0.003 s
% 2.93/1.67 % (26315)Instructions burned: 3 (million)
% 2.93/1.67 % (26315)------------------------------
% 2.93/1.67 % (26315)------------------------------
% 2.93/1.67 % (26316)Instruction limit reached!
% 2.93/1.67 % (26316)------------------------------
% 2.93/1.67 % (26316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (26316)Termination reason: Unknown
% 2.93/1.67 % (26316)Termination phase: shuffling
% 2.93/1.67
% 2.93/1.67 % (26316)Memory used [KB]: 1791
% 2.93/1.67 % (26316)Time elapsed: 0.004 s
% 2.93/1.67 % (26316)Instructions burned: 9 (million)
% 2.93/1.67 % (26316)------------------------------
% 2.93/1.67 % (26316)------------------------------
% 2.93/1.67 % (26318)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/4Mi)
% 2.93/1.67 % (26300)Instruction limit reached!
% 2.93/1.67 % (26300)------------------------------
% 2.93/1.67 % (26300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (26300)Termination reason: Unknown
% 2.93/1.67 % (26300)Termination phase: Property scanning
% 2.93/1.67
% 2.93/1.67 % (26300)Memory used [KB]: 3582
% 2.93/1.67 % (26300)Time elapsed: 0.052 s
% 2.93/1.67 % (26300)Instructions burned: 184 (million)
% 2.93/1.67 % (26300)------------------------------
% 2.93/1.67 % (26300)------------------------------
% 2.93/1.67 % (26318)Instruction limit reached!
% 2.93/1.67 % (26318)------------------------------
% 2.93/1.67 % (26318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (26318)Termination reason: Unknown
% 2.93/1.67 % (26318)Termination phase: shuffling
% 2.93/1.67
% 2.93/1.67 % (26318)Memory used [KB]: 1663
% 2.93/1.67 % (26318)Time elapsed: 0.003 s
% 2.93/1.67 % (26318)Instructions burned: 6 (million)
% 2.93/1.67 % (26318)------------------------------
% 2.93/1.67 % (26318)------------------------------
% 2.93/1.67 % (26317)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/3Mi)
% 2.93/1.68 % (26317)Instruction limit reached!
% 2.93/1.68 % (26317)------------------------------
% 2.93/1.68 % (26317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (26317)Termination reason: Unknown
% 2.93/1.68 % (26317)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (26317)Memory used [KB]: 1663
% 2.93/1.68 % (26317)Time elapsed: 0.004 s
% 2.93/1.68 % (26319)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/18Mi)
% 2.93/1.68 % (26317)Instructions burned: 3 (million)
% 2.93/1.68 % (26317)------------------------------
% 2.93/1.68 % (26317)------------------------------
% 2.93/1.68 % (26320)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/710Mi)
% 2.93/1.68 % (26321)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/6Mi)
% 2.93/1.68 % (26322)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_26179 for (2999ds/902Mi)
% 2.93/1.68 % (26321)Instruction limit reached!
% 2.93/1.68 % (26321)------------------------------
% 2.93/1.68 % (26321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (26321)Termination reason: Unknown
% 2.93/1.68 % (26321)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (26321)Memory used [KB]: 1663
% 2.93/1.68 % (26321)Time elapsed: 0.003 s
% 2.93/1.68 % (26321)Instructions burned: 6 (million)
% 2.93/1.68 % (26321)------------------------------
% 2.93/1.68 % (26321)------------------------------
% 2.93/1.68 % (26319)Instruction limit reached!
% 2.93/1.68 % (26319)------------------------------
% 2.93/1.68 % (26319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (26319)Termination reason: Unknown
% 2.93/1.68 % (26319)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (26319)Memory used [KB]: 1918
% 2.93/1.68 % (26319)Time elapsed: 0.008 s
% 2.93/1.68 % (26319)Instructions burned: 18 (million)
% 2.93/1.68 % (26319)------------------------------
% 2.93/1.68 % (26319)------------------------------
% 2.93/1.69 % (26325)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_26179 for (2999ds/6Mi)
% 2.93/1.69 % (26323)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_26179 for (2999ds/21Mi)
% 2.93/1.70 % (26325)Instruction limit reached!
% 2.93/1.70 % (26325)------------------------------
% 2.93/1.70 % (26325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.70 % (26325)Termination reason: Unknown
% 2.93/1.70 % (26325)Termination phase: shuffling
% 2.93/1.70
% 2.93/1.70 % (26325)Memory used [KB]: 1663
% 2.93/1.70 % (26325)Time elapsed: 0.004 s
% 2.93/1.70 % (26325)Instructions burned: 6 (million)
% 2.93/1.70 % (26325)------------------------------
% 2.93/1.70 % (26325)------------------------------
% 2.93/1.70 % (26324)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26179 for (2999ds/5Mi)
% 2.93/1.70 % (26324)Instruction limit reached!
% 2.93/1.70 % (26324)------------------------------
% 2.93/1.70 % (26324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.70 % (26324)Termination reason: Unknown
% 2.93/1.70 % (26324)Termination phase: shuffling
% 2.93/1.70
% 2.93/1.70 % (26324)Memory used [KB]: 1663
% 2.93/1.70 % (26324)Time elapsed: 0.004 s
% 2.93/1.70 % (26324)Instructions burned: 5 (million)
% 2.93/1.70 % (26324)------------------------------
% 2.93/1.70 % (26324)------------------------------
% 2.93/1.70 % (26323)Instruction limit reached!
% 2.93/1.70 % (26323)------------------------------
% 2.93/1.70 % (26323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.70 % (26323)Termination reason: Unknown
% 2.93/1.70 % (26323)Termination phase: shuffling
% 2.93/1.70
% 2.93/1.70 % (26323)Memory used [KB]: 1918
% 2.93/1.70 % (26323)Time elapsed: 0.012 s
% 2.93/1.70 % (26323)Instructions burned: 21 (million)
% 2.93/1.70 % (26323)------------------------------
% 2.93/1.70 % (26323)------------------------------
% 2.93/1.71 % (26326)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26179 for (2998ds/377Mi)
% 2.93/1.72 % (26328)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_26179 for (2998ds/19Mi)
% 2.93/1.72 % (26327)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_26179 for (2998ds/779Mi)
% 2.93/1.72 % (26328)Instruction limit reached!
% 2.93/1.72 % (26328)------------------------------
% 2.93/1.72 % (26328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.72 % (26328)Termination reason: Unknown
% 2.93/1.72 % (26328)Termination phase: shuffling
% 2.93/1.72
% 2.93/1.72 % (26328)Memory used [KB]: 2046
% 2.93/1.72 % (26328)Time elapsed: 0.007 s
% 2.93/1.72 % (26328)Instructions burned: 19 (million)
% 2.93/1.72 % (26328)------------------------------
% 2.93/1.72 % (26328)------------------------------
% 2.93/1.73 % (26329)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26179 for (2998ds/879Mi)
% 2.93/1.74 % (26305)Instruction limit reached!
% 2.93/1.74 % (26305)------------------------------
% 2.93/1.74 % (26305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.74 % (26305)Termination reason: Unknown
% 2.93/1.74 % (26305)Termination phase: Saturation
% 2.93/1.74
% 2.93/1.74 % (26305)Memory used [KB]: 8571
% 2.93/1.74 % (26305)Time elapsed: 0.101 s
% 2.93/1.74 % (26305)Instructions burned: 275 (million)
% 2.93/1.74 % (26305)------------------------------
% 2.93/1.74 % (26305)------------------------------
% 2.93/1.74 % (26330)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26179 for (2998ds/17Mi)
% 2.93/1.75 % (26330)Instruction limit reached!
% 2.93/1.75 % (26330)------------------------------
% 2.93/1.75 % (26330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.75 % (26330)Termination reason: Unknown
% 2.93/1.75 % (26330)Termination phase: shuffling
% 2.93/1.75
% 2.93/1.75 % (26330)Memory used [KB]: 1918
% 2.93/1.75 % (26330)Time elapsed: 0.007 s
% 2.93/1.75 % (26330)Instructions burned: 19 (million)
% 2.93/1.75 % (26330)------------------------------
% 2.93/1.75 % (26330)------------------------------
% 2.93/1.76 % (26331)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26179 for (2998ds/3Mi)
% 2.93/1.76 % (26331)Instruction limit reached!
% 2.93/1.76 % (26331)------------------------------
% 2.93/1.76 % (26331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.76 % (26331)Termination reason: Unknown
% 2.93/1.76 % (26331)Termination phase: shuffling
% 2.93/1.76
% 2.93/1.76 % (26331)Memory used [KB]: 1663
% 2.93/1.76 % (26331)Time elapsed: 0.003 s
% 2.93/1.76 % (26331)Instructions burned: 5 (million)
% 2.93/1.76 % (26331)------------------------------
% 2.93/1.76 % (26331)------------------------------
% 2.93/1.77 % (26332)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26179 for (2998ds/30Mi)
% 2.93/1.78 % (26332)Instruction limit reached!
% 2.93/1.78 % (26332)------------------------------
% 2.93/1.78 % (26332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.78 % (26332)Termination reason: Unknown
% 2.93/1.78 % (26332)Termination phase: shuffling
% 2.93/1.78
% 2.93/1.78 % (26332)Memory used [KB]: 2174
% 2.93/1.78 % (26332)Time elapsed: 0.011 s
% 2.93/1.78 % (26332)Instructions burned: 31 (million)
% 2.93/1.78 % (26332)------------------------------
% 2.93/1.78 % (26332)------------------------------
% 2.93/1.79 % (26333)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26179 for (2998ds/127Mi)
% 2.93/1.81 % (26326)Instruction limit reached!
% 2.93/1.81 % (26326)------------------------------
% 2.93/1.81 % (26326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.81 % (26326)Termination reason: Unknown
% 2.93/1.81 % (26326)Termination phase: Saturation
% 2.93/1.81
% 2.93/1.81 % (26326)Memory used [KB]: 9338
% 2.93/1.81 % (26326)Time elapsed: 0.111 s
% 2.93/1.81 % (26326)Instructions burned: 379 (million)
% 2.93/1.81 % (26326)------------------------------
% 2.93/1.81 % (26326)------------------------------
% 2.93/1.82 % (26334)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26179 for (2997ds/100Mi)
% 2.93/1.83 % (26333)Instruction limit reached!
% 2.93/1.83 % (26333)------------------------------
% 2.93/1.83 % (26333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.83 % (26333)Termination reason: Unknown
% 2.93/1.83 % (26333)Termination phase: Property scanning
% 2.93/1.83
% 2.93/1.83 % (26333)Memory used [KB]: 3454
% 2.93/1.83 % (26333)Time elapsed: 0.038 s
% 2.93/1.83 % (26333)Instructions burned: 127 (million)
% 2.93/1.83 % (26333)------------------------------
% 2.93/1.83 % (26333)------------------------------
% 2.93/1.84 % (26335)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_26179 for (2997ds/3Mi)
% 2.93/1.84 % (26335)Instruction limit reached!
% 2.93/1.84 % (26335)------------------------------
% 2.93/1.84 % (26335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.84 % (26335)Termination reason: Unknown
% 2.93/1.84 % (26335)Termination phase: shuffling
% 2.93/1.84
% 2.93/1.84 % (26335)Memory used [KB]: 1663
% 2.93/1.84 % (26335)Time elapsed: 0.003 s
% 2.93/1.84 % (26335)Instructions burned: 5 (million)
% 2.93/1.84 % (26335)------------------------------
% 2.93/1.84 % (26335)------------------------------
% 2.93/1.85 % (26336)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_26179 for (2997ds/20Mi)
% 2.93/1.85 % (26334)Instruction limit reached!
% 2.93/1.85 % (26334)------------------------------
% 2.93/1.85 % (26334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.85 % (26334)Termination reason: Unknown
% 2.93/1.85 % (26334)Termination phase: Property scanning
% 2.93/1.85
% 2.93/1.85 % (26334)Memory used [KB]: 3198
% 2.93/1.85 % (26334)Time elapsed: 0.029 s
% 2.93/1.85 % (26334)Instructions burned: 102 (million)
% 2.93/1.85 % (26334)------------------------------
% 2.93/1.85 % (26334)------------------------------
% 2.93/1.86 % (26336)Instruction limit reached!
% 2.93/1.86 % (26336)------------------------------
% 2.93/1.86 % (26336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.86 % (26336)Termination reason: Unknown
% 2.93/1.86 % (26336)Termination phase: shuffling
% 2.93/1.86
% 2.93/1.86 % (26336)Memory used [KB]: 1918
% 2.93/1.86 % (26336)Time elapsed: 0.008 s
% 2.93/1.86 % (26336)Instructions burned: 20 (million)
% 2.93/1.86 % (26336)------------------------------
% 2.93/1.86 % (26336)------------------------------
% 2.93/1.86 % (26337)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_26179 for (2997ds/86Mi)
% 2.93/1.87 % (26338)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_26179 for (2997ds/107Mi)
% 2.93/1.89 % (26337)Instruction limit reached!
% 2.93/1.89 % (26337)------------------------------
% 2.93/1.89 % (26337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.89 % (26337)Termination reason: Unknown
% 2.93/1.89 % (26337)Termination phase: Preprocessing 3
% 2.93/1.89
% 2.93/1.89 % (26337)Memory used [KB]: 2814
% 2.93/1.89 % (26337)Time elapsed: 0.027 s
% 2.93/1.89 % (26337)Instructions burned: 88 (million)
% 2.93/1.89 % (26337)------------------------------
% 2.93/1.89 % (26337)------------------------------
% 2.93/1.90 % (26338)Instruction limit reached!
% 2.93/1.90 % (26338)------------------------------
% 2.93/1.90 % (26338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.90 % (26338)Termination reason: Unknown
% 2.93/1.90 % (26338)Termination phase: Preprocessing 3
% 2.93/1.90
% 2.93/1.90 % (26338)Memory used [KB]: 2942
% 2.93/1.90 % (26338)Time elapsed: 0.032 s
% 2.93/1.90 % (26338)Instructions burned: 107 (million)
% 2.93/1.90 % (26338)------------------------------
% 2.93/1.90 % (26338)------------------------------
% 2.93/1.90 % (26339)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_26179 for (2997ds/39Mi)
% 2.93/1.91 % (26340)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_26179 for (2997ds/448Mi)
% 2.93/1.91 % (26339)Instruction limit reached!
% 2.93/1.91 % (26339)------------------------------
% 2.93/1.91 % (26339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.91 % (26339)Termination reason: Unknown
% 2.93/1.91 % (26339)Termination phase: shuffling
% 2.93/1.91
% 2.93/1.91 % (26339)Memory used [KB]: 2302
% 2.93/1.91 % (26339)Time elapsed: 0.012 s
% 2.93/1.91 % (26339)Instructions burned: 39 (million)
% 2.93/1.91 % (26339)------------------------------
% 2.93/1.91 % (26339)------------------------------
% 2.93/1.92 % (26320)Instruction limit reached!
% 2.93/1.92 % (26320)------------------------------
% 2.93/1.92 % (26320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.92 % (26320)Termination reason: Unknown
% 2.93/1.92 % (26320)Termination phase: Saturation
% 2.93/1.92
% 2.93/1.92 % (26320)Memory used [KB]: 9466
% 2.93/1.92 % (26320)Time elapsed: 0.239 s
% 2.93/1.92 % (26320)Instructions burned: 711 (million)
% 2.93/1.92 % (26320)------------------------------
% 2.93/1.92 % (26320)------------------------------
% 2.93/1.92 % (26341)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_26179 for (2996ds/46Mi)
% 2.93/1.93 % (26342)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_26179 for (2996ds/98Mi)
% 2.93/1.93 % (26341)Instruction limit reached!
% 2.93/1.93 % (26341)------------------------------
% 2.93/1.93 % (26341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (26341)Termination reason: Unknown
% 2.93/1.93 % (26341)Termination phase: shuffling
% 2.93/1.93
% 2.93/1.93 % (26341)Memory used [KB]: 2430
% 2.93/1.93 % (26341)Time elapsed: 0.016 s
% 2.93/1.93 % (26341)Instructions burned: 47 (million)
% 2.93/1.93 % (26341)------------------------------
% 2.93/1.93 % (26341)------------------------------
% 2.93/1.94 % (26343)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_26179 for (2996ds/507Mi)
% 2.93/1.95 % (26322)Instruction limit reached!
% 2.93/1.95 % (26322)------------------------------
% 2.93/1.95 % (26322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (26322)Termination reason: Unknown
% 2.93/1.95 % (26322)Termination phase: Saturation
% 2.93/1.95
% 2.93/1.95 % (26322)Memory used [KB]: 11513
% 2.93/1.95 % (26322)Time elapsed: 0.266 s
% 2.93/1.95 % (26322)Instructions burned: 903 (million)
% 2.93/1.95 % (26322)------------------------------
% 2.93/1.95 % (26322)------------------------------
% 2.93/1.95 % (26342)Instruction limit reached!
% 2.93/1.95 % (26342)------------------------------
% 2.93/1.95 % (26342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (26342)Termination reason: Unknown
% 2.93/1.95 % (26342)Termination phase: Property scanning
% 2.93/1.95
% 2.93/1.95 % (26342)Memory used [KB]: 3198
% 2.93/1.95 % (26342)Time elapsed: 0.028 s
% 2.93/1.95 % (26342)Instructions burned: 101 (million)
% 2.93/1.95 % (26342)------------------------------
% 2.93/1.95 % (26342)------------------------------
% 2.93/1.96 % (26344)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_26179 for (2996ds/149Mi)
% 2.93/1.96 % (26345)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26179 for (2996ds/39Mi)
% 2.93/1.97 % (26327)Instruction limit reached!
% 2.93/1.97 % (26327)------------------------------
% 2.93/1.97 % (26327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.97 % (26327)Termination reason: Unknown
% 2.93/1.97 % (26327)Termination phase: Saturation
% 2.93/1.97
% 2.93/1.97 % (26327)Memory used [KB]: 11513
% 2.93/1.97 % (26327)Time elapsed: 0.254 s
% 2.93/1.97 % (26327)Instructions burned: 780 (million)
% 2.93/1.97 % (26327)------------------------------
% 2.93/1.97 % (26327)------------------------------
% 2.93/1.98 % (26345)Instruction limit reached!
% 2.93/1.98 % (26345)------------------------------
% 2.93/1.98 % (26345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (26345)Termination reason: Unknown
% 2.93/1.98 % (26345)Termination phase: shuffling
% 2.93/1.98
% 2.93/1.98 % (26345)Memory used [KB]: 2302
% 2.93/1.98 % (26345)Time elapsed: 0.014 s
% 2.93/1.98 % (26345)Instructions burned: 41 (million)
% 2.93/1.98 % (26345)------------------------------
% 2.93/1.98 % (26345)------------------------------
% 2.93/1.98 % (26346)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_26179 for (2996ds/6Mi)
% 2.93/1.98 % (26346)Instruction limit reached!
% 2.93/1.98 % (26346)------------------------------
% 2.93/1.98 % (26346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (26346)Termination reason: Unknown
% 2.93/1.98 % (26346)Termination phase: shuffling
% 2.93/1.98
% 2.93/1.98 % (26346)Memory used [KB]: 1663
% 2.93/1.98 % (26346)Time elapsed: 0.003 s
% 2.93/1.98 % (26346)Instructions burned: 6 (million)
% 2.93/1.98 % (26346)------------------------------
% 2.93/1.98 % (26346)------------------------------
% 2.93/1.98 % (26347)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_26179 for (2996ds/1087Mi)
% 2.93/1.99 % (26348)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26179 for (2996ds/47Mi)
% 2.93/2.00 % (26344)Instruction limit reached!
% 2.93/2.00 % (26344)------------------------------
% 2.93/2.00 % (26344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.00 % (26344)Termination reason: Unknown
% 2.93/2.00 % (26344)Termination phase: Property scanning
% 2.93/2.00
% 2.93/2.00 % (26344)Memory used [KB]: 3454
% 2.93/2.00 % (26344)Time elapsed: 0.043 s
% 2.93/2.00 % (26344)Instructions burned: 151 (million)
% 2.93/2.00 % (26344)------------------------------
% 2.93/2.00 % (26344)------------------------------
% 2.93/2.01 % (26348)Instruction limit reached!
% 2.93/2.01 % (26348)------------------------------
% 2.93/2.01 % (26348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.01 % (26348)Termination reason: Unknown
% 2.93/2.01 % (26348)Termination phase: shuffling
% 2.93/2.01
% 2.93/2.01 % (26348)Memory used [KB]: 2430
% 2.93/2.01 % (26348)Time elapsed: 0.016 s
% 2.93/2.01 % (26348)Instructions burned: 47 (million)
% 2.93/2.01 % (26348)------------------------------
% 2.93/2.01 % (26348)------------------------------
% 2.93/2.01 % (26349)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_26179 for (2996ds/44Mi)
% 2.93/2.02 % (26350)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_26179 for (2995ds/432Mi)
% 2.93/2.02 % (26349)Instruction limit reached!
% 2.93/2.02 % (26349)------------------------------
% 2.93/2.02 % (26349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.02 % (26349)Termination reason: Unknown
% 2.93/2.02 % (26349)Termination phase: shuffling
% 2.93/2.02
% 2.93/2.02 % (26349)Memory used [KB]: 2686
% 2.93/2.02 % (26349)Time elapsed: 0.013 s
% 2.93/2.02 % (26349)Instructions burned: 44 (million)
% 2.93/2.02 % (26349)------------------------------
% 2.93/2.02 % (26349)------------------------------
% 5.70/2.03 % (26311)Instruction limit reached!
% 5.70/2.03 % (26311)------------------------------
% 5.70/2.03 % (26311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.03 % (26340)Instruction limit reached!
% 5.70/2.03 % (26340)------------------------------
% 5.70/2.03 % (26340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.03 % (26340)Termination reason: Unknown
% 5.70/2.03 % (26340)Termination phase: Saturation
% 5.70/2.03
% 5.70/2.03 % (26340)Memory used [KB]: 9850
% 5.70/2.03 % (26340)Time elapsed: 0.121 s
% 5.70/2.03 % (26340)Instructions burned: 448 (million)
% 5.70/2.03 % (26340)------------------------------
% 5.70/2.03 % (26340)------------------------------
% 5.70/2.03 % (26311)Termination reason: Unknown
% 5.70/2.03 % (26311)Termination phase: Saturation
% 5.70/2.03
% 5.70/2.03 % (26311)Memory used [KB]: 10618
% 5.70/2.03 % (26311)Time elapsed: 0.400 s
% 5.70/2.03 % (26311)Instructions burned: 1043 (million)
% 5.70/2.03 % (26311)------------------------------
% 5.70/2.03 % (26311)------------------------------
% 5.70/2.03 % (26351)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26179 for (2995ds/62Mi)
% 5.70/2.04 % (26352)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_26179 for (2995ds/31Mi)
% 5.70/2.04 % (26353)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26179 for (2995ds/96Mi)
% 5.70/2.05 % (26352)Instruction limit reached!
% 5.70/2.05 % (26352)------------------------------
% 5.70/2.05 % (26352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.05 % (26352)Termination reason: Unknown
% 5.70/2.05 % (26352)Termination phase: shuffling
% 5.70/2.05
% 5.70/2.05 % (26352)Memory used [KB]: 2174
% 5.70/2.05 % (26352)Time elapsed: 0.011 s
% 5.70/2.05 % (26352)Instructions burned: 32 (million)
% 5.70/2.05 % (26352)------------------------------
% 5.70/2.05 % (26352)------------------------------
% 5.70/2.05 % (26351)Instruction limit reached!
% 5.70/2.05 % (26351)------------------------------
% 5.70/2.05 % (26351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.05 % (26351)Termination reason: Unknown
% 5.70/2.05 % (26351)Termination phase: shuffling
% 5.70/2.05
% 5.70/2.05 % (26351)Memory used [KB]: 2814
% 5.70/2.05 % (26351)Time elapsed: 0.018 s
% 5.70/2.05 % (26351)Instructions burned: 63 (million)
% 5.70/2.05 % (26351)------------------------------
% 5.70/2.05 % (26351)------------------------------
% 5.70/2.06 % (26354)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_26179 for (2995ds/453Mi)
% 5.70/2.06 % (26355)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_26179 for (2995ds/71Mi)
% 5.70/2.06 % (26353)Instruction limit reached!
% 5.70/2.06 % (26353)------------------------------
% 5.70/2.06 % (26353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.06 % (26353)Termination reason: Unknown
% 5.70/2.06 % (26353)Termination phase: Preprocessing 3
% 5.70/2.06
% 5.70/2.06 % (26353)Memory used [KB]: 2942
% 5.70/2.06 % (26353)Time elapsed: 0.030 s
% 5.70/2.06 % (26353)Instructions burned: 98 (million)
% 5.70/2.06 % (26353)------------------------------
% 5.70/2.06 % (26353)------------------------------
% 5.70/2.07 % (26356)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26179 for (2995ds/83Mi)
% 5.70/2.08 % (26355)Instruction limit reached!
% 5.70/2.08 % (26355)------------------------------
% 5.70/2.08 % (26355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.08 % (26355)Termination reason: Unknown
% 5.70/2.08 % (26355)Termination phase: Property scanning
% 5.70/2.08
% 5.70/2.08 % (26355)Memory used [KB]: 2558
% 5.70/2.08 % (26355)Time elapsed: 0.022 s
% 5.70/2.08 % (26355)Instructions burned: 71 (million)
% 5.70/2.08 % (26355)------------------------------
% 5.70/2.08 % (26355)------------------------------
% 5.70/2.09 % (26357)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26179 for (2995ds/11Mi)
% 5.70/2.09 % (26357)Instruction limit reached!
% 5.70/2.09 % (26357)------------------------------
% 5.70/2.09 % (26357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.09 % (26357)Termination reason: Unknown
% 5.70/2.09 % (26357)Termination phase: shuffling
% 5.70/2.09
% 5.70/2.09 % (26357)Memory used [KB]: 1918
% 5.70/2.09 % (26357)Time elapsed: 0.005 s
% 5.70/2.09 % (26357)Instructions burned: 14 (million)
% 5.70/2.09 % (26357)------------------------------
% 5.70/2.09 % (26357)------------------------------
% 5.70/2.09 % (26343)Instruction limit reached!
% 5.70/2.09 % (26343)------------------------------
% 5.70/2.09 % (26343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.09 % (26343)Termination reason: Unknown
% 5.70/2.09 % (26343)Termination phase: Saturation
% 5.70/2.09
% 5.70/2.09 % (26343)Memory used [KB]: 11257
% 5.70/2.09 % (26343)Time elapsed: 0.151 s
% 5.70/2.09 % (26343)Instructions burned: 508 (million)
% 5.70/2.09 % (26343)------------------------------
% 5.70/2.09 % (26343)------------------------------
% 5.70/2.10 % (26356)Instruction limit reached!
% 5.70/2.10 % (26356)------------------------------
% 5.70/2.10 % (26356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.10 % (26356)Termination reason: Unknown
% 5.70/2.10 % (26356)Termination phase: SInE selection
% 5.70/2.10
% 5.70/2.10 % (26356)Memory used [KB]: 2558
% 5.70/2.10 % (26356)Time elapsed: 0.025 s
% 5.70/2.10 % (26356)Instructions burned: 83 (million)
% 5.70/2.10 % (26356)------------------------------
% 5.70/2.10 % (26356)------------------------------
% 5.70/2.10 % (26358)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_26179 for (2994ds/41Mi)
% 5.70/2.10 % (26359)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26179 for (2994ds/6Mi)
% 5.70/2.10 % (26359)Instruction limit reached!
% 5.70/2.10 % (26359)------------------------------
% 5.70/2.10 % (26359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.10 % (26359)Termination reason: Unknown
% 5.70/2.10 % (26359)Termination phase: shuffling
% 5.70/2.10
% 5.70/2.10 % (26359)Memory used [KB]: 1663
% 5.70/2.10 % (26359)Time elapsed: 0.003 s
% 5.70/2.10 % (26359)Instructions burned: 6 (million)
% 5.70/2.10 % (26359)------------------------------
% 5.70/2.10 % (26359)------------------------------
% 5.70/2.11 % (26360)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26179 for (2994ds/150Mi)
% 5.70/2.11 % (26358)Instruction limit reached!
% 5.70/2.11 % (26358)------------------------------
% 5.70/2.11 % (26358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.11 % (26358)Termination reason: Unknown
% 5.70/2.11 % (26358)Termination phase: shuffling
% 5.70/2.11
% 5.70/2.11 % (26358)Memory used [KB]: 2686
% 5.70/2.11 % (26358)Time elapsed: 0.013 s
% 5.70/2.11 % (26358)Instructions burned: 44 (million)
% 5.70/2.11 % (26358)------------------------------
% 5.70/2.11 % (26358)------------------------------
% 5.70/2.11 % (26361)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26179 for (2994ds/343Mi)
% 5.70/2.12 % (26362)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_26179 for (2994ds/109Mi)
% 6.22/2.14 % (26350)Instruction limit reached!
% 6.22/2.14 % (26350)------------------------------
% 6.22/2.14 % (26350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.14 % (26350)Termination reason: Unknown
% 6.22/2.14 % (26350)Termination phase: Saturation
% 6.22/2.14
% 6.22/2.14 % (26350)Memory used [KB]: 4605
% 6.22/2.14 % (26350)Time elapsed: 0.122 s
% 6.22/2.14 % (26350)Instructions burned: 434 (million)
% 6.22/2.14 % (26350)------------------------------
% 6.22/2.14 % (26350)------------------------------
% 6.22/2.15 % (26363)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_26179 for (2994ds/253Mi)
% 6.22/2.15 % (26362)Instruction limit reached!
% 6.22/2.15 % (26362)------------------------------
% 6.22/2.15 % (26362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.15 % (26362)Termination reason: Unknown
% 6.22/2.15 % (26362)Termination phase: Preprocessing 3
% 6.22/2.15
% 6.22/2.15 % (26362)Memory used [KB]: 2942
% 6.22/2.15 % (26362)Time elapsed: 0.034 s
% 6.22/2.15 % (26362)Instructions burned: 110 (million)
% 6.22/2.15 % (26362)------------------------------
% 6.22/2.15 % (26362)------------------------------
% 6.22/2.16 % (26360)Instruction limit reached!
% 6.22/2.16 % (26360)------------------------------
% 6.22/2.16 % (26360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.16 % (26360)Termination reason: Unknown
% 6.22/2.16 % (26360)Termination phase: Property scanning
% 6.22/2.16
% 6.22/2.16 % (26360)Memory used [KB]: 3709
% 6.22/2.16 % (26360)Time elapsed: 0.050 s
% 6.22/2.16 % (26360)Instructions burned: 151 (million)
% 6.22/2.16 % (26360)------------------------------
% 6.22/2.16 % (26360)------------------------------
% 6.22/2.16 % (26364)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26179 for (2994ds/140Mi)
% 6.22/2.17 % (26365)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_26179 for (2994ds/614Mi)
% 6.22/2.17 % (26329)Instruction limit reached!
% 6.22/2.17 % (26329)------------------------------
% 6.22/2.17 % (26329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.17 % (26329)Termination reason: Unknown
% 6.22/2.17 % (26329)Termination phase: Saturation
% 6.22/2.17
% 6.22/2.17 % (26329)Memory used [KB]: 8955
% 6.22/2.17 % (26329)Time elapsed: 0.443 s
% 6.22/2.17 % (26329)Instructions burned: 881 (million)
% 6.22/2.17 % (26329)------------------------------
% 6.22/2.17 % (26329)------------------------------
% 6.22/2.18 % (26354)Instruction limit reached!
% 6.22/2.18 % (26354)------------------------------
% 6.22/2.18 % (26354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.18 % (26354)Termination reason: Unknown
% 6.22/2.18 % (26354)Termination phase: Saturation
% 6.22/2.18
% 6.22/2.18 % (26354)Memory used [KB]: 9083
% 6.22/2.18 % (26354)Time elapsed: 0.143 s
% 6.22/2.18 % (26354)Instructions burned: 454 (million)
% 6.22/2.18 % (26354)------------------------------
% 6.22/2.18 % (26354)------------------------------
% 6.22/2.18 % (26366)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_26179 for (2994ds/202Mi)
% 6.22/2.19 % (26367)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_26179 for (2994ds/339Mi)
% 6.70/2.20 % (26364)Instruction limit reached!
% 6.70/2.20 % (26364)------------------------------
% 6.70/2.20 % (26364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.20 % (26364)Termination reason: Unknown
% 6.70/2.20 % (26364)Termination phase: Saturation
% 6.70/2.20
% 6.70/2.20 % (26364)Memory used [KB]: 7419
% 6.70/2.20 % (26364)Time elapsed: 0.041 s
% 6.70/2.20 % (26364)Instructions burned: 142 (million)
% 6.70/2.20 % (26364)------------------------------
% 6.70/2.20 % (26364)------------------------------
% 6.70/2.21 % (26368)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_26179 for (2993ds/283Mi)
% 6.70/2.21 % (26361)Instruction limit reached!
% 6.70/2.21 % (26361)------------------------------
% 6.70/2.21 % (26361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.21 % (26361)Termination reason: Unknown
% 6.70/2.21 % (26361)Termination phase: Saturation
% 6.70/2.21
% 6.70/2.21 % (26361)Memory used [KB]: 8571
% 6.70/2.21 % (26361)Time elapsed: 0.102 s
% 6.70/2.21 % (26361)Instructions burned: 345 (million)
% 6.70/2.21 % (26361)------------------------------
% 6.70/2.21 % (26361)------------------------------
% 6.70/2.22 % (26363)Instruction limit reached!
% 6.70/2.22 % (26363)------------------------------
% 6.70/2.22 % (26363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.22 % (26363)Termination reason: Unknown
% 6.70/2.22 % (26363)Termination phase: Saturation
% 6.70/2.22
% 6.70/2.22 % (26363)Memory used [KB]: 9083
% 6.70/2.22 % (26363)Time elapsed: 0.074 s
% 6.70/2.22 % (26363)Instructions burned: 253 (million)
% 6.70/2.22 % (26363)------------------------------
% 6.70/2.22 % (26363)------------------------------
% 6.70/2.22 % (26369)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26179 for (2993ds/134Mi)
% 6.70/2.23 % (26370)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26179 for (2993ds/298Mi)
% 6.70/2.24 % (26366)Instruction limit reached!
% 6.70/2.24 % (26366)------------------------------
% 6.70/2.24 % (26366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.24 % (26366)Termination reason: Unknown
% 6.70/2.24 % (26366)Termination phase: Saturation
% 6.70/2.24
% 6.70/2.24 % (26366)Memory used [KB]: 8571
% 6.70/2.24 % (26366)Time elapsed: 0.059 s
% 6.70/2.24 % (26366)Instructions burned: 202 (million)
% 6.70/2.24 % (26366)------------------------------
% 6.70/2.24 % (26366)------------------------------
% 6.70/2.25 % (26371)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26179 for (2993ds/192Mi)
% 6.70/2.26 % (26369)Instruction limit reached!
% 6.70/2.26 % (26369)------------------------------
% 6.70/2.26 % (26369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.26 % (26369)Termination reason: Unknown
% 6.70/2.26 % (26369)Termination phase: Property scanning
% 6.70/2.26
% 6.70/2.26 % (26369)Memory used [KB]: 3454
% 6.70/2.26 % (26369)Time elapsed: 0.039 s
% 6.70/2.26 % (26369)Instructions burned: 135 (million)
% 6.70/2.26 % (26369)------------------------------
% 6.70/2.26 % (26369)------------------------------
% 6.70/2.27 % (26372)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_26179 for (2993ds/258Mi)
% 6.70/2.28 % (26367)Instruction limit reached!
% 6.70/2.28 % (26367)------------------------------
% 6.70/2.28 % (26367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.28 % (26367)Termination reason: Unknown
% 6.70/2.28 % (26367)Termination phase: Saturation
% 6.70/2.28
% 6.70/2.28 % (26367)Memory used [KB]: 8443
% 6.70/2.28 % (26367)Time elapsed: 0.093 s
% 6.70/2.28 % (26367)Instructions burned: 340 (million)
% 6.70/2.28 % (26367)------------------------------
% 6.70/2.28 % (26367)------------------------------
% 6.70/2.28 % (26368)Instruction limit reached!
% 6.70/2.28 % (26368)------------------------------
% 6.70/2.28 % (26368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.28 % (26368)Termination reason: Unknown
% 6.70/2.28 % (26368)Termination phase: Saturation
% 6.70/2.28
% 6.70/2.28 % (26368)Memory used [KB]: 7803
% 6.70/2.28 % (26368)Time elapsed: 0.072 s
% 6.70/2.28 % (26368)Instructions burned: 283 (million)
% 6.70/2.28 % (26368)------------------------------
% 6.70/2.28 % (26368)------------------------------
% 6.70/2.29 % (26373)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_26179 for (2993ds/90Mi)
% 6.70/2.29 % (26374)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_26179 for (2993ds/231Mi)
% 7.33/2.30 % (26371)Instruction limit reached!
% 7.33/2.30 % (26371)------------------------------
% 7.33/2.30 % (26371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.30 % (26371)Termination reason: Unknown
% 7.33/2.30 % (26371)Termination phase: Property scanning
% 7.33/2.30
% 7.33/2.30 % (26371)Memory used [KB]: 3582
% 7.33/2.30 % (26371)Time elapsed: 0.053 s
% 7.33/2.30 % (26371)Instructions burned: 192 (million)
% 7.33/2.30 % (26371)------------------------------
% 7.33/2.30 % (26371)------------------------------
% 7.33/2.31 % (26370)Instruction limit reached!
% 7.33/2.31 % (26370)------------------------------
% 7.33/2.31 % (26370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.31 % (26370)Termination reason: Unknown
% 7.33/2.31 % (26370)Termination phase: Saturation
% 7.33/2.31
% 7.33/2.31 % (26370)Memory used [KB]: 7931
% 7.33/2.31 % (26370)Time elapsed: 0.077 s
% 7.33/2.31 % (26370)Instructions burned: 298 (million)
% 7.33/2.31 % (26370)------------------------------
% 7.33/2.31 % (26370)------------------------------
% 7.33/2.31 % (26375)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_26179 for (2992ds/458Mi)
% 7.33/2.31 % (26373)Instruction limit reached!
% 7.33/2.31 % (26373)------------------------------
% 7.33/2.31 % (26373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.31 % (26373)Termination reason: Unknown
% 7.33/2.31 % (26373)Termination phase: Preprocessing 3
% 7.33/2.31
% 7.33/2.31 % (26373)Memory used [KB]: 2942
% 7.33/2.31 % (26373)Time elapsed: 0.028 s
% 7.33/2.31 % (26373)Instructions burned: 92 (million)
% 7.33/2.31 % (26373)------------------------------
% 7.33/2.31 % (26373)------------------------------
% 7.33/2.32 % (26376)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_26179 for (2992ds/31Mi)
% 7.33/2.32 % (26377)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_26179 for (2992ds/297Mi)
% 7.33/2.33 % (26376)Instruction limit reached!
% 7.33/2.33 % (26376)------------------------------
% 7.33/2.33 % (26376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.33 % (26376)Termination reason: Unknown
% 7.33/2.33 % (26376)Termination phase: shuffling
% 7.33/2.33
% 7.33/2.33 % (26376)Memory used [KB]: 2174
% 7.33/2.33 % (26376)Time elapsed: 0.011 s
% 7.33/2.33 % (26376)Instructions burned: 32 (million)
% 7.33/2.33 % (26376)------------------------------
% 7.33/2.33 % (26376)------------------------------
% 7.33/2.33 % (26347)Instruction limit reached!
% 7.33/2.33 % (26347)------------------------------
% 7.33/2.33 % (26347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.33 % (26347)Termination reason: Unknown
% 7.33/2.33 % (26347)Termination phase: Saturation
% 7.33/2.33
% 7.33/2.33 % (26347)Memory used [KB]: 9338
% 7.33/2.33 % (26347)Time elapsed: 0.342 s
% 7.33/2.33 % (26347)Instructions burned: 1088 (million)
% 7.33/2.33 % (26347)------------------------------
% 7.33/2.33 % (26347)------------------------------
% 7.33/2.33 % (26378)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_26179 for (2992ds/987Mi)
% 7.33/2.34 % (26379)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_26179 for (2992ds/182Mi)
% 7.33/2.35 % (26372)Instruction limit reached!
% 7.33/2.35 % (26372)------------------------------
% 7.33/2.35 % (26372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.35 % (26372)Termination reason: Unknown
% 7.33/2.35 % (26372)Termination phase: Saturation
% 7.33/2.35
% 7.33/2.35 % (26372)Memory used [KB]: 8955
% 7.33/2.35 % (26372)Time elapsed: 0.074 s
% 7.33/2.35 % (26372)Instructions burned: 258 (million)
% 7.33/2.35 % (26372)------------------------------
% 7.33/2.35 % (26372)------------------------------
% 7.33/2.35 % (26374)Instruction limit reached!
% 7.33/2.35 % (26374)------------------------------
% 7.33/2.35 % (26374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.35 % (26374)Termination reason: Unknown
% 7.33/2.35 % (26374)Termination phase: Property scanning
% 7.33/2.35
% 7.33/2.35 % (26374)Memory used [KB]: 3326
% 7.33/2.35 % (26374)Time elapsed: 0.060 s
% 7.33/2.35 % (26374)Instructions burned: 234 (million)
% 7.33/2.35 % (26374)------------------------------
% 7.33/2.35 % (26374)------------------------------
% 7.33/2.35 % (26380)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_26179 for (2992ds/182Mi)
% 7.33/2.36 % (26365)Instruction limit reached!
% 7.33/2.36 % (26365)------------------------------
% 7.33/2.36 % (26365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.36 % (26365)Termination reason: Unknown
% 7.33/2.36 % (26365)Termination phase: Saturation
% 7.33/2.36
% 7.33/2.36 % (26365)Memory used [KB]: 10618
% 7.33/2.36 % (26365)Time elapsed: 0.193 s
% 7.33/2.36 % (26365)Instructions burned: 614 (million)
% 7.33/2.36 % (26365)------------------------------
% 7.33/2.36 % (26365)------------------------------
% 7.33/2.36 % (26381)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_26179 for (2992ds/154Mi)
% 7.33/2.37 % (26382)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_26179 for (2992ds/79Mi)
% 7.33/2.39 % (26379)Instruction limit reached!
% 7.33/2.39 % (26379)------------------------------
% 7.33/2.39 % (26379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.39 % (26379)Termination reason: Unknown
% 7.33/2.39 % (26379)Termination phase: Property scanning
% 7.33/2.39
% 7.33/2.39 % (26379)Memory used [KB]: 3582
% 7.33/2.39 % (26379)Time elapsed: 0.051 s
% 7.33/2.39 % (26379)Instructions burned: 183 (million)
% 7.33/2.39 % (26379)------------------------------
% 7.33/2.39 % (26379)------------------------------
% 7.33/2.39 % (26382)Instruction limit reached!
% 7.33/2.39 % (26382)------------------------------
% 7.33/2.39 % (26382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.39 % (26382)Termination reason: Unknown
% 7.33/2.39 % (26382)Termination phase: Preprocessing 1
% 7.33/2.39
% 7.33/2.39 % (26382)Memory used [KB]: 2558
% 7.33/2.39 % (26382)Time elapsed: 0.025 s
% 7.33/2.39 % (26382)Instructions burned: 81 (million)
% 7.33/2.39 % (26382)------------------------------
% 7.33/2.39 % (26382)------------------------------
% 7.33/2.40 % (26383)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_26179 for (2992ds/216Mi)
% 8.03/2.40 % (26384)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_26179 for (2992ds/114Mi)
% 8.03/2.40 % (26381)Instruction limit reached!
% 8.03/2.40 % (26381)------------------------------
% 8.03/2.40 % (26381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.40 % (26381)Termination reason: Unknown
% 8.03/2.40 % (26381)Termination phase: Property scanning
% 8.03/2.40
% 8.03/2.40 % (26381)Memory used [KB]: 3326
% 8.03/2.40 % (26381)Time elapsed: 0.041 s
% 8.03/2.40 % (26381)Instructions burned: 156 (million)
% 8.03/2.40 % (26381)------------------------------
% 8.03/2.40 % (26381)------------------------------
% 8.03/2.40 % (26380)Instruction limit reached!
% 8.03/2.40 % (26380)------------------------------
% 8.03/2.40 % (26380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.40 % (26380)Termination reason: Unknown
% 8.03/2.40 % (26380)Termination phase: Equality resolution with deletion
% 8.03/2.40
% 8.03/2.40 % (26380)Memory used [KB]: 3709
% 8.03/2.40 % (26380)Time elapsed: 0.051 s
% 8.03/2.40 % (26380)Instructions burned: 183 (million)
% 8.03/2.40 % (26380)------------------------------
% 8.03/2.40 % (26380)------------------------------
% 8.03/2.41 % (26377)Instruction limit reached!
% 8.03/2.41 % (26377)------------------------------
% 8.03/2.41 % (26377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.41 % (26377)Termination reason: Unknown
% 8.03/2.41 % (26377)Termination phase: Saturation
% 8.03/2.41
% 8.03/2.41 % (26377)Memory used [KB]: 8187
% 8.03/2.41 % (26377)Time elapsed: 0.082 s
% 8.03/2.41 % (26377)Instructions burned: 299 (million)
% 8.03/2.41 % (26377)------------------------------
% 8.03/2.41 % (26377)------------------------------
% 8.03/2.41 % (26385)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_26179 for (2991ds/922Mi)
% 8.03/2.41 % (26386)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_26179 for (2991ds/182Mi)
% 8.03/2.41 % (26387)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_26179 for (2991ds/164Mi)
% 8.03/2.44 % (26384)Instruction limit reached!
% 8.03/2.44 % (26384)------------------------------
% 8.03/2.44 % (26384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.44 % (26384)Termination reason: Unknown
% 8.03/2.44 % (26384)Termination phase: Property scanning
% 8.03/2.44
% 8.03/2.44 % (26384)Memory used [KB]: 3454
% 8.03/2.44 % (26384)Time elapsed: 0.035 s
% 8.03/2.44 % (26384)Instructions burned: 116 (million)
% 8.03/2.44 % (26384)------------------------------
% 8.03/2.44 % (26384)------------------------------
% 8.03/2.44 % (26375)Instruction limit reached!
% 8.03/2.44 % (26375)------------------------------
% 8.03/2.44 % (26375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.44 % (26375)Termination reason: Unknown
% 8.03/2.44 % (26375)Termination phase: Saturation
% 8.03/2.44
% 8.03/2.44 % (26375)Memory used [KB]: 9594
% 8.03/2.44 % (26375)Time elapsed: 0.131 s
% 8.03/2.44 % (26375)Instructions burned: 459 (million)
% 8.03/2.44 % (26375)------------------------------
% 8.03/2.44 % (26375)------------------------------
% 8.03/2.45 % (26388)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_26179 for (2991ds/50Mi)
% 8.03/2.45 % (26383)Instruction limit reached!
% 8.03/2.45 % (26383)------------------------------
% 8.03/2.45 % (26383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.45 % (26383)Termination reason: Unknown
% 8.03/2.45 % (26383)Termination phase: Property scanning
% 8.03/2.45
% 8.03/2.45 % (26383)Memory used [KB]: 3326
% 8.03/2.45 % (26383)Time elapsed: 0.056 s
% 8.03/2.45 % (26383)Instructions burned: 217 (million)
% 8.03/2.45 % (26383)------------------------------
% 8.03/2.45 % (26383)------------------------------
% 8.03/2.45 % (26389)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_26179 for (2991ds/368Mi)
% 8.03/2.46 % (26387)Instruction limit reached!
% 8.03/2.46 % (26387)------------------------------
% 8.03/2.46 % (26387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.46 % (26387)Termination reason: Unknown
% 8.03/2.46 % (26387)Termination phase: SInE selection
% 8.03/2.46
% 8.03/2.46 % (26387)Memory used [KB]: 3198
% 8.03/2.46 % (26387)Time elapsed: 0.044 s
% 8.03/2.46 % (26387)Instructions burned: 166 (million)
% 8.03/2.46 % (26387)------------------------------
% 8.03/2.46 % (26387)------------------------------
% 8.03/2.46 % (26388)Instruction limit reached!
% 8.03/2.46 % (26388)------------------------------
% 8.03/2.46 % (26388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.46 % (26388)Termination reason: Unknown
% 8.03/2.46 % (26388)Termination phase: shuffling
% 8.03/2.46
% 8.03/2.46 % (26388)Memory used [KB]: 2686
% 8.03/2.46 % (26388)Time elapsed: 0.015 s
% 8.03/2.46 % (26388)Instructions burned: 51 (million)
% 8.03/2.46 % (26388)------------------------------
% 8.03/2.46 % (26388)------------------------------
% 8.03/2.46 % (26390)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_26179 for (2991ds/1021Mi)
% 8.03/2.46 % (26386)Instruction limit reached!
% 8.03/2.46 % (26386)------------------------------
% 8.03/2.46 % (26386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.46 % (26386)Termination reason: Unknown
% 8.03/2.46 % (26386)Termination phase: Property scanning
% 8.03/2.46
% 8.03/2.46 % (26386)Memory used [KB]: 3326
% 8.03/2.46 % (26386)Time elapsed: 0.048 s
% 8.03/2.46 % (26386)Instructions burned: 185 (million)
% 8.03/2.46 % (26386)------------------------------
% 8.03/2.46 % (26386)------------------------------
% 8.03/2.47 % (26391)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_26179 for (2991ds/267Mi)
% 8.03/2.47 % (26392)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_26179 for (2991ds/204Mi)
% 8.03/2.47 % (26393)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_26179 for (2991ds/26Mi)
% 8.03/2.48 % (26393)Instruction limit reached!
% 8.03/2.48 % (26393)------------------------------
% 8.03/2.48 % (26393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.48 % (26393)Termination reason: Unknown
% 8.03/2.48 % (26393)Termination phase: shuffling
% 8.03/2.48
% 8.03/2.48 % (26393)Memory used [KB]: 2174
% 8.03/2.48 % (26393)Time elapsed: 0.009 s
% 8.03/2.48 % (26393)Instructions burned: 29 (million)
% 8.03/2.48 % (26393)------------------------------
% 8.03/2.48 % (26393)------------------------------
% 8.03/2.49 % (26394)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_26179 for (2991ds/53Mi)
% 8.62/2.50 % (26394)Instruction limit reached!
% 8.62/2.50 % (26394)------------------------------
% 8.62/2.50 % (26394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.50 % (26394)Termination reason: Unknown
% 8.62/2.50 % (26394)Termination phase: shuffling
% 8.62/2.50
% 8.62/2.50 % (26394)Memory used [KB]: 2686
% 8.62/2.50 % (26394)Time elapsed: 0.016 s
% 8.62/2.50 % (26394)Instructions burned: 55 (million)
% 8.62/2.50 % (26394)------------------------------
% 8.62/2.50 % (26394)------------------------------
% 8.62/2.51 % (26395)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_26179 for (2991ds/4436Mi)
% 8.62/2.53 % (26392)Instruction limit reached!
% 8.62/2.53 % (26392)------------------------------
% 8.62/2.53 % (26392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.53 % (26392)Termination reason: Unknown
% 8.62/2.53 % (26392)Termination phase: Property scanning
% 8.62/2.53
% 8.62/2.53 % (26392)Memory used [KB]: 3582
% 8.62/2.53 % (26392)Time elapsed: 0.057 s
% 8.62/2.53 % (26392)Instructions burned: 205 (million)
% 8.62/2.53 % (26392)------------------------------
% 8.62/2.53 % (26392)------------------------------
% 8.62/2.53 % (26391)Instruction limit reached!
% 8.62/2.53 % (26391)------------------------------
% 8.62/2.53 % (26391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.53 % (26391)Termination reason: Unknown
% 8.62/2.53 % (26391)Termination phase: Saturation
% 8.62/2.53
% 8.62/2.53 % (26391)Memory used [KB]: 7803
% 8.62/2.53 % (26391)Time elapsed: 0.068 s
% 8.62/2.53 % (26391)Instructions burned: 269 (million)
% 8.62/2.53 % (26391)------------------------------
% 8.62/2.53 % (26391)------------------------------
% 8.62/2.53 % (26396)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_26179 for (2990ds/1539Mi)
% 8.62/2.54 % (26397)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_26179 for (2990ds/408Mi)
% 8.62/2.55 % (26389)Instruction limit reached!
% 8.62/2.55 % (26389)------------------------------
% 8.62/2.55 % (26389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.55 % (26389)Termination reason: Unknown
% 8.62/2.55 % (26389)Termination phase: Saturation
% 8.62/2.55
% 8.62/2.55 % (26389)Memory used [KB]: 8955
% 8.62/2.55 % (26389)Time elapsed: 0.105 s
% 8.62/2.56 % (26389)Instructions burned: 370 (million)
% 8.62/2.56 % (26389)------------------------------
% 8.62/2.56 % (26389)------------------------------
% 8.62/2.56 % (26398)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_26179 for (2990ds/5205Mi)
% 8.90/2.63 % (26378)Instruction limit reached!
% 8.90/2.63 % (26378)------------------------------
% 8.90/2.63 % (26378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.63 % (26378)Termination reason: Unknown
% 8.90/2.63 % (26378)Termination phase: Saturation
% 8.90/2.63
% 8.90/2.63 % (26378)Memory used [KB]: 10746
% 8.90/2.63 % (26378)Time elapsed: 0.292 s
% 8.90/2.63 % (26378)Instructions burned: 987 (million)
% 8.90/2.63 % (26378)------------------------------
% 8.90/2.63 % (26378)------------------------------
% 8.90/2.64 % (26399)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_26179 for (2989ds/1913Mi)
% 8.90/2.66 % (26397)Instruction limit reached!
% 8.90/2.66 % (26397)------------------------------
% 8.90/2.66 % (26397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.66 % (26397)Termination reason: Unknown
% 8.90/2.66 % (26397)Termination phase: Saturation
% 8.90/2.66
% 8.90/2.66 % (26397)Memory used [KB]: 10874
% 8.90/2.66 % (26397)Time elapsed: 0.116 s
% 8.90/2.66 % (26397)Instructions burned: 409 (million)
% 8.90/2.66 % (26397)------------------------------
% 8.90/2.66 % (26397)------------------------------
% 8.90/2.67 % (26400)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_26179 for (2989ds/4350Mi)
% 9.34/2.70 % (26385)Instruction limit reached!
% 9.34/2.70 % (26385)------------------------------
% 9.34/2.70 % (26385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.34/2.70 % (26385)Termination reason: Unknown
% 9.34/2.70 % (26385)Termination phase: Saturation
% 9.34/2.70
% 9.34/2.70 % (26385)Memory used [KB]: 9210
% 9.34/2.70 % (26385)Time elapsed: 0.290 s
% 9.34/2.70 % (26385)Instructions burned: 922 (million)
% 9.34/2.70 % (26385)------------------------------
% 9.34/2.70 % (26385)------------------------------
% 9.34/2.71 % (26401)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_26179 for (2988ds/68Mi)
% 9.34/2.73 % (26401)Instruction limit reached!
% 9.34/2.73 % (26401)------------------------------
% 9.34/2.73 % (26401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.34/2.73 % (26401)Termination reason: Unknown
% 9.34/2.73 % (26401)Termination phase: Property scanning
% 9.34/2.73
% 9.34/2.73 % (26401)Memory used [KB]: 2430
% 9.34/2.73 % (26401)Time elapsed: 0.022 s
% 9.34/2.73 % (26401)Instructions burned: 70 (million)
% 9.34/2.73 % (26401)------------------------------
% 9.34/2.73 % (26401)------------------------------
% 9.34/2.74 % (26402)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_26179 for (2988ds/358Mi)
% 9.34/2.77 % (26390)Instruction limit reached!
% 9.34/2.77 % (26390)------------------------------
% 9.34/2.77 % (26390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.34/2.77 % (26390)Termination reason: Unknown
% 9.34/2.77 % (26390)Termination phase: Saturation
% 9.34/2.77
% 9.34/2.77 % (26390)Memory used [KB]: 10362
% 9.34/2.77 % (26390)Time elapsed: 0.308 s
% 9.34/2.77 % (26390)Instructions burned: 1021 (million)
% 9.34/2.77 % (26390)------------------------------
% 9.34/2.77 % (26390)------------------------------
% 9.34/2.78 % (26403)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_26179 for (2988ds/31Mi)
% 9.34/2.79 % (26403)Instruction limit reached!
% 9.34/2.79 % (26403)------------------------------
% 9.34/2.79 % (26403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.34/2.79 % (26403)Termination reason: Unknown
% 9.34/2.79 % (26403)Termination phase: shuffling
% 9.34/2.79
% 9.34/2.79 % (26403)Memory used [KB]: 2174
% 9.34/2.79 % (26403)Time elapsed: 0.011 s
% 9.34/2.79 % (26403)Instructions burned: 31 (million)
% 9.34/2.79 % (26403)------------------------------
% 9.34/2.79 % (26403)------------------------------
% 10.00/2.80 % (26404)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_26179 for (2988ds/279Mi)
% 10.00/2.85 % (26402)Instruction limit reached!
% 10.00/2.85 % (26402)------------------------------
% 10.00/2.85 % (26402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.85 % (26402)Termination reason: Unknown
% 10.00/2.85 % (26402)Termination phase: Saturation
% 10.00/2.85
% 10.00/2.85 % (26402)Memory used [KB]: 8187
% 10.00/2.85 % (26402)Time elapsed: 0.108 s
% 10.00/2.85 % (26402)Instructions burned: 360 (million)
% 10.00/2.85 % (26402)------------------------------
% 10.00/2.85 % (26402)------------------------------
% 10.00/2.85 % (26404)Refutation not found, incomplete strategy
% 10.00/2.85 % (26404)------------------------------
% 10.00/2.85 % (26404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.85 % (26404)Termination reason: Refutation not found, incomplete strategy
% 10.00/2.85
% 10.00/2.85
% 10.00/2.85 % (26404)Memory used [KB]: 8059
% 10.00/2.85 % (26404)Time elapsed: 0.057 s
% 10.00/2.85 % (26404)Instructions burned: 214 (million)
% 10.00/2.85 % (26404)------------------------------
% 10.00/2.85 % (26404)------------------------------
% 10.00/2.86 % (26405)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_26179 for (2987ds/258Mi)
% 10.00/2.86 % (26406)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_26179 for (2987ds/26Mi)
% 10.00/2.87 % (26406)Instruction limit reached!
% 10.00/2.87 % (26406)------------------------------
% 10.00/2.87 % (26406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.87 % (26406)Termination reason: Unknown
% 10.00/2.87 % (26406)Termination phase: shuffling
% 10.00/2.87
% 10.00/2.87 % (26406)Memory used [KB]: 2174
% 10.00/2.87 % (26406)Time elapsed: 0.009 s
% 10.00/2.87 % (26406)Instructions burned: 29 (million)
% 10.00/2.87 % (26406)------------------------------
% 10.00/2.87 % (26406)------------------------------
% 10.00/2.88 % (26407)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_26179 for (2987ds/995Mi)
% 10.20/2.93 % (26405)Instruction limit reached!
% 10.20/2.93 % (26405)------------------------------
% 10.20/2.93 % (26405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.93 % (26405)Termination reason: Unknown
% 10.20/2.93 % (26405)Termination phase: Saturation
% 10.20/2.93
% 10.20/2.93 % (26405)Memory used [KB]: 8187
% 10.20/2.93 % (26405)Time elapsed: 0.071 s
% 10.20/2.93 % (26405)Instructions burned: 258 (million)
% 10.20/2.93 % (26405)------------------------------
% 10.20/2.93 % (26405)------------------------------
% 10.20/2.94 % (26408)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_26179 for (2986ds/373Mi)
% 12.62/3.02 % (26396)Instruction limit reached!
% 12.62/3.02 % (26396)------------------------------
% 12.62/3.02 % (26396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.02 % (26396)Termination reason: Unknown
% 12.62/3.02 % (26396)Termination phase: Saturation
% 12.62/3.02
% 12.62/3.02 % (26396)Memory used [KB]: 11001
% 12.62/3.02 % (26396)Time elapsed: 0.496 s
% 12.62/3.02 % (26396)Instructions burned: 1539 (million)
% 12.62/3.02 % (26396)------------------------------
% 12.62/3.02 % (26396)------------------------------
% 12.62/3.03 % (26409)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_26179 for (2985ds/253Mi)
% 12.62/3.04 % (26408)Instruction limit reached!
% 12.62/3.04 % (26408)------------------------------
% 12.62/3.04 % (26408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.04 % (26408)Termination reason: Unknown
% 12.62/3.04 % (26408)Termination phase: Saturation
% 12.62/3.04
% 12.62/3.04 % (26408)Memory used [KB]: 9210
% 12.62/3.04 % (26408)Time elapsed: 0.106 s
% 12.62/3.04 % (26408)Instructions burned: 373 (million)
% 12.62/3.04 % (26408)------------------------------
% 12.62/3.04 % (26408)------------------------------
% 12.62/3.05 % (26410)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_26179 for (2985ds/832Mi)
% 12.62/3.08 % (26399)Instruction limit reached!
% 12.62/3.08 % (26399)------------------------------
% 12.62/3.08 % (26399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.08 % (26399)Termination reason: Unknown
% 12.62/3.08 % (26399)Termination phase: Saturation
% 12.62/3.08
% 12.62/3.08 % (26399)Memory used [KB]: 4349
% 12.62/3.08 % (26399)Time elapsed: 0.443 s
% 12.62/3.08 % (26399)Instructions burned: 1914 (million)
% 12.62/3.08 % (26399)------------------------------
% 12.62/3.08 % (26399)------------------------------
% 12.62/3.09 % (26411)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_26179 for (2985ds/668Mi)
% 12.62/3.09 % (26409)Instruction limit reached!
% 12.62/3.09 % (26409)------------------------------
% 12.62/3.09 % (26409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.09 % (26409)Termination reason: Unknown
% 12.62/3.09 % (26409)Termination phase: Property scanning
% 12.62/3.09
% 12.62/3.09 % (26409)Memory used [KB]: 3326
% 12.62/3.09 % (26409)Time elapsed: 0.065 s
% 12.62/3.09 % (26409)Instructions burned: 254 (million)
% 12.62/3.09 % (26409)------------------------------
% 12.62/3.09 % (26409)------------------------------
% 12.62/3.10 % (26412)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_26179 for (2985ds/40Mi)
% 12.62/3.11 % (26412)Instruction limit reached!
% 12.62/3.11 % (26412)------------------------------
% 12.62/3.11 % (26412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.11 % (26412)Termination reason: Unknown
% 12.62/3.11 % (26412)Termination phase: shuffling
% 12.62/3.11
% 12.62/3.11 % (26412)Memory used [KB]: 2430
% 12.62/3.11 % (26412)Time elapsed: 0.012 s
% 12.62/3.11 % (26412)Instructions burned: 40 (million)
% 12.62/3.11 % (26412)------------------------------
% 12.62/3.11 % (26412)------------------------------
% 13.24/3.12 % (26413)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_26179 for (2984ds/294Mi)
% 13.24/3.17 % (26407)Instruction limit reached!
% 13.24/3.17 % (26407)------------------------------
% 13.24/3.17 % (26407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.24/3.17 % (26407)Termination reason: Unknown
% 13.24/3.17 % (26407)Termination phase: Saturation
% 13.24/3.17
% 13.24/3.17 % (26407)Memory used [KB]: 12537
% 13.24/3.17 % (26407)Time elapsed: 0.287 s
% 13.24/3.17 % (26407)Instructions burned: 996 (million)
% 13.24/3.17 % (26407)------------------------------
% 13.24/3.17 % (26407)------------------------------
% 13.24/3.18 % (26414)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_26179 for (2984ds/187Mi)
% 13.24/3.18 % (26413)Refutation not found, incomplete strategy
% 13.24/3.18 % (26413)------------------------------
% 13.24/3.18 % (26413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.24/3.18 % (26413)Termination reason: Refutation not found, incomplete strategy
% 13.24/3.18
% 13.24/3.18
% 13.24/3.18 % (26413)Memory used [KB]: 7931
% 13.24/3.18 % (26413)Time elapsed: 0.058 s
% 13.24/3.18 % (26413)Instructions burned: 220 (million)
% 13.24/3.18 % (26413)------------------------------
% 13.24/3.18 % (26413)------------------------------
% 13.24/3.19 % (26415)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_26179 for (2984ds/371Mi)
% 13.24/3.19 % (26395)First to succeed.
% 13.24/3.20 % (26395)Refutation found. Thanks to Tanya!
% 13.24/3.20 % SZS status Theorem for DTF2THF_26179
% 13.24/3.20 % SZS output start Proof for DTF2THF_26179
% 13.24/3.20 thf(type_def_5, type, nat: $tType).
% 13.24/3.20 thf(type_def_6, type, list_list_com: $tType).
% 13.24/3.20 thf(type_def_8, type, list_com: $tType).
% 13.24/3.20 thf(type_def_9, type, list_P1040014977_state: $tType).
% 13.24/3.20 thf(type_def_10, type, list_P890094829_state: $tType).
% 13.24/3.20 thf(type_def_11, type, com: $tType).
% 13.24/3.20 thf(type_def_12, type, set_Pr1822651163om_com: $tType).
% 13.24/3.20 thf(type_def_13, type, set_Pr602326075st_com: $tType).
% 13.24/3.20 thf(type_def_14, type, set_Pr1165141447_state: $tType).
% 13.24/3.20 thf(type_def_15, type, set_Pr1142642759_state: $tType).
% 13.24/3.20 thf(type_def_16, type, set_Pr2096893127_state: $tType).
% 13.24/3.20 thf(type_def_17, type, set_Pr1325664839_state: $tType).
% 13.24/3.20 thf(type_def_18, type, state: $tType).
% 13.24/3.20 thf(type_def_19, type, list_state: $tType).
% 13.24/3.20 thf(type_def_20, type, produc2041926651_state: $tType).
% 13.24/3.20 thf(type_def_21, type, produc410756839_state: $tType).
% 13.24/3.20 thf(type_def_22, type, set_Pr849496667_state: $tType).
% 13.24/3.20 thf(type_def_23, type, set_Pr391631483_state: $tType).
% 13.24/3.20 thf(type_def_24, type, set_nat: $tType).
% 13.24/3.20 thf(type_def_25, type, set_state: $tType).
% 13.24/3.20 thf(type_def_26, type, produc2058209240st_com: $tType).
% 13.24/3.20 thf(type_def_27, type, produc1393453339_state: $tType).
% 13.24/3.20 thf(type_def_28, type, produc258871771st_com: $tType).
% 13.24/3.20 thf(type_def_29, type, produc1225889383_state: $tType).
% 13.24/3.20 thf(type_def_30, type, produc1586269031_state: $tType).
% 13.24/3.20 thf(type_def_31, type, product_prod_com_com: $tType).
% 13.24/3.20 thf(type_def_32, type, produc186437863_state: $tType).
% 13.24/3.20 thf(type_def_33, type, produc2046512871_state: $tType).
% 13.24/3.20 thf(type_def_34, type, set_Pr541394119_state: $tType).
% 13.24/3.20 thf(func_def_0, type, set_Pr541394119_state: $tType).
% 13.24/3.20 thf(func_def_1, type, produc2046512871_state: $tType).
% 13.24/3.20 thf(func_def_2, type, set_Pr1325664839_state: $tType).
% 13.24/3.20 thf(func_def_3, type, produc1586269031_state: $tType).
% 13.24/3.20 thf(func_def_4, type, set_Pr2096893127_state: $tType).
% 13.24/3.20 thf(func_def_5, type, produc186437863_state: $tType).
% 13.24/3.20 thf(func_def_6, type, set_Pr1142642759_state: $tType).
% 13.24/3.20 thf(func_def_7, type, produc1225889383_state: $tType).
% 13.24/3.20 thf(func_def_8, type, list_P890094829_state: $tType).
% 13.24/3.20 thf(func_def_9, type, set_Pr1165141447_state: $tType).
% 13.24/3.20 thf(func_def_10, type, produc410756839_state: $tType).
% 13.24/3.20 thf(func_def_11, type, set_Pr391631483_state: $tType).
% 13.24/3.20 thf(func_def_12, type, produc1393453339_state: $tType).
% 13.24/3.20 thf(func_def_13, type, produc2058209240st_com: $tType).
% 13.24/3.20 thf(func_def_14, type, set_Pr602326075st_com: $tType).
% 13.24/3.20 thf(func_def_15, type, list_P1040014977_state: $tType).
% 13.24/3.20 thf(func_def_16, type, set_Pr849496667_state: $tType).
% 13.24/3.20 thf(func_def_17, type, produc258871771st_com: $tType).
% 13.24/3.20 thf(func_def_18, type, produc2041926651_state: $tType).
% 13.24/3.20 thf(func_def_19, type, set_Pr1822651163om_com: $tType).
% 13.24/3.20 thf(func_def_20, type, product_prod_com_com: $tType).
% 13.24/3.20 thf(func_def_21, type, list_list_com: $tType).
% 13.24/3.20 thf(func_def_22, type, list_state: $tType).
% 13.24/3.20 thf(func_def_23, type, set_state: $tType).
% 13.24/3.20 thf(func_def_24, type, list_com: $tType).
% 13.24/3.20 thf(func_def_25, type, set_nat: $tType).
% 13.24/3.20 thf(func_def_26, type, state: $tType).
% 13.24/3.20 thf(func_def_27, type, com: $tType).
% 13.24/3.20 thf(func_def_28, type, nat: $tType).
% 13.24/3.20 thf(func_def_29, type, zero_zero_nat: nat).
% 13.24/3.20 thf(func_def_30, type, append_list_com: list_list_com > list_list_com > list_list_com).
% 13.24/3.20 thf(func_def_31, type, append_com: list_com > list_com > list_com).
% 13.24/3.20 thf(func_def_32, type, append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state).
% 13.24/3.20 thf(func_def_33, type, append221843330_state: list_P890094829_state > list_P890094829_state > list_P890094829_state).
% 13.24/3.20 thf(func_def_34, type, bind_com_com: list_com > (com > list_com) > list_com).
% 13.24/3.20 thf(func_def_35, type, concat_com: list_list_com > list_com).
% 13.24/3.20 thf(func_def_36, type, gen_length_com: nat > list_com > nat).
% 13.24/3.20 thf(func_def_37, type, insert_com: com > list_com > list_com).
% 13.24/3.20 thf(func_def_38, type, lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 13.24/3.20 thf(func_def_39, type, lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 13.24/3.20 thf(func_def_40, type, lexord1893203674_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 13.24/3.20 thf(func_def_41, type, cons_list_com: list_com > list_list_com > list_list_com).
% 13.24/3.20 thf(func_def_42, type, cons_com: com > list_com > list_com).
% 13.24/3.20 thf(func_def_43, type, cons_state: state > list_state > list_state).
% 13.24/3.20 thf(func_def_44, type, cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state).
% 13.24/3.20 thf(func_def_45, type, cons_P438230685_state: produc410756839_state > list_P890094829_state > list_P890094829_state).
% 13.24/3.20 thf(func_def_46, type, nil_list_com: list_list_com).
% 13.24/3.20 thf(func_def_47, type, nil_com: list_com).
% 13.24/3.20 thf(func_def_48, type, nil_state: list_state).
% 13.24/3.20 thf(func_def_49, type, nil_Pr1844458753_state: list_P1040014977_state).
% 13.24/3.20 thf(func_def_50, type, nil_Pr1347322605_state: list_P890094829_state).
% 13.24/3.20 thf(func_def_51, type, listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 13.24/3.20 thf(func_def_52, type, listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 13.24/3.20 thf(func_def_53, type, listre1725776070_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 13.24/3.20 thf(func_def_54, type, listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state).
% 13.24/3.20 thf(func_def_55, type, listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 13.24/3.20 thf(func_def_56, type, listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 13.24/3.20 thf(func_def_57, type, listre1244407729_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 13.24/3.20 thf(func_def_58, type, maps_com_com: (com > list_com) > list_com > list_com).
% 13.24/3.20 thf(func_def_59, type, n_lists_com: nat > list_com > list_list_com).
% 13.24/3.20 thf(func_def_60, type, nths_com: list_com > set_nat > list_com).
% 13.24/3.20 thf(func_def_61, type, product_lists_com: list_list_com > list_list_com).
% 13.24/3.20 thf(func_def_62, type, subseqs_com: list_com > list_list_com).
% 13.24/3.20 thf(func_def_63, type, suc: nat > nat).
% 13.24/3.20 thf(func_def_64, type, pHoare259243666_exec1: set_Pr1165141447_state).
% 13.24/3.20 thf(func_def_65, type, pHoare259243732_execs: state > list_com > state > $o).
% 13.24/3.20 thf(func_def_66, type, pHoare2126160787le_inf: list_com > state > $o).
% 13.24/3.20 thf(func_def_67, type, pHoare806997636termis: list_com > state > $o).
% 13.24/3.20 thf(func_def_68, type, cond: (state > $o) > com > com > com).
% 13.24/3.20 thf(func_def_69, type, do: (state > set_state) > com).
% 13.24/3.20 thf(func_def_70, type, semi: com > com > com).
% 13.24/3.20 thf(func_def_71, type, while: (state > $o) > com > com).
% 13.24/3.20 thf(func_def_72, type, exec: state > com > state > $o).
% 13.24/3.20 thf(func_def_73, type, termi: com > state > $o).
% 13.24/3.20 thf(func_def_74, type, produc1914379986st_com: (com > com > $o) > list_com > produc2058209240st_com).
% 13.24/3.20 thf(func_def_75, type, produc1742567891_state: list_list_com > list_state > produc1393453339_state).
% 13.24/3.20 thf(func_def_76, type, produc1307105171st_com: list_com > list_com > produc258871771st_com).
% 13.24/3.20 thf(func_def_77, type, produc1204172211_state: list_com > state > produc2041926651_state).
% 13.24/3.20 thf(func_def_78, type, produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state).
% 13.24/3.20 thf(func_def_79, type, produc1354769367_state: list_P890094829_state > list_P890094829_state > produc1586269031_state).
% 13.24/3.20 thf(func_def_80, type, product_Pair_com_com: com > com > product_prod_com_com).
% 13.24/3.20 thf(func_def_81, type, produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state).
% 13.24/3.20 thf(func_def_82, type, produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state).
% 13.24/3.20 thf(func_def_83, type, produc2049704791_state: produc186437863_state > produc186437863_state > produc2046512871_state).
% 13.24/3.20 thf(func_def_84, type, irrefl_com: set_Pr1822651163om_com > $o).
% 13.24/3.20 thf(func_def_85, type, collect_state: (state > $o) > set_state).
% 13.24/3.20 thf(func_def_86, type, collec300063826_state: (produc410756839_state > $o) > set_Pr1165141447_state).
% 13.24/3.20 thf(func_def_87, type, collec489924946_state: (produc186437863_state > $o) > set_Pr2096893127_state).
% 13.24/3.20 thf(func_def_88, type, transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com).
% 13.24/3.20 thf(func_def_89, type, transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state).
% 13.24/3.20 thf(func_def_90, type, transi1965148016_state: set_Pr1325664839_state > set_Pr1325664839_state).
% 13.24/3.20 thf(func_def_91, type, transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com).
% 13.24/3.20 thf(func_def_92, type, transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state).
% 13.24/3.20 thf(func_def_93, type, transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state).
% 13.24/3.20 thf(func_def_94, type, transi152726506_state: set_Pr541394119_state > set_Pr541394119_state).
% 13.24/3.20 thf(func_def_95, type, transi1726587420_state: set_Pr1165141447_state > set_Pr1165141447_state).
% 13.24/3.20 thf(func_def_96, type, transi1666849160_state: set_Pr2096893127_state > set_Pr2096893127_state).
% 13.24/3.20 thf(func_def_97, type, transi1995721864_state: set_Pr541394119_state > set_Pr541394119_state).
% 13.24/3.20 thf(func_def_98, type, member_nat: nat > set_nat > $o).
% 13.24/3.20 thf(func_def_99, type, member_state: state > set_state > $o).
% 13.24/3.20 thf(func_def_100, type, member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o).
% 13.24/3.20 thf(func_def_101, type, member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o).
% 13.24/3.20 thf(func_def_102, type, member64234660_state: produc2041926651_state > set_Pr849496667_state > $o).
% 13.24/3.20 thf(func_def_103, type, member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o).
% 13.24/3.20 thf(func_def_104, type, member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o).
% 13.24/3.20 thf(func_def_105, type, member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o).
% 13.24/3.20 thf(func_def_106, type, member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_107, type, member512523024_state: produc186437863_state > set_Pr2096893127_state > $o).
% 13.24/3.20 thf(func_def_108, type, member284400400_state: produc2046512871_state > set_Pr541394119_state > $o).
% 13.24/3.20 thf(func_def_109, type, c: com).
% 13.24/3.20 thf(func_def_110, type, f: nat > produc2041926651_state).
% 13.24/3.20 thf(func_def_111, type, n: nat).
% 13.24/3.20 thf(func_def_112, type, s: state).
% 13.24/3.20 thf(func_def_130, type, sP0: state > (state > $o) > state > com > list_com > list_com > $o).
% 13.24/3.20 thf(func_def_131, type, sP1: state > com > list_com > list_com > (state > $o) > state > $o).
% 13.24/3.20 thf(func_def_132, type, sP2: (list_com > $o) > $o).
% 13.24/3.20 thf(func_def_133, type, sP3: list_com > list_com > com > list_com > $o).
% 13.24/3.20 thf(func_def_134, type, sP4: com > list_com > list_com > list_com > $o).
% 13.24/3.20 thf(func_def_135, type, sP5: (state > $o) > state > state > list_com > list_com > $o).
% 13.24/3.20 thf(func_def_136, type, sP6: com > list_com > list_com > (state > $o) > state > state > $o).
% 13.24/3.20 thf(func_def_137, type, sP7: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_138, type, sP8: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > $o).
% 13.24/3.20 thf(func_def_139, type, sP9: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > $o).
% 13.24/3.20 thf(func_def_140, type, sP10: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_141, type, sP11: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_142, type, sP12: (list_com > $o) > $o).
% 13.24/3.20 thf(func_def_143, type, sP13: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_144, type, sP14: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_145, type, sP15: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_146, type, sP16: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > $o).
% 13.24/3.20 thf(func_def_147, type, sP17: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_148, type, sP18: (produc2041926651_state > $o) > produc2041926651_state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_149, type, sP19: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > $o).
% 13.24/3.20 thf(func_def_150, type, sP20: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_151, type, sP21: (list_com > $o) > $o).
% 13.24/3.20 thf(func_def_152, type, sP22: (list_com > list_com > $o) > $o).
% 13.24/3.20 thf(func_def_153, type, sP23: (list_com > state > $o) > list_com > state > set_Pr1165141447_state > $o).
% 13.24/3.20 thf(func_def_154, type, sP24: list_com > com > list_com > list_com > $o).
% 13.24/3.20 thf(func_def_155, type, sP25: list_com > list_com > com > list_com > $o).
% 13.24/3.20 thf(func_def_156, type, sP26: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > $o).
% 13.24/3.20 thf(func_def_157, type, sP27: (list_com > $o) > $o).
% 13.24/3.20 thf(func_def_158, type, sK28: list_com > com).
% 13.24/3.20 thf(func_def_159, type, sK29: list_com > list_com).
% 13.24/3.20 thf(func_def_160, type, sK30: produc186437863_state > produc2041926651_state).
% 13.24/3.20 thf(func_def_161, type, sK31: produc186437863_state > produc2041926651_state).
% 13.24/3.20 thf(func_def_162, type, sK32: produc186437863_state > produc410756839_state).
% 13.24/3.20 thf(func_def_163, type, sK33: produc2041926651_state > (nat > produc2041926651_state) > set_Pr1165141447_state > nat).
% 13.24/3.20 thf(func_def_164, type, sK34: produc2041926651_state > set_Pr1165141447_state > nat > produc2041926651_state).
% 13.24/3.20 thf(func_def_165, type, sK35: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_166, type, sK36: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_167, type, sK37: (list_com > list_com > $o) > com).
% 13.24/3.20 thf(func_def_168, type, sK38: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_169, type, sK39: nat > nat).
% 13.24/3.20 thf(func_def_170, type, sK40: produc2041926651_state > list_com).
% 13.24/3.20 thf(func_def_171, type, sK41: produc2041926651_state > state).
% 13.24/3.20 thf(func_def_172, type, sK42: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_173, type, sK43: (list_com > list_com > $o) > com).
% 13.24/3.20 thf(func_def_174, type, sK44: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_175, type, sK45: (list_com > list_com > $o) > com).
% 13.24/3.20 thf(func_def_176, type, sK46: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_177, type, sK47: (list_com > list_com > $o) > com).
% 13.24/3.20 thf(func_def_178, type, sK48: (list_com > list_com > $o) > com).
% 13.24/3.20 thf(func_def_179, type, sK49: (list_com > list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_180, type, sK50: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_181, type, sK51: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_182, type, sK52: produc258871771st_com > com).
% 13.24/3.20 thf(func_def_183, type, sK53: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_184, type, sK54: (list_com > $o) > com).
% 13.24/3.20 thf(func_def_185, type, sK55: (list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_186, type, sK56: (list_com > $o) > com).
% 13.24/3.20 thf(func_def_187, type, sK57: list_com > list_com > com > list_com > list_com).
% 13.24/3.20 thf(func_def_188, type, sK58: (list_com > $o) > com).
% 13.24/3.20 thf(func_def_189, type, sK59: (list_com > $o) > list_com).
% 13.24/3.20 thf(func_def_190, type, sK60: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_191, type, sK61: produc258871771st_com > com).
% 13.24/3.20 thf(func_def_192, type, sK62: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_193, type, sK63: produc258871771st_com > com).
% 13.24/3.20 thf(func_def_194, type, sK64: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_195, type, sK65: produc258871771st_com > list_com).
% 13.24/3.20 thf(func_def_196, type, sK66: (produc186437863_state > $o) > list_com).
% 13.24/3.20 thf(func_def_197, type, sK67: (produc186437863_state > $o) > produc2041926651_state).
% 13.24/3.20 thf(func_def_198, type, sK68: (produc186437863_state > $o) > produc410756839_state).
% 12.49/3.20 thf(func_def_199, type, sK69: (produc186437863_state > $o) > state).
% 12.49/3.20 thf(func_def_200, type, sK70: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_201, type, sK71: (list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_202, type, sK72: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_203, type, sK73: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_204, type, sK74: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_205, type, sK75: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_206, type, sK76: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_207, type, sK77: state > com > (state > $o) > state).
% 12.49/3.20 thf(func_def_208, type, sK78: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_209, type, sK79: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_210, type, sK80: ((com > com > $o) > list_com > $o) > com > com > $o).
% 12.49/3.20 thf(func_def_211, type, sK81: ((com > com > $o) > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_212, type, sK82: ((com > com > $o) > list_com > $o) > com > com > $o).
% 12.49/3.20 thf(func_def_213, type, sK83: ((com > com > $o) > list_com > $o) > com).
% 12.49/3.20 thf(func_def_214, type, sK84: nat > nat).
% 12.49/3.20 thf(func_def_215, type, sK85: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_216, type, sK86: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_217, type, sK87: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_218, type, sK88: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_219, type, sK89: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_220, type, sK90: (nat > $o) > nat).
% 12.49/3.20 thf(func_def_221, type, sK91: (nat > state) > com > nat).
% 12.49/3.20 thf(func_def_222, type, sK92: (state > $o) > (nat > state) > nat).
% 12.49/3.20 thf(func_def_223, type, sK93: (nat > $o) > nat).
% 12.49/3.20 thf(func_def_224, type, sK94: (nat > state) > (state > $o) > nat).
% 12.49/3.20 thf(func_def_225, type, sK95: (nat > state) > com > nat).
% 12.49/3.20 thf(func_def_226, type, sK96: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_227, type, sK97: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_228, type, sK98: set_Pr1165141447_state > (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_229, type, sK99: (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_230, type, sK100: ((com > com) > list_com > list_com > $o) > com).
% 12.49/3.20 thf(func_def_231, type, sK101: ((com > com) > list_com > list_com > $o) > com > com).
% 12.49/3.20 thf(func_def_232, type, sK102: ((com > com) > list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_233, type, sK103: ((com > com) > list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_234, type, sK104: ((com > com) > list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_235, type, sK105: ((com > com) > list_com > list_com > $o) > com > com).
% 12.49/3.20 thf(func_def_236, type, sK106: (produc186437863_state > $o) > produc410756839_state).
% 12.49/3.20 thf(func_def_237, type, sK107: (produc186437863_state > $o) > produc410756839_state).
% 12.49/3.20 thf(func_def_238, type, sK108: produc186437863_state > produc410756839_state).
% 12.49/3.20 thf(func_def_239, type, sK109: produc186437863_state > produc410756839_state).
% 12.49/3.20 thf(func_def_240, type, sK110: list_com > list_com > list_com).
% 12.49/3.20 thf(func_def_241, type, sK111: ((com > com > $o) > list_com > $o) > com).
% 12.49/3.20 thf(func_def_242, type, sK112: ((com > com > $o) > list_com > $o) > com > com > $o).
% 12.49/3.20 thf(func_def_243, type, sK113: ((com > com > $o) > list_com > $o) > com > com > $o).
% 12.49/3.20 thf(func_def_244, type, sK114: ((com > com > $o) > list_com > $o) > com).
% 12.49/3.20 thf(func_def_245, type, sK115: ((com > com > $o) > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_246, type, sK116: ((com > com > $o) > list_com > $o) > com > com > $o).
% 12.49/3.20 thf(func_def_247, type, sK117: ((com > com > $o) > list_com > $o) > com).
% 12.49/3.20 thf(func_def_248, type, sK118: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_249, type, sK119: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_250, type, sK120: produc2041926651_state > set_Pr1165141447_state > (produc2041926651_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_251, type, sK121: list_com > list_com > list_com).
% 12.49/3.20 thf(func_def_252, type, sK122: (nat > produc410756839_state) > set_Pr2096893127_state > produc410756839_state > nat).
% 12.49/3.20 thf(func_def_253, type, sK123: set_Pr2096893127_state > produc410756839_state > nat > produc410756839_state).
% 12.49/3.20 thf(func_def_254, type, sK124: com > com > state > state).
% 12.49/3.20 thf(func_def_255, type, sK125: (produc410756839_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_256, type, sK126: (produc410756839_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_257, type, sK127: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_258, type, sK128: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_259, type, sK129: (produc186437863_state > $o) > produc410756839_state).
% 12.49/3.20 thf(func_def_260, type, sK130: (produc186437863_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_261, type, sK131: (produc186437863_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_262, type, sK132: (nat > $o) > nat).
% 12.49/3.20 thf(func_def_263, type, sK133: (list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_264, type, sK134: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_265, type, sK135: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_266, type, sK136: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_267, type, sK137: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_268, type, sK138: produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_269, type, sK139: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_270, type, sK140: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_271, type, sK141: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_272, type, sK142: list_com > list_com).
% 12.49/3.20 thf(func_def_273, type, sK143: list_com > com).
% 12.49/3.20 thf(func_def_274, type, sK144: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_275, type, sK145: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_276, type, sK146: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_277, type, sK147: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_278, type, sK148: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_279, type, sK149: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_280, type, sK150: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_281, type, sK151: (produc2041926651_state > $o) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_282, type, sK152: (produc2041926651_state > $o) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_283, type, sK153: produc2041926651_state > (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_284, type, sK154: set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_285, type, sK155: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > state).
% 12.49/3.20 thf(func_def_286, type, sK156: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > list_com).
% 12.49/3.20 thf(func_def_287, type, sK157: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > state).
% 12.49/3.20 thf(func_def_288, type, sK158: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > list_com).
% 12.49/3.20 thf(func_def_289, type, sK159: (list_com > state > $o) > list_com > set_Pr1165141447_state > state > state).
% 12.49/3.20 thf(func_def_290, type, sK160: (list_com > state > $o) > list_com > set_Pr1165141447_state > state > list_com).
% 12.49/3.20 thf(func_def_291, type, sK161: state > list_com > set_Pr1165141447_state > state > list_com > list_com).
% 12.49/3.20 thf(func_def_292, type, sK162: state > list_com > set_Pr1165141447_state > state > list_com > state).
% 12.49/3.20 thf(func_def_293, type, sK163: produc410756839_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_294, type, sK164: produc410756839_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_295, type, sK165: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_296, type, sK166: (list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_297, type, sK167: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_298, type, sK168: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_299, type, sK169: produc410756839_state > set_Pr2096893127_state > nat > produc410756839_state).
% 12.49/3.20 thf(func_def_300, type, sK170: (nat > produc410756839_state) > produc410756839_state > set_Pr2096893127_state > nat).
% 12.49/3.20 thf(func_def_301, type, sK171: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_302, type, sK172: (produc186437863_state > $o) > produc410756839_state).
% 12.49/3.20 thf(func_def_303, type, sK173: (produc186437863_state > $o) > produc410756839_state).
% 12.49/3.20 thf(func_def_304, type, sK174: (list_com > list_com > $o) > com).
% 12.49/3.20 thf(func_def_305, type, sK175: (list_com > list_com > $o) > com).
% 12.49/3.20 thf(func_def_306, type, sK176: (list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_307, type, sK177: (list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_308, type, sK178: (list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_309, type, sK179: (list_com > list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_310, type, sK180: list_com > com).
% 12.49/3.20 thf(func_def_311, type, sK181: list_com > com).
% 12.49/3.20 thf(func_def_312, type, sK182: list_com > list_com).
% 12.49/3.20 thf(func_def_313, type, sK183: list_com > com).
% 12.49/3.20 thf(func_def_314, type, sK184: produc410756839_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_315, type, sK185: produc410756839_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_316, type, sK186: (list_com > state > $o) > list_com > state > set_Pr1165141447_state > list_com).
% 12.49/3.20 thf(func_def_317, type, sK187: (list_com > state > $o) > list_com > state > set_Pr1165141447_state > list_com).
% 12.49/3.20 thf(func_def_318, type, sK188: (list_com > state > $o) > list_com > state > set_Pr1165141447_state > state).
% 12.49/3.20 thf(func_def_319, type, sK189: (list_com > state > $o) > list_com > state > set_Pr1165141447_state > state).
% 12.49/3.20 thf(func_def_320, type, sK190: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_321, type, sK191: list_com > list_com > com > list_com > list_com).
% 12.49/3.20 thf(func_def_322, type, sK192: (produc2041926651_state > $o) > list_com).
% 12.49/3.20 thf(func_def_323, type, sK193: (produc2041926651_state > $o) > state).
% 12.49/3.20 thf(func_def_324, type, sK194: produc186437863_state > produc410756839_state).
% 12.49/3.20 thf(func_def_325, type, sK195: produc186437863_state > produc410756839_state).
% 12.49/3.20 thf(func_def_326, type, sK196: (produc410756839_state > $o) > list_com).
% 12.49/3.20 thf(func_def_327, type, sK197: (produc410756839_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_328, type, sK198: (produc410756839_state > $o) > state).
% 12.49/3.20 thf(func_def_329, type, sK199: produc2041926651_state > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_330, type, sK200: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > state).
% 12.49/3.20 thf(func_def_331, type, sK201: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > state).
% 12.49/3.20 thf(func_def_332, type, sK202: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > list_com).
% 12.49/3.20 thf(func_def_333, type, sK203: list_com > state > set_Pr1165141447_state > (list_com > state > $o) > list_com).
% 12.49/3.20 thf(func_def_334, type, sK204: produc2041926651_state > list_com).
% 12.49/3.20 thf(func_def_335, type, sK205: produc2041926651_state > state).
% 12.49/3.20 thf(func_def_336, type, sK206: (nat > nat > $o) > nat).
% 12.49/3.20 thf(func_def_337, type, sK207: (nat > nat > $o) > nat).
% 12.49/3.20 thf(func_def_338, type, sK208: (nat > nat > $o) > nat).
% 12.49/3.20 thf(func_def_339, type, sK209: (nat > nat > $o) > nat).
% 12.49/3.20 thf(func_def_340, type, sK210: set_Pr1165141447_state > produc2041926651_state > (nat > produc2041926651_state) > nat).
% 12.49/3.20 thf(func_def_341, type, sK211: set_Pr1165141447_state > produc2041926651_state > nat > produc2041926651_state).
% 12.49/3.20 thf(func_def_342, type, sK212: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_343, type, sK213: (produc2041926651_state > $o) > list_com).
% 12.49/3.20 thf(func_def_344, type, sK214: (produc2041926651_state > $o) > state).
% 12.49/3.20 thf(func_def_345, type, sK215: produc186437863_state > produc410756839_state).
% 12.49/3.20 thf(func_def_346, type, sK216: produc186437863_state > state).
% 12.49/3.20 thf(func_def_347, type, sK217: produc186437863_state > list_com).
% 12.49/3.20 thf(func_def_348, type, sK218: produc186437863_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_349, type, sK219: (list_com > $o) > list_com).
% 12.49/3.20 thf(func_def_350, type, sK220: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_351, type, sK221: (list_com > $o) > com).
% 12.49/3.20 thf(func_def_352, type, sK222: (produc410756839_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_353, type, sK223: (produc410756839_state > $o) > produc2041926651_state).
% 12.49/3.20 thf(func_def_354, type, sK224: list_com > list_com).
% 12.49/3.20 thf(func_def_355, type, sK225: list_com > com).
% 12.49/3.20 thf(func_def_356, type, sK226: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_357, type, sK227: produc410756839_state > list_com).
% 12.49/3.20 thf(func_def_358, type, sK228: produc410756839_state > state).
% 12.49/3.20 thf(func_def_359, type, sK229: produc410756839_state > produc2041926651_state).
% 12.49/3.20 thf(func_def_362, type, ph231: !>[X0: $tType]:(X0)).
% 12.49/3.20 thf(f6077,plain,(
% 12.49/3.20 $false),
% 12.49/3.20 inference(avatar_sat_refutation,[status(thm)],[f6053,f6076])).
% 12.49/3.20 thf(f6076,plain,(
% 12.49/3.20 ~spl230_45),
% 12.49/3.20 inference(avatar_contradiction_clause,[status(thm)],[f6075])).
% 12.49/3.20 thf(f6075,plain,(
% 12.49/3.20 $false | ~spl230_45),
% 12.49/3.20 inference(subsumption_resolution,[status(thm)],[f6074,f3345])).
% 12.49/3.20 thf(f3345,plain,(
% 12.49/3.20 ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ n))) @ (transi1726587420_state @ pHoare259243666_exec1)))),
% 12.49/3.20 inference(trivial_inequality_removal,[status(thm)],[f3339])).
% 12.49/3.20 thf(f3339,plain,(
% 12.49/3.20 ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ n))) @ (transi1726587420_state @ pHoare259243666_exec1))) | ($true != $true)),
% 12.49/3.20 inference(superposition,[status(thm)],[f2123,f1627])).
% 12.49/3.20 thf(f1627,plain,(
% 12.49/3.20 ( ! [X2 : produc2041926651_state,X0 : set_Pr1165141447_state,X1 : produc2041926651_state] : (($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1302705790_state @ X0))) | ((member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X0)) != $true)) )),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f1044])).
% 12.49/3.20 thf(f1044,plain,(
% 12.49/3.20 ! [X0 : set_Pr1165141447_state,X1 : produc2041926651_state,X2 : produc2041926651_state] : (($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1302705790_state @ X0))) | ((member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X0)) != $true))),
% 12.49/3.20 inference(ennf_transformation,[status(thm)],[f411])).
% 12.49/3.20 thf(f411,plain,(
% 12.49/3.20 ! [X0 : set_Pr1165141447_state,X1 : produc2041926651_state,X2 : produc2041926651_state] : (((member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X0)) = $true) => ($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1302705790_state @ X0))))),
% 12.49/3.20 inference(fool_elimination,[status(thm)],[f410])).
% 12.49/3.20 thf(f410,plain,(
% 12.49/3.20 ! [X0 : set_Pr1165141447_state,X1 : produc2041926651_state,X2 : produc2041926651_state] : ((member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X0)) => (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1302705790_state @ X0)))),
% 12.49/3.20 inference(rectify,[status(thm)],[f30])).
% 12.49/3.20 thf(f30,axiom,(
% 12.49/3.20 ! [X5 : set_Pr1165141447_state,X9 : produc2041926651_state,X3 : produc2041926651_state] : ((member1069318160_state @ (produc1909270103_state @ X3 @ X9) @ (transi1726587420_state @ X5)) => (member1069318160_state @ (produc1909270103_state @ X3 @ X9) @ (transi1302705790_state @ X5)))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',fact_29_trancl__into__rtrancl)).
% 12.49/3.20 thf(f2123,plain,(
% 12.49/3.20 ((member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1)) != $true)),
% 12.49/3.20 inference(backward_demodulation,[status(thm)],[f1585,f1583])).
% 12.49/3.20 thf(f1583,plain,(
% 12.49/3.20 ((f @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ c @ nil_com) @ s))),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f352])).
% 12.49/3.20 thf(f352,axiom,(
% 12.49/3.20 ((f @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ c @ nil_com) @ s))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_1)).
% 12.49/3.20 thf(f1585,plain,(
% 12.49/3.20 ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1)) != $true)),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f912])).
% 12.49/3.20 thf(f912,plain,(
% 12.49/3.20 ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1)) != $true)),
% 12.49/3.20 inference(flattening,[status(thm)],[f393])).
% 12.49/3.20 thf(f393,plain,(
% 12.49/3.20 ~((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1)) = $true)),
% 12.49/3.20 inference(fool_elimination,[status(thm)],[f392])).
% 12.49/3.20 thf(f392,plain,(
% 12.49/3.20 ~(member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 12.49/3.20 inference(rectify,[status(thm)],[f356])).
% 12.49/3.20 thf(f356,negated_conjecture,(
% 12.49/3.20 ~(member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 12.49/3.20 inference(negated_conjecture,[status(cth)],[f355])).
% 12.49/3.20 thf(f355,conjecture,(
% 12.49/3.20 (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_4)).
% 12.49/3.20 thf(f6074,plain,(
% 12.49/3.20 ($true = (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ (suc @ n))) @ (transi1726587420_state @ pHoare259243666_exec1))) | ~spl230_45),
% 12.49/3.20 inference(superposition,[status(thm)],[f1631,f6050])).
% 12.49/3.20 thf(f6050,plain,(
% 12.49/3.20 ((f @ zero_zero_nat) = (f @ n)) | ~spl230_45),
% 12.49/3.20 inference(avatar_component_clause,[status(thm)],[f6049])).
% 12.49/3.20 thf(f6049,definition,(
% 12.49/3.20 spl230_45 <=> ((f @ zero_zero_nat) = (f @ n))),
% 12.49/3.20 introduced(definition,[new_symbols(naming,[spl230_45])],[avatar_definition])).
% 12.49/3.20 thf(f1631,plain,(
% 12.49/3.20 ( ! [X0 : nat] : (($true = (member1069318160_state @ (produc1909270103_state @ (f @ X0) @ (f @ (suc @ X0))) @ (transi1726587420_state @ pHoare259243666_exec1)))) )),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f509])).
% 12.49/3.20 thf(f509,plain,(
% 12.49/3.20 ! [X0 : nat] : ($true = (member1069318160_state @ (produc1909270103_state @ (f @ X0) @ (f @ (suc @ X0))) @ (transi1726587420_state @ pHoare259243666_exec1)))),
% 12.49/3.20 inference(fool_elimination,[status(thm)],[f508])).
% 12.49/3.20 thf(f508,plain,(
% 12.49/3.20 ! [X0 : nat] : (member1069318160_state @ (produc1909270103_state @ (f @ X0) @ (f @ (suc @ X0))) @ (transi1726587420_state @ pHoare259243666_exec1))),
% 12.49/3.20 inference(rectify,[status(thm)],[f353])).
% 12.49/3.20 thf(f353,axiom,(
% 12.49/3.20 ! [X8 : nat] : (member1069318160_state @ (produc1909270103_state @ (f @ X8) @ (f @ (suc @ X8))) @ (transi1726587420_state @ pHoare259243666_exec1))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_2)).
% 12.49/3.20 thf(f6053,plain,(
% 12.49/3.20 spl230_45),
% 12.49/3.20 inference(avatar_split_clause,[status(thm)],[f6052,f6049])).
% 12.49/3.20 thf(f6052,plain,(
% 12.49/3.20 ((f @ zero_zero_nat) = (f @ n))),
% 12.49/3.20 inference(subsumption_resolution,[status(thm)],[f6032,f2990])).
% 12.49/3.20 thf(f2990,plain,(
% 12.49/3.20 ($true = (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1)))),
% 12.49/3.20 inference(forward_demodulation,[status(thm)],[f1664,f1583])).
% 12.49/3.20 thf(f1664,plain,(
% 12.49/3.20 ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1)) = $true)),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f429])).
% 12.49/3.20 thf(f429,plain,(
% 12.49/3.20 ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1)) = $true)),
% 12.49/3.20 inference(fool_elimination,[status(thm)],[f428])).
% 12.49/3.20 thf(f428,plain,(
% 12.49/3.20 (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 12.49/3.20 inference(rectify,[status(thm)],[f354])).
% 12.49/3.20 thf(f354,axiom,(
% 12.49/3.20 (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',conj_3)).
% 12.49/3.20 thf(f6032,plain,(
% 12.49/3.20 ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1))) | ((f @ zero_zero_nat) = (f @ n))),
% 12.49/3.20 inference(trivial_inequality_removal,[status(thm)],[f6025])).
% 12.49/3.20 thf(f6025,plain,(
% 12.49/3.20 ((f @ zero_zero_nat) = (f @ n)) | ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1))) | ($true != $true)),
% 12.49/3.20 inference(superposition,[status(thm)],[f5999,f1626])).
% 12.49/3.20 thf(f1626,plain,(
% 12.49/3.20 ( ! [X2 : produc2041926651_state,X0 : produc2041926651_state,X1 : set_Pr1165141447_state] : (((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X1)) = $true) | ((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1302705790_state @ X1)) != $true) | (X0 = X2)) )),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f981])).
% 12.49/3.20 thf(f981,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : set_Pr1165141447_state,X2 : produc2041926651_state] : (((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1302705790_state @ X1)) != $true) | (((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X1)) = $true) & (X0 != X2)) | (X0 = X2))),
% 12.49/3.20 inference(flattening,[status(thm)],[f980])).
% 12.49/3.20 thf(f980,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : set_Pr1165141447_state,X2 : produc2041926651_state] : (((X0 = X2) | (((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X1)) = $true) & (X0 != X2))) | ((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1302705790_state @ X1)) != $true))),
% 12.49/3.20 inference(ennf_transformation,[status(thm)],[f525])).
% 12.49/3.20 thf(f525,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : set_Pr1165141447_state,X2 : produc2041926651_state] : (((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1302705790_state @ X1)) = $true) => ((X0 = X2) | (((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X1)) = $true) & (X0 != X2))))),
% 12.49/3.20 inference(fool_elimination,[status(thm)],[f524])).
% 12.49/3.20 thf(f524,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : set_Pr1165141447_state,X2 : produc2041926651_state] : ((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1302705790_state @ X1)) => ((X0 = X2) | ((X0 != X2) & (member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X1)))))),
% 12.49/3.20 inference(rectify,[status(thm)],[f26])).
% 12.49/3.20 thf(f26,axiom,(
% 12.49/3.20 ! [X9 : produc2041926651_state,X12 : set_Pr1165141447_state,X3 : produc2041926651_state] : ((member1069318160_state @ (produc1909270103_state @ X3 @ X9) @ (transi1302705790_state @ X12)) => ((X3 = X9) | ((X3 != X9) & (member1069318160_state @ (produc1909270103_state @ X3 @ X9) @ (transi1726587420_state @ X12)))))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',fact_25_rtranclD)).
% 12.49/3.20 thf(f5999,plain,(
% 12.49/3.20 ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ n)) @ (transi1726587420_state @ pHoare259243666_exec1)))),
% 12.49/3.20 inference(trivial_inequality_removal,[status(thm)],[f5964])).
% 12.49/3.20 thf(f5964,plain,(
% 12.49/3.20 ($true != $true) | ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ (f @ n)) @ (transi1726587420_state @ pHoare259243666_exec1)))),
% 12.49/3.20 inference(superposition,[status(thm)],[f5271,f1631])).
% 12.49/3.20 thf(f5271,plain,(
% 12.49/3.20 ( ! [X0 : produc2041926651_state] : (($true != (member1069318160_state @ (produc1909270103_state @ X0 @ (f @ (suc @ n))) @ (transi1726587420_state @ pHoare259243666_exec1))) | ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ X0) @ (transi1726587420_state @ pHoare259243666_exec1)))) )),
% 12.49/3.20 inference(trivial_inequality_removal,[status(thm)],[f5266])).
% 12.49/3.20 thf(f5266,plain,(
% 12.49/3.20 ( ! [X0 : produc2041926651_state] : (($true != $true) | ($true != (member1069318160_state @ (produc1909270103_state @ (f @ zero_zero_nat) @ X0) @ (transi1726587420_state @ pHoare259243666_exec1))) | ($true != (member1069318160_state @ (produc1909270103_state @ X0 @ (f @ (suc @ n))) @ (transi1726587420_state @ pHoare259243666_exec1)))) )),
% 12.49/3.20 inference(superposition,[status(thm)],[f3345,f1567])).
% 12.49/3.20 thf(f1567,plain,(
% 12.49/3.20 ( ! [X2 : produc2041926651_state,X3 : set_Pr1165141447_state,X0 : produc2041926651_state,X1 : produc2041926651_state] : (($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X3))) | ($true != (member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X3))) | ($true != (member1069318160_state @ (produc1909270103_state @ X0 @ X1) @ (transi1726587420_state @ X3)))) )),
% 12.49/3.20 inference(cnf_transformation,[status(thm)],[f999])).
% 12.49/3.20 thf(f999,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : produc2041926651_state,X2 : produc2041926651_state,X3 : set_Pr1165141447_state] : (($true != (member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X3))) | ($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X3))) | ($true != (member1069318160_state @ (produc1909270103_state @ X0 @ X1) @ (transi1726587420_state @ X3))))),
% 12.49/3.20 inference(flattening,[status(thm)],[f998])).
% 12.49/3.20 thf(f998,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : produc2041926651_state,X2 : produc2041926651_state,X3 : set_Pr1165141447_state] : ((($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X3))) | ($true != (member1069318160_state @ (produc1909270103_state @ X0 @ X1) @ (transi1726587420_state @ X3)))) | ($true != (member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X3))))),
% 12.49/3.20 inference(ennf_transformation,[status(thm)],[f753])).
% 12.49/3.20 thf(f753,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : produc2041926651_state,X2 : produc2041926651_state,X3 : set_Pr1165141447_state] : (($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X3))) => (($true = (member1069318160_state @ (produc1909270103_state @ X0 @ X1) @ (transi1726587420_state @ X3))) => ($true = (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X3)))))),
% 12.49/3.20 inference(fool_elimination,[status(thm)],[f752])).
% 12.49/3.20 thf(f752,plain,(
% 12.49/3.20 ! [X0 : produc2041926651_state,X1 : produc2041926651_state,X2 : produc2041926651_state,X3 : set_Pr1165141447_state] : ((member1069318160_state @ (produc1909270103_state @ X2 @ X0) @ (transi1726587420_state @ X3)) => ((member1069318160_state @ (produc1909270103_state @ X0 @ X1) @ (transi1726587420_state @ X3)) => (member1069318160_state @ (produc1909270103_state @ X2 @ X1) @ (transi1726587420_state @ X3))))),
% 12.49/3.20 inference(rectify,[status(thm)],[f82])).
% 12.49/3.20 thf(f82,axiom,(
% 12.49/3.20 ! [X31 : produc2041926651_state,X35 : produc2041926651_state,X30 : produc2041926651_state,X5 : set_Pr1165141447_state] : ((member1069318160_state @ (produc1909270103_state @ X30 @ X31) @ (transi1726587420_state @ X5)) => ((member1069318160_state @ (produc1909270103_state @ X31 @ X35) @ (transi1726587420_state @ X5)) => (member1069318160_state @ (produc1909270103_state @ X30 @ X35) @ (transi1726587420_state @ X5))))),
% 12.49/3.20 file('/export/starexec/sandbox/tmp/tmp.IlOYhUUvy8/DTF2THF_26179.p',fact_81_trancl__trans)).
% 12.49/3.20 % SZS output end Proof for DTF2THF_26179
% 12.49/3.20 % (26395)------------------------------
% 12.49/3.20 % (26395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.49/3.20 % (26395)Termination reason: Refutation
% 12.49/3.20
% 12.49/3.20 % (26395)Memory used [KB]: 10874
% 12.49/3.20 % (26395)Time elapsed: 0.703 s
% 12.49/3.20 % (26395)Instructions burned: 2199 (million)
% 12.49/3.20 % (26395)------------------------------
% 12.49/3.20 % (26395)------------------------------
% 12.49/3.20 % (26299)Success in time 1.599 s
%------------------------------------------------------------------------------