DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP142^1 : 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 : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Feb 25 08:55:53 AM UTC 2026

% Result   : Theorem 3.14s 1.78s
% Output   : Refutation 3.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   24 (  16 unt;   0 typ;   0 def)
%            Number of atoms       :  111 (  31 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  251 (  17   ~;  11   |;   5   &; 209   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :   41 (  40 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  268 ( 265 usr;  15 con; 0-6 aty)
%            Number of variables   :   17 (   0   ^;  17   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    list_list_com: $tType ).

thf(type_def_7,type,
    list_com: $tType ).

thf(type_def_8,type,
    list_P1040014977_state: $tType ).

thf(type_def_9,type,
    list_P890094829_state: $tType ).

thf(type_def_10,type,
    com: $tType ).

thf(type_def_11,type,
    set_Pr1822651163om_com: $tType ).

thf(type_def_12,type,
    set_Pr602326075st_com: $tType ).

thf(type_def_13,type,
    set_Pr1165141447_state: $tType ).

thf(type_def_14,type,
    set_Pr1142642759_state: $tType ).

thf(type_def_15,type,
    set_Pr2096893127_state: $tType ).

thf(type_def_16,type,
    set_Pr1325664839_state: $tType ).

thf(type_def_17,type,
    produc2041926651_state: $tType ).

thf(type_def_18,type,
    nat: $tType ).

thf(type_def_19,type,
    list_P1178430914te_nat: $tType ).

thf(type_def_20,type,
    produc410756839_state: $tType ).

thf(type_def_21,type,
    list_P1627643054te_nat: $tType ).

thf(type_def_22,type,
    state: $tType ).

thf(type_def_23,type,
    list_state: $tType ).

thf(type_def_24,type,
    set_Pr849496667_state: $tType ).

thf(type_def_25,type,
    set_Pr391631483_state: $tType ).

thf(type_def_26,type,
    set_state: $tType ).

thf(type_def_27,type,
    produc2058209240st_com: $tType ).

thf(type_def_28,type,
    produc1393453339_state: $tType ).

thf(type_def_29,type,
    produc258871771st_com: $tType ).

thf(type_def_30,type,
    produc1225889383_state: $tType ).

thf(type_def_31,type,
    produc1586269031_state: $tType ).

thf(type_def_32,type,
    product_prod_com_com: $tType ).

thf(type_def_33,type,
    produc1440412305st_com: $tType ).

thf(type_def_34,type,
    produc392316135_state: $tType ).

thf(type_def_35,type,
    produc1762014951st_com: $tType ).

thf(type_def_36,type,
    produc1519776487_state: $tType ).

thf(type_def_37,type,
    produc270545127_state: $tType ).

thf(type_def_38,type,
    produc186437863_state: $tType ).

thf(type_def_39,type,
    produc2046512871_state: $tType ).

thf(type_def_40,type,
    set_Pr135335153st_com: $tType ).

thf(type_def_41,type,
    set_Pr1419004359_state: $tType ).

thf(type_def_42,type,
    set_Pr2083163591st_com: $tType ).

thf(type_def_43,type,
    set_Pr1847866567_state: $tType ).

thf(type_def_44,type,
    set_Pr1696918727_state: $tType ).

thf(type_def_45,type,
    set_Pr541394119_state: $tType ).

thf(func_def_0,type,
    set_Pr1696918727_state: $tType ).

thf(func_def_1,type,
    produc270545127_state: $tType ).

thf(func_def_2,type,
    set_Pr541394119_state: $tType ).

thf(func_def_3,type,
    produc2046512871_state: $tType ).

thf(func_def_4,type,
    set_Pr1847866567_state: $tType ).

thf(func_def_5,type,
    produc1519776487_state: $tType ).

thf(func_def_6,type,
    set_Pr1325664839_state: $tType ).

thf(func_def_7,type,
    produc1586269031_state: $tType ).

thf(func_def_8,type,
    set_Pr2096893127_state: $tType ).

thf(func_def_9,type,
    produc186437863_state: $tType ).

thf(func_def_10,type,
    set_Pr1419004359_state: $tType ).

thf(func_def_11,type,
    set_Pr135335153st_com: $tType ).

thf(func_def_12,type,
    produc392316135_state: $tType ).

thf(func_def_13,type,
    produc1440412305st_com: $tType ).

thf(func_def_14,type,
    set_Pr1142642759_state: $tType ).

thf(func_def_15,type,
    set_Pr2083163591st_com: $tType ).

thf(func_def_16,type,
    list_P1627643054te_nat: $tType ).

thf(func_def_17,type,
    produc1225889383_state: $tType ).

thf(func_def_18,type,
    produc1762014951st_com: $tType ).

thf(func_def_19,type,
    list_P890094829_state: $tType ).

thf(func_def_20,type,
    set_Pr1165141447_state: $tType ).

thf(func_def_21,type,
    produc410756839_state: $tType ).

thf(func_def_22,type,
    set_Pr391631483_state: $tType ).

thf(func_def_23,type,
    list_P1178430914te_nat: $tType ).

thf(func_def_24,type,
    produc1393453339_state: $tType ).

thf(func_def_25,type,
    produc2058209240st_com: $tType ).

thf(func_def_26,type,
    set_Pr602326075st_com: $tType ).

thf(func_def_27,type,
    list_P1040014977_state: $tType ).

thf(func_def_28,type,
    set_Pr849496667_state: $tType ).

thf(func_def_29,type,
    produc258871771st_com: $tType ).

thf(func_def_30,type,
    produc2041926651_state: $tType ).

thf(func_def_31,type,
    set_Pr1822651163om_com: $tType ).

thf(func_def_32,type,
    product_prod_com_com: $tType ).

thf(func_def_33,type,
    list_list_com: $tType ).

thf(func_def_34,type,
    list_state: $tType ).

thf(func_def_35,type,
    set_state: $tType ).

thf(func_def_36,type,
    list_com: $tType ).

thf(func_def_37,type,
    state: $tType ).

thf(func_def_38,type,
    com: $tType ).

thf(func_def_39,type,
    nat: $tType ).

thf(func_def_40,type,
    append_list_com: list_list_com > list_list_com > list_list_com ).

thf(func_def_41,type,
    append_com: list_com > list_com > list_com ).

thf(func_def_42,type,
    append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state ).

thf(func_def_43,type,
    append221843330_state: list_P890094829_state > list_P890094829_state > list_P890094829_state ).

thf(func_def_44,type,
    bind_com_com: list_com > ( com > list_com ) > list_com ).

thf(func_def_45,type,
    butlast_com: list_com > list_com ).

thf(func_def_46,type,
    concat_com: list_list_com > list_com ).

thf(func_def_47,type,
    insert_com: com > list_com > list_com ).

thf(func_def_48,type,
    last_com: list_com > com ).

thf(func_def_49,type,
    lenlex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).

thf(func_def_50,type,
    lenlex295247238_state: set_Pr1165141447_state > set_Pr1142642759_state ).

thf(func_def_51,type,
    lenlex1401983474_state: set_Pr2096893127_state > set_Pr1325664839_state ).

thf(func_def_52,type,
    lex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).

thf(func_def_53,type,
    lex_Pr570247525_state: set_Pr1165141447_state > set_Pr1142642759_state ).

thf(func_def_54,type,
    lex_Pr1762629969_state: set_Pr2096893127_state > set_Pr1325664839_state ).

thf(func_def_55,type,
    lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com ).

thf(func_def_56,type,
    lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state ).

thf(func_def_57,type,
    lexord1893203674_state: set_Pr2096893127_state > set_Pr1325664839_state ).

thf(func_def_58,type,
    cons_P1821701106te_nat: ( produc2041926651_state > nat ) > list_P1178430914te_nat > list_P1178430914te_nat ).

thf(func_def_59,type,
    cons_P1631380062te_nat: ( produc410756839_state > nat ) > list_P1627643054te_nat > list_P1627643054te_nat ).

thf(func_def_60,type,
    cons_list_com: list_com > list_list_com > list_list_com ).

thf(func_def_61,type,
    cons_com: com > list_com > list_com ).

thf(func_def_62,type,
    cons_state: state > list_state > list_state ).

thf(func_def_63,type,
    cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state ).

thf(func_def_64,type,
    cons_P438230685_state: produc410756839_state > list_P890094829_state > list_P890094829_state ).

thf(func_def_65,type,
    nil_Pr1876916290te_nat: list_P1178430914te_nat ).

thf(func_def_66,type,
    nil_Pr164089518te_nat: list_P1627643054te_nat ).

thf(func_def_67,type,
    nil_list_com: list_list_com ).

thf(func_def_68,type,
    nil_com: list_com ).

thf(func_def_69,type,
    nil_state: list_state ).

thf(func_def_70,type,
    nil_Pr1844458753_state: list_P1040014977_state ).

thf(func_def_71,type,
    nil_Pr1347322605_state: list_P890094829_state ).

thf(func_def_72,type,
    list_ex1_com: ( com > $o ) > list_com > $o ).

thf(func_def_73,type,
    list_update_com: list_com > nat > com > list_com ).

thf(func_def_74,type,
    list_u737668969_state: list_P1040014977_state > nat > produc2041926651_state > list_P1040014977_state ).

thf(func_def_75,type,
    list_u364351829_state: list_P890094829_state > nat > produc410756839_state > list_P890094829_state ).

thf(func_def_76,type,
    listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com ).

thf(func_def_77,type,
    listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state ).

thf(func_def_78,type,
    listre1725776070_state: set_Pr2096893127_state > set_Pr1325664839_state ).

thf(func_def_79,type,
    listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state ).

thf(func_def_80,type,
    listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com ).

thf(func_def_81,type,
    listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state ).

thf(func_def_82,type,
    listre1244407729_state: set_Pr2096893127_state > set_Pr1325664839_state ).

thf(func_def_83,type,
    maps_com_com: ( com > list_com ) > list_com > list_com ).

thf(func_def_84,type,
    measur1071343867_state: list_P1178430914te_nat > set_Pr1165141447_state ).

thf(func_def_85,type,
    measur768621543_state: list_P1627643054te_nat > set_Pr2096893127_state ).

thf(func_def_86,type,
    nth_list_com: list_list_com > nat > list_com ).

thf(func_def_87,type,
    nth_com: list_com > nat > com ).

thf(func_def_88,type,
    nth_state: list_state > nat > state ).

thf(func_def_89,type,
    nth_Pr553241858_state: list_P1040014977_state > nat > produc2041926651_state ).

thf(func_def_90,type,
    nth_Pr526167918_state: list_P890094829_state > nat > produc410756839_state ).

thf(func_def_91,type,
    product_lists_com: list_list_com > list_list_com ).

thf(func_def_92,type,
    rotate1_com: list_com > list_com ).

thf(func_def_93,type,
    subseqs_com: list_com > list_list_com ).

thf(func_def_94,type,
    take_P558217449_state: nat > list_P1040014977_state > list_P1040014977_state ).

thf(func_def_95,type,
    take_P1852316373_state: nat > list_P890094829_state > list_P890094829_state ).

thf(func_def_96,type,
    size_s318434721st_com: list_list_com > nat ).

thf(func_def_97,type,
    size_size_list_com: list_com > nat ).

thf(func_def_98,type,
    size_size_list_state: list_state > nat ).

thf(func_def_99,type,
    size_s213202669_state: list_P1040014977_state > nat ).

thf(func_def_100,type,
    size_s837829465_state: list_P890094829_state > nat ).

thf(func_def_101,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_102,type,
    pHoare259243666_exec1: set_Pr1165141447_state ).

thf(func_def_103,type,
    pHoare259243732_execs: state > list_com > state > $o ).

thf(func_def_104,type,
    pHoare806997636termis: list_com > state > $o ).

thf(func_def_105,type,
    cond: ( state > $o ) > com > com > com ).

thf(func_def_106,type,
    do: ( state > set_state ) > com ).

thf(func_def_107,type,
    semi: com > com > com ).

thf(func_def_108,type,
    while: ( state > $o ) > com > com ).

thf(func_def_109,type,
    exec: state > com > state > $o ).

thf(func_def_110,type,
    termi: com > state > $o ).

thf(func_def_111,type,
    produc1914379986st_com: ( com > com > $o ) > list_com > produc2058209240st_com ).

thf(func_def_112,type,
    produc1742567891_state: list_list_com > list_state > produc1393453339_state ).

thf(func_def_113,type,
    produc1307105171st_com: list_com > list_com > produc258871771st_com ).

thf(func_def_114,type,
    produc1204172211_state: list_com > state > produc2041926651_state ).

thf(func_def_115,type,
    produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state ).

thf(func_def_116,type,
    produc1354769367_state: list_P890094829_state > list_P890094829_state > produc1586269031_state ).

thf(func_def_117,type,
    product_Pair_com_com: com > com > product_prod_com_com ).

thf(func_def_118,type,
    produc67337417st_com: produc2058209240st_com > produc2058209240st_com > produc1440412305st_com ).

thf(func_def_119,type,
    produc67381847_state: produc1393453339_state > produc1393453339_state > produc392316135_state ).

thf(func_def_120,type,
    produc313736791st_com: produc258871771st_com > produc258871771st_com > produc1762014951st_com ).

thf(func_def_121,type,
    produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).

thf(func_def_122,type,
    produc984060759_state: produc1225889383_state > produc1225889383_state > produc1519776487_state ).

thf(func_def_123,type,
    produc1576663895_state: produc1586269031_state > produc1586269031_state > produc270545127_state ).

thf(func_def_124,type,
    produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state ).

thf(func_def_125,type,
    produc2049704791_state: produc186437863_state > produc186437863_state > produc2046512871_state ).

thf(func_def_126,type,
    irrefl_com: set_Pr1822651163om_com > $o ).

thf(func_def_127,type,
    irrefl654089520_state: set_Pr1165141447_state > $o ).

thf(func_def_128,type,
    irrefl1358048924_state: set_Pr2096893127_state > $o ).

thf(func_def_129,type,
    collect_state: ( state > $o ) > set_state ).

thf(func_def_130,type,
    collec300063826_state: ( produc410756839_state > $o ) > set_Pr1165141447_state ).

thf(func_def_131,type,
    collec489924946_state: ( produc186437863_state > $o ) > set_Pr2096893127_state ).

thf(func_def_132,type,
    transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com ).

thf(func_def_133,type,
    transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state ).

thf(func_def_134,type,
    transi1965148016_state: set_Pr1325664839_state > set_Pr1325664839_state ).

thf(func_def_135,type,
    transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com ).

thf(func_def_136,type,
    transi1592315797st_com: set_Pr135335153st_com > set_Pr135335153st_com ).

thf(func_def_137,type,
    transi89280670_state: set_Pr1419004359_state > set_Pr1419004359_state ).

thf(func_def_138,type,
    transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com ).

thf(func_def_139,type,
    transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).

thf(func_def_140,type,
    transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state ).

thf(func_def_141,type,
    transi445721450_state: set_Pr1696918727_state > set_Pr1696918727_state ).

thf(func_def_142,type,
    transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).

thf(func_def_143,type,
    transi152726506_state: set_Pr541394119_state > set_Pr541394119_state ).

thf(func_def_144,type,
    member_state: state > set_state > $o ).

thf(func_def_145,type,
    member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).

thf(func_def_146,type,
    member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).

thf(func_def_147,type,
    member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).

thf(func_def_148,type,
    member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).

thf(func_def_149,type,
    member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o ).

thf(func_def_150,type,
    member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).

thf(func_def_151,type,
    member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o ).

thf(func_def_152,type,
    member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o ).

thf(func_def_153,type,
    member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o ).

thf(func_def_154,type,
    member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).

thf(func_def_155,type,
    member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o ).

thf(func_def_156,type,
    member1642814224_state: produc270545127_state > set_Pr1696918727_state > $o ).

thf(func_def_157,type,
    member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).

thf(func_def_158,type,
    member284400400_state: produc2046512871_state > set_Pr541394119_state > $o ).

thf(func_def_159,type,
    c: com ).

thf(func_def_160,type,
    c2: com ).

thf(func_def_161,type,
    cs: list_com ).

thf(func_def_162,type,
    s: state ).

thf(func_def_163,type,
    s2: state ).

thf(func_def_182,type,
    sP0: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > $o ).

thf(func_def_183,type,
    sP1: state > ( state > $o ) > state > com > list_com > list_com > $o ).

thf(func_def_184,type,
    sP2: com > list_com > list_com > ( state > $o ) > state > state > $o ).

thf(func_def_185,type,
    sK3: produc410756839_state > state ).

thf(func_def_186,type,
    sK4: produc410756839_state > list_com ).

thf(func_def_187,type,
    sK5: produc410756839_state > produc2041926651_state ).

thf(func_def_188,type,
    sK6: ( produc410756839_state > $o ) > produc2041926651_state ).

thf(func_def_189,type,
    sK7: ( produc410756839_state > $o ) > produc2041926651_state ).

thf(func_def_190,type,
    sK8: ( produc186437863_state > $o ) > produc2041926651_state ).

thf(func_def_191,type,
    sK9: ( produc186437863_state > $o ) > produc2041926651_state ).

thf(func_def_192,type,
    sK10: ( produc186437863_state > $o ) > produc410756839_state ).

thf(func_def_193,type,
    sK11: ( produc410756839_state > $o ) > list_com ).

thf(func_def_194,type,
    sK12: ( produc410756839_state > $o ) > produc2041926651_state ).

thf(func_def_195,type,
    sK13: ( produc410756839_state > $o ) > state ).

thf(func_def_196,type,
    sK14: ( list_com > state > $o ) > set_Pr1165141447_state > state > list_com > state ).

thf(func_def_197,type,
    sK15: ( list_com > state > $o ) > set_Pr1165141447_state > state > list_com > list_com ).

thf(func_def_198,type,
    sK16: ( list_com > state > $o ) > set_Pr1165141447_state > state > list_com > list_com ).

thf(func_def_199,type,
    sK17: ( list_com > state > $o ) > set_Pr1165141447_state > state > list_com > state ).

thf(func_def_200,type,
    sK18: produc410756839_state > produc2041926651_state ).

thf(func_def_201,type,
    sK19: produc410756839_state > produc2041926651_state ).

thf(func_def_202,type,
    sK20: ( ( com > com ) > list_com > list_com > $o ) > list_com ).

thf(func_def_203,type,
    sK21: ( ( com > com ) > list_com > list_com > $o ) > com > com ).

thf(func_def_204,type,
    sK22: ( ( com > com ) > list_com > list_com > $o ) > list_com ).

thf(func_def_205,type,
    sK23: ( ( com > com ) > list_com > list_com > $o ) > com ).

thf(func_def_206,type,
    sK24: ( ( com > com ) > list_com > list_com > $o ) > com > com ).

thf(func_def_207,type,
    sK25: ( ( com > com ) > list_com > list_com > $o ) > list_com ).

thf(func_def_208,type,
    sK26: produc2041926651_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_209,type,
    sK27: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_210,type,
    sK28: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_211,type,
    sK29: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_212,type,
    sK30: state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com > state ).

thf(func_def_213,type,
    sK31: state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com > state ).

thf(func_def_214,type,
    sK32: state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com > list_com ).

thf(func_def_215,type,
    sK33: state > set_Pr1165141447_state > ( list_com > state > $o ) > list_com > list_com ).

thf(func_def_216,type,
    sK34: ( list_com > list_com > $o ) > list_com ).

thf(func_def_217,type,
    sK35: ( list_com > list_com > $o ) > list_com ).

thf(func_def_218,type,
    sK36: ( list_com > list_com > $o ) > com ).

thf(func_def_219,type,
    sK37: ( list_com > list_com > $o ) > com ).

thf(func_def_220,type,
    sK38: ( list_com > list_com > $o ) > list_com ).

thf(func_def_221,type,
    sK39: ( list_com > list_com > $o ) > list_com ).

thf(func_def_222,type,
    sK40: ( produc186437863_state > $o ) > produc410756839_state ).

thf(func_def_223,type,
    sK41: ( produc186437863_state > $o ) > produc410756839_state ).

thf(func_def_224,type,
    sK42: produc2041926651_state > list_com ).

thf(func_def_225,type,
    sK43: produc2041926651_state > state ).

thf(func_def_226,type,
    sK44: list_com > list_com > list_com > list_com > list_com ).

thf(func_def_227,type,
    sK45: state > state > list_com > list_com > set_Pr1165141447_state > state ).

thf(func_def_228,type,
    sK46: state > state > list_com > list_com > set_Pr1165141447_state > list_com ).

thf(func_def_229,type,
    sK47: produc410756839_state > produc2041926651_state ).

thf(func_def_230,type,
    sK48: produc410756839_state > produc2041926651_state ).

thf(func_def_231,type,
    sK49: ( produc186437863_state > $o ) > produc410756839_state ).

thf(func_def_232,type,
    sK50: ( produc186437863_state > $o ) > state ).

thf(func_def_233,type,
    sK51: ( produc186437863_state > $o ) > produc2041926651_state ).

thf(func_def_234,type,
    sK52: ( produc186437863_state > $o ) > list_com ).

thf(func_def_235,type,
    sK53: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).

thf(func_def_236,type,
    sK54: ( ( com > com > $o ) > list_com > $o ) > list_com ).

thf(func_def_237,type,
    sK55: ( ( com > com > $o ) > list_com > $o ) > com ).

thf(func_def_238,type,
    sK56: ( ( com > com > $o ) > list_com > $o ) > com ).

thf(func_def_239,type,
    sK57: ( ( com > com > $o ) > list_com > $o ) > com ).

thf(func_def_240,type,
    sK58: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).

thf(func_def_241,type,
    sK59: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).

thf(func_def_242,type,
    sK60: list_com > list_com ).

thf(func_def_243,type,
    sK61: list_com > com ).

thf(func_def_244,type,
    sK62: ( produc2041926651_state > $o ) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).

thf(func_def_245,type,
    sK63: ( produc2041926651_state > $o ) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state ).

thf(func_def_246,type,
    sK64: ( list_com > $o ) > list_com ).

thf(func_def_247,type,
    sK65: ( list_com > $o ) > com ).

thf(func_def_248,type,
    sK66: list_com > com ).

thf(func_def_249,type,
    sK67: list_com > list_com ).

thf(func_def_250,type,
    sK68: list_com > com ).

thf(func_def_251,type,
    sK69: list_com > com ).

thf(func_def_252,type,
    sK70: produc186437863_state > produc410756839_state ).

thf(func_def_253,type,
    sK71: produc186437863_state > produc410756839_state ).

thf(func_def_254,type,
    sK72: produc186437863_state > produc410756839_state ).

thf(func_def_255,type,
    sK73: produc186437863_state > produc2041926651_state ).

thf(func_def_256,type,
    sK74: produc186437863_state > produc2041926651_state ).

thf(func_def_257,type,
    sK75: list_com > com > list_com > list_com > list_com ).

thf(func_def_258,type,
    sK76: list_com > list_com ).

thf(func_def_259,type,
    sK77: list_com > com ).

thf(func_def_260,type,
    sK78: ( produc2041926651_state > produc2041926651_state > $o ) > produc2041926651_state ).

thf(func_def_261,type,
    sK79: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).

thf(func_def_262,type,
    sK80: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).

thf(func_def_263,type,
    sK81: ( produc2041926651_state > produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state ).

thf(func_def_264,type,
    sK82: state > ( state > $o ) > com > state ).

thf(func_def_265,type,
    sK83: state > list_com > com > state ).

thf(func_def_266,type,
    sK84: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_267,type,
    sK85: ( list_com > $o ) > com ).

thf(func_def_268,type,
    sK86: ( list_com > $o ) > list_com ).

thf(func_def_269,type,
    sK87: ( list_com > $o ) > com ).

thf(func_def_270,type,
    sK88: ( produc186437863_state > $o ) > produc410756839_state ).

thf(func_def_271,type,
    sK89: ( produc186437863_state > $o ) > produc410756839_state ).

thf(func_def_272,type,
    sK90: ( list_com > list_com > $o ) > list_com ).

thf(func_def_273,type,
    sK91: ( list_com > list_com > $o ) > com ).

thf(func_def_274,type,
    sK92: ( list_com > list_com > $o ) > list_com ).

thf(func_def_275,type,
    sK93: ( list_com > list_com > $o ) > list_com ).

thf(func_def_276,type,
    sK94: ( list_com > $o ) > com ).

thf(func_def_277,type,
    sK95: ( list_com > $o ) > list_com ).

thf(func_def_278,type,
    sK96: ( list_com > $o ) > com ).

thf(func_def_279,type,
    sK97: ( produc2041926651_state > $o ) > state ).

thf(func_def_280,type,
    sK98: ( produc2041926651_state > $o ) > list_com ).

thf(func_def_281,type,
    sK99: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_282,type,
    sK100: ( produc2041926651_state > $o ) > list_com ).

thf(func_def_283,type,
    sK101: ( produc2041926651_state > $o ) > state ).

thf(func_def_284,type,
    sK102: ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_285,type,
    sK103: ( produc2041926651_state > $o ) > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_286,type,
    sK104: ( produc410756839_state > $o ) > produc2041926651_state ).

thf(func_def_287,type,
    sK105: ( produc410756839_state > $o ) > produc2041926651_state ).

thf(func_def_288,type,
    sK106: ( list_com > $o ) > list_com ).

thf(func_def_289,type,
    sK107: ( list_com > $o ) > com ).

thf(func_def_290,type,
    sK108: ( list_com > $o ) > com ).

thf(func_def_291,type,
    sK109: ( list_com > $o ) > com ).

thf(func_def_292,type,
    sK110: ( list_com > list_com > $o ) > com ).

thf(func_def_293,type,
    sK111: ( list_com > list_com > $o ) > list_com ).

thf(func_def_294,type,
    sK112: ( list_com > list_com > $o ) > com ).

thf(func_def_295,type,
    sK113: ( list_com > list_com > $o ) > list_com ).

thf(func_def_296,type,
    sK114: ( list_com > list_com > $o ) > com ).

thf(func_def_297,type,
    sK115: ( list_com > list_com > $o ) > list_com ).

thf(func_def_298,type,
    sK116: ( list_com > list_com > $o ) > com ).

thf(func_def_299,type,
    sK117: ( list_com > list_com > $o ) > list_com ).

thf(func_def_300,type,
    sK118: ( list_com > $o ) > com ).

thf(func_def_301,type,
    sK119: ( list_com > $o ) > list_com ).

thf(func_def_302,type,
    sK120: ( list_com > $o ) > com ).

thf(func_def_303,type,
    sK121: ( list_com > $o ) > com ).

thf(func_def_304,type,
    sK122: produc186437863_state > produc410756839_state ).

thf(func_def_305,type,
    sK123: produc186437863_state > produc410756839_state ).

thf(func_def_306,type,
    sK124: list_com > com ).

thf(func_def_307,type,
    sK125: list_com > list_com ).

thf(func_def_308,type,
    sK126: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state ).

thf(func_def_309,type,
    sK127: ( list_com > $o ) > com ).

thf(func_def_310,type,
    sK128: ( list_com > $o ) > list_com ).

thf(func_def_311,type,
    sK129: produc2041926651_state > list_com ).

thf(func_def_312,type,
    sK130: produc2041926651_state > state ).

thf(func_def_313,type,
    sK131: produc186437863_state > state ).

thf(func_def_314,type,
    sK132: produc186437863_state > list_com ).

thf(func_def_315,type,
    sK133: produc186437863_state > produc410756839_state ).

thf(func_def_316,type,
    sK134: produc186437863_state > produc2041926651_state ).

thf(func_def_317,type,
    sK135: ( ( com > com > $o ) > list_com > $o ) > com ).

thf(func_def_318,type,
    sK136: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).

thf(func_def_319,type,
    sK137: ( ( com > com > $o ) > list_com > $o ) > list_com ).

thf(func_def_320,type,
    sK138: ( ( com > com > $o ) > list_com > $o ) > com > com > $o ).

thf(func_def_321,type,
    sK139: list_com > list_com > com > list_com > list_com ).

thf(func_def_323,type,
    ph141: 
      !>[X0: $tType] : X0 ).

thf(f1569,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f1568,f1362]) ).

thf(f1362,plain,
    ( ( termi @ c @ s )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f884]) ).

thf(f884,plain,
    ( ( termi @ c @ s )
    = $true ),
    inference(fool_elimination,[status(thm)],[f883]) ).

thf(f883,plain,
    termi @ c @ s,
    inference(rectify,[status(thm)],[f356]) ).

thf(f356,axiom,
    termi @ c @ s,
    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_1) ).

thf(f1568,plain,
    ( ( termi @ c @ s )
   != $true ),
    inference(subsumption_resolution,[status(thm)],[f1567,f1411]) ).

thf(f1411,plain,
    ( ( termi @ c2 @ s2 )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f919]) ).

thf(f919,plain,
    ( ( termi @ c2 @ s2 )
   != $true ),
    inference(flattening,[status(thm)],[f558]) ).

thf(f558,plain,
    ( ( termi @ c2 @ s2 )
   != $true ),
    inference(fool_elimination,[status(thm)],[f557]) ).

thf(f557,plain,
    ~ ( termi @ c2 @ s2 ),
    inference(rectify,[status(thm)],[f359]) ).

thf(f359,negated_conjecture,
    ~ ( termi @ c2 @ s2 ),
    inference(negated_conjecture,[status(cth)],[f358]) ).

thf(f358,conjecture,
    termi @ c2 @ s2,
    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_3) ).

thf(f1567,plain,
    ( ( ( termi @ c2 @ s2 )
      = $true )
    | ( ( termi @ c @ s )
     != $true ) ),
    inference(trivial_inequality_removal,[status(thm)],[f1556]) ).

thf(f1556,plain,
    ( ( ( termi @ c @ s )
     != $true )
    | ( $true != $true )
    | ( ( termi @ c2 @ s2 )
      = $true ) ),
    inference(superposition,[status(thm)],[f1386,f1416]) ).

thf(f1416,plain,
    ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f854]) ).

thf(f854,plain,
    ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f853]) ).

thf(f853,plain,
    member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
    inference(rectify,[status(thm)],[f355]) ).

thf(f355,axiom,
    member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_0) ).

thf(f1386,plain,
    ! [X0: state,X1: state] :
      ( ( $true
       != ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X1 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X0 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
      | ( ( termi @ c @ X1 )
       != $true )
      | ( ( termi @ c2 @ X0 )
        = $true ) ),
    inference(cnf_transformation,[status(thm)],[f985]) ).

thf(f985,plain,
    ! [X0: state,X1: state] :
      ( ( ! [X2: state] :
            ( ( $true
             != ( exec @ X0 @ c2 @ X2 ) )
            | ( ( pHoare806997636termis @ cs @ X2 )
              = $true ) )
        & ( ( termi @ c2 @ X0 )
          = $true ) )
      | ( $true
       != ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X1 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X0 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
      | ( ( termi @ c @ X1 )
       != $true ) ),
    inference(flattening,[status(thm)],[f984]) ).

thf(f984,plain,
    ! [X0: state,X1: state] :
      ( ( ! [X2: state] :
            ( ( $true
             != ( exec @ X0 @ c2 @ X2 ) )
            | ( ( pHoare806997636termis @ cs @ X2 )
              = $true ) )
        & ( ( termi @ c2 @ X0 )
          = $true ) )
      | ( ( termi @ c @ X1 )
       != $true )
      | ( $true
       != ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X1 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X0 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
    inference(ennf_transformation,[status(thm)],[f746]) ).

thf(f746,plain,
    ! [X0: state,X1: state] :
      ( ( $true
        = ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X1 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X0 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
     => ( ( ( termi @ c @ X1 )
          = $true )
       => ( ! [X2: state] :
              ( ( $true
                = ( exec @ X0 @ c2 @ X2 ) )
             => ( ( pHoare806997636termis @ cs @ X2 )
                = $true ) )
          & ( ( termi @ c2 @ X0 )
            = $true ) ) ) ),
    inference(fool_elimination,[status(thm)],[f745]) ).

thf(f745,plain,
    ! [X0: state,X1: state] :
      ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X1 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X0 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
     => ( ( termi @ c @ X1 )
       => ( ! [X2: state] :
              ( ( exec @ X0 @ c2 @ X2 )
             => ( pHoare806997636termis @ cs @ X2 ) )
          & ( termi @ c2 @ X0 ) ) ) ),
    inference(rectify,[status(thm)],[f357]) ).

thf(f357,axiom,
    ! [X135: state,X134: state] :
      ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X134 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X135 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
     => ( ( termi @ c @ X134 )
       => ( ! [X136: state] :
              ( ( exec @ X135 @ c2 @ X136 )
             => ( pHoare806997636termis @ cs @ X136 ) )
          & ( termi @ c2 @ X135 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP142^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34  % Computer : n019.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue Feb 24 08:27:39 EST 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46  ---- Original DTF file ---
% 0.31/0.46  thf(spec,logic,$$dhol).
% 0.31/0.46  %------------------------------------------------------------------------------
% 0.31/0.46  % File     : ITP142^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46  % Domain   : Interactive Theorem Proving
% 0.31/0.46  % Problem  : Sledgehammer PHoareTotal problem prob_304__3261994_1
% 0.31/0.46  % Version  : Especial.
% 0.31/0.46  % English  :
% 0.31/0.46  
% 0.31/0.46  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46  % Source   : [Des21]
% 0.31/0.46  % Names    : PHoareTotal/prob_304__3261994_1 [Des21]
% 0.31/0.46  
% 0.31/0.46  % Status   : Theorem
% 0.31/0.46  % Rating   : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.31/0.46  % Syntax   : Number of formulae    :  522 ( 152 unt; 164 typ;   0 def)
% 0.31/0.46  %            Number of atoms       : 1042 ( 497 equ;   0 cnn)
% 0.31/0.46  %            Maximal formula atoms :    7 (   2 avg)
% 0.31/0.46  %            Number of connectives : 5299 ( 222   ~;  42   |; 115   &;4342   @)
% 0.31/0.46  %                                         (   0 <=>; 578  =>;   0  <=;   0 <~>)
% 0.31/0.46  %            Maximal formula depth :   23 (  10 avg)
% 0.31/0.46  %            Number of types       :   41 (  40 usr)
% 0.31/0.46  %            Number of type conns  :  389 ( 389   >;   0   *;   0   +;   0  <<)
% 0.31/0.46  %            Number of symbols     :  125 ( 124 usr;  13 con; 0-3 aty)
% 0.31/0.46  %            Number of variables   : 1572 (   8   ^;1499   !;  65   ?;1572   :)
% 0.31/0.46  % SPC      : TH0_THM_EQU_NAR
% 0.31/0.46  
% 0.31/0.46  % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:07.515
% 0.31/0.46  %------------------------------------------------------------------------------
% 0.31/0.46  % Could-be-implicit typings (40)
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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_Mt__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_J,type,
% 0.31/0.46      set_Pr1696918727_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_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_Mt__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,
% 0.31/0.46      produc270545127_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      set_Pr541394119_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      produc2046512871_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J_J,type,
% 0.31/0.46      set_Pr1847866567_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/0.46      produc1519776487_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      set_Pr1325664839_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      produc1586269031_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/0.46      set_Pr2096893127_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      produc186437863_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J_J,type,
% 0.31/0.46      set_Pr1419004359_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J_J,type,
% 0.31/0.46      set_Pr135335153st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.31/0.46      produc392316135_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/0.46      produc1440412305st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/0.46      set_Pr1142642759_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J_J,type,
% 0.31/0.46      set_Pr2083163591st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__List__Olist_I_062_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__Nat__Onat_J_J,type,
% 0.31/0.46      list_P1627643054te_nat: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      produc1225889383_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/0.46      produc1762014951st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      list_P890094829_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      set_Pr1165141447_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      produc410756839_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.31/0.46      set_Pr391631483_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__List__Olist_I_062_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Nat__Onat_J_J,type,
% 0.31/0.46      list_P1178430914te_nat: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.31/0.46      produc1393453339_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      produc2058209240st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/0.46      set_Pr602326075st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      list_P1040014977_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      set_Pr849496667_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      produc258871771st_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      produc2041926651_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J,type,
% 0.31/0.46      set_Pr1822651163om_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.31/0.46      product_prod_com_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      list_list_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__List__Olist_It__PLang__Ostate_J,type,
% 0.31/0.46      list_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Set__Oset_It__PLang__Ostate_J,type,
% 0.31/0.46      set_state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      list_com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__PLang__Ostate,type,
% 0.31/0.46      state: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__PLang__Ocom,type,
% 0.31/0.46      com: $tType ).
% 0.31/0.46  
% 0.31/0.46  thf(ty_n_t__Nat__Onat,type,
% 0.31/0.46      nat: $tType ).
% 0.31/0.46  
% 0.31/0.46  % Explicit typings (124)
% 0.31/0.46  thf(sy_c_List_Oappend_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      append_list_com: list_list_com > list_list_com > list_list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Oappend_001t__PLang__Ocom,type,
% 0.31/0.46      append_com: list_com > list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      append221843330_state: list_P890094829_state > list_P890094829_state > list_P890094829_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Obind_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 0.31/0.46      bind_com_com: list_com > ( com > list_com ) > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Obutlast_001t__PLang__Ocom,type,
% 0.31/0.46      butlast_com: list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Oconcat_001t__PLang__Ocom,type,
% 0.31/0.46      concat_com: list_list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Oinsert_001t__PLang__Ocom,type,
% 0.31/0.46      insert_com: com > list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olast_001t__PLang__Ocom,type,
% 0.31/0.46      last_com: list_com > com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olenlex_001t__PLang__Ocom,type,
% 0.31/0.46      lenlex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olenlex_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      lenlex295247238_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olenlex_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      lenlex1401983474_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olex_001t__PLang__Ocom,type,
% 0.31/0.46      lex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      lex_Pr570247525_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      lex_Pr1762629969_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olexord_001t__PLang__Ocom,type,
% 0.31/0.46      lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olexord_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olexord_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      lexord1893203674_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001_062_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Nat__Onat_J,type,
% 0.31/0.46      cons_P1821701106te_nat: ( produc2041926651_state > nat ) > list_P1178430914te_nat > list_P1178430914te_nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001_062_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__Nat__Onat_J,type,
% 0.31/0.46      cons_P1631380062te_nat: ( produc410756839_state > nat ) > list_P1627643054te_nat > list_P1627643054te_nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      cons_list_com: list_com > list_list_com > list_list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001t__PLang__Ocom,type,
% 0.31/0.46      cons_com: com > list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001t__PLang__Ostate,type,
% 0.31/0.46      cons_state: state > list_state > list_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      cons_P438230685_state: produc410756839_state > list_P890094829_state > list_P890094829_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001_062_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Nat__Onat_J,type,
% 0.31/0.46      nil_Pr1876916290te_nat: list_P1178430914te_nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001_062_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__Nat__Onat_J,type,
% 0.31/0.46      nil_Pr164089518te_nat: list_P1627643054te_nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      nil_list_com: list_list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001t__PLang__Ocom,type,
% 0.31/0.46      nil_com: list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001t__PLang__Ostate,type,
% 0.31/0.46      nil_state: list_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      nil_Pr1844458753_state: list_P1040014977_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      nil_Pr1347322605_state: list_P890094829_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist__ex1_001t__PLang__Ocom,type,
% 0.31/0.46      list_ex1_com: ( com > $o ) > list_com > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist__update_001t__PLang__Ocom,type,
% 0.31/0.46      list_update_com: list_com > nat > com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      list_u737668969_state: list_P1040014977_state > nat > produc2041926651_state > list_P1040014977_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      list_u364351829_state: list_P890094829_state > nat > produc410756839_state > list_P890094829_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel1_001t__PLang__Ocom,type,
% 0.31/0.46      listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel1_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel1_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      listre1725776070_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel_001t__List__Olist_It__PLang__Ocom_J_001t__PLang__Ostate,type,
% 0.31/0.46      listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 0.31/0.46      listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Olistrel_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      listre1244407729_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Omaps_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 0.31/0.46      maps_com_com: ( com > list_com ) > list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Omeasures_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      measur1071343867_state: list_P1178430914te_nat > set_Pr1165141447_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Omeasures_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      measur768621543_state: list_P1627643054te_nat > set_Pr2096893127_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Onth_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      nth_list_com: list_list_com > nat > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Onth_001t__PLang__Ocom,type,
% 0.31/0.46      nth_com: list_com > nat > com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Onth_001t__PLang__Ostate,type,
% 0.31/0.46      nth_state: list_state > nat > state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      nth_Pr553241858_state: list_P1040014977_state > nat > produc2041926651_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      nth_Pr526167918_state: list_P890094829_state > nat > produc410756839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Oproduct__lists_001t__PLang__Ocom,type,
% 0.31/0.46      product_lists_com: list_list_com > list_list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Orotate1_001t__PLang__Ocom,type,
% 0.31/0.46      rotate1_com: list_com > list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Osubseqs_001t__PLang__Ocom,type,
% 0.31/0.46      subseqs_com: list_com > list_list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Otake_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      take_P558217449_state: nat > list_P1040014977_state > list_P1040014977_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_List_Otake_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      take_P1852316373_state: nat > list_P890094829_state > list_P890094829_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      size_s318434721st_com: list_list_com > nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      size_size_list_com: list_com > nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__PLang__Ostate_J,type,
% 0.31/0.46      size_size_list_state: list_state > nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      size_s213202669_state: list_P1040014977_state > nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Nat_Osize__class_Osize_001t__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,
% 0.31/0.46      size_s837829465_state: list_P890094829_state > nat ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.31/0.46      ord_less_nat: nat > nat > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Oexec1,type,
% 0.31/0.46      pHoare259243666_exec1: set_Pr1165141447_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Oexecs,type,
% 0.31/0.46      pHoare259243732_execs: state > list_com > state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Otermis,type,
% 0.31/0.46      pHoare806997636termis: list_com > state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PLang_Ocom_OCond,type,
% 0.31/0.46      cond: ( state > $o ) > com > com > com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PLang_Ocom_ODo,type,
% 0.31/0.46      do: ( state > set_state ) > com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PLang_Ocom_OSemi,type,
% 0.31/0.46      semi: com > com > com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PLang_Ocom_OWhile,type,
% 0.31/0.46      while: ( state > $o ) > com > com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PLang_Oexec,type,
% 0.31/0.46      exec: state > com > state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_PTermi_Otermi,type,
% 0.31/0.46      termi: com > state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      produc1914379986st_com: ( com > com > $o ) > list_com > produc2058209240st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_001t__List__Olist_It__PLang__Ostate_J,type,
% 0.31/0.46      produc1742567891_state: list_list_com > list_state > produc1393453339_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__PLang__Ocom_J_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      produc1307105171st_com: list_com > list_com > produc258871771st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__PLang__Ocom_J_001t__PLang__Ostate,type,
% 0.31/0.46      produc1204172211_state: list_com > state > produc2041926651_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__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_001t__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,
% 0.31/0.46      produc1354769367_state: list_P890094829_state > list_P890094829_state > produc1586269031_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 0.31/0.46      product_Pair_com_com: com > com > product_prod_com_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__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_001t__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      produc67337417st_com: produc2058209240st_com > produc2058209240st_com > produc1440412305st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.31/0.46      produc67381847_state: produc1393453339_state > produc1393453339_state > produc392316135_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      produc313736791st_com: produc258871771st_com > produc258871771st_com > produc1762014951st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_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_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      produc984060759_state: produc1225889383_state > produc1225889383_state > produc1519776487_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_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_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,
% 0.31/0.46      produc1576663895_state: produc1586269031_state > produc1586269031_state > produc270545127_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Product__Type_OPair_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      produc2049704791_state: produc186437863_state > produc186437863_state > produc2046512871_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Relation_Oirrefl_001t__PLang__Ocom,type,
% 0.31/0.46      irrefl_com: set_Pr1822651163om_com > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Relation_Oirrefl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      irrefl654089520_state: set_Pr1165141447_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Relation_Oirrefl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      irrefl1358048924_state: set_Pr2096893127_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Set_OCollect_001t__PLang__Ostate,type,
% 0.31/0.46      collect_state: ( state > $o ) > set_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      collec300063826_state: ( produc410756839_state > $o ) > set_Pr1165141447_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      collec489924946_state: ( produc186437863_state > $o ) > set_Pr2096893127_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__PLang__Ocom_J,type,
% 0.31/0.46      transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__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,
% 0.31/0.46      transi1965148016_state: set_Pr1325664839_state > set_Pr1325664839_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__PLang__Ocom,type,
% 0.31/0.46      transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      transi1592315797st_com: set_Pr135335153st_com > set_Pr135335153st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.31/0.46      transi89280670_state: set_Pr1419004359_state > set_Pr1419004359_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_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,
% 0.31/0.46      transi445721450_state: set_Pr1696918727_state > set_Pr1696918727_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      transi152726506_state: set_Pr541394119_state > set_Pr541394119_state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__PLang__Ostate,type,
% 0.31/0.46      member_state: state > set_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 0.31/0.46      member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 0.31/0.46      member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 0.31/0.46      member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 0.31/0.46      member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/0.46      member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 0.31/0.46      member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 0.31/0.46      member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46      member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.31/0.46      member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__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,
% 0.31/0.46      member1642814224_state: produc270545127_state > set_Pr1696918727_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46      member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
% 0.31/0.46  
% 0.31/0.46  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,
% 0.31/0.46      member284400400_state: produc2046512871_state > set_Pr541394119_state > $o ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_v_c,type,
% 0.31/0.46      c: com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_v_c_H,type,
% 0.31/0.46      c2: com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_v_cs_H,type,
% 0.31/0.46      cs: list_com ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_v_s,type,
% 0.31/0.46      s: state ).
% 0.31/0.46  
% 0.31/0.46  thf(sy_v_s_H,type,
% 0.31/0.46      s2: state ).
% 0.31/0.46  
% 0.31/0.46  % Relevant facts (354)
% 0.31/0.46  thf(fact_0_exec1E_I1_J,axiom,
% 0.31/0.46      ! [S: state,Cs: list_com,S2: state] :
% 0.31/0.46        ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ nil_com @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 ) ).
% 0.31/0.46  
% 0.31/0.46  % exec1E(1)
% 0.31/0.46  thf(fact_1_termis_Osimps_I2_J,axiom,
% 0.31/0.46      ! [C: com,Cs2: list_com,S: state] :
% 0.31/0.46        ( ( pHoare806997636termis @ ( cons_com @ C @ Cs2 ) @ S )
% 0.31/0.46        = ( ( termi @ C @ S )
% 0.31/0.46          & ! [T: state] :
% 0.31/0.46              ( ( exec @ S @ C @ T )
% 0.31/0.46             => ( pHoare806997636termis @ Cs2 @ T ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % termis.simps(2)
% 0.31/0.46  thf(fact_2_termis_Osimps_I1_J,axiom,
% 0.31/0.46      ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 0.31/0.46  
% 0.31/0.46  % termis.simps(1)
% 0.31/0.46  thf(fact_3_exec__impl__execs,axiom,
% 0.31/0.46      ! [S: state,C: com,S2: state,Cs2: list_com] :
% 0.31/0.46        ( ( exec @ S @ C @ S2 )
% 0.31/0.46       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % exec_impl_execs
% 0.31/0.46  thf(fact_4_exec1s__impl__exec,axiom,
% 0.31/0.46      ! [C: com,S: state,T2: state] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/0.46       => ( exec @ S @ C @ T2 ) ) ).
% 0.31/0.46  
% 0.31/0.46  % exec1s_impl_exec
% 0.31/0.46  thf(fact_5_exec1__pres__termis,axiom,
% 0.31/0.46      ! [Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/0.46       => ( ( pHoare806997636termis @ Cs2 @ S )
% 0.31/0.46         => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % exec1_pres_termis
% 0.31/0.46  thf(fact_6_execs__pres__termis,axiom,
% 0.31/0.46      ! [Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/0.46       => ( ( pHoare806997636termis @ Cs2 @ S )
% 0.31/0.46         => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % execs_pres_termis
% 0.31/0.46  thf(fact_7_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_P890094829_state,Ay: list_P890094829_state,Bx: list_P890094829_state,By: list_P890094829_state,R: set_Pr1696918727_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.31/0.46        ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: list_P890094829_state,B: list_P890094829_state,Aa: list_P890094829_state,Ba: list_P890094829_state] :
% 0.31/0.46                ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ A @ B ) ) @ ( transi445721450_state @ R ) )
% 0.31/0.46               => ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_8_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.31/0.46        ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: list_P1040014977_state,B: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.31/0.46                ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ A @ B ) ) @ ( transi1428749162_state @ R ) )
% 0.31/0.46               => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_9_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.31/0.46        ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: list_com,B: list_com,Aa: list_com,Ba: list_com] :
% 0.31/0.46                ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ A @ B ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/0.46               => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_10_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.31/0.46        ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: list_list_com,B: list_state,Aa: list_list_com,Ba: list_state] :
% 0.31/0.46                ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ A @ B ) ) @ ( transi89280670_state @ R ) )
% 0.31/0.46               => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_11_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.31/0.46        ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: com > com > $o,B: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.31/0.46                ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ A @ B ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/0.46               => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_12_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.31/0.46        ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: produc410756839_state,B: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.31/0.46                ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A @ B ) ) @ ( transi152726506_state @ R ) )
% 0.31/0.46               => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_13_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.31/0.46        ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: produc2041926651_state,B: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.31/0.46                ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A @ B ) ) @ ( transi463013610_state @ R ) )
% 0.31/0.46               => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_14_rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.31/0.46       => ( ( P @ Ax @ Ay )
% 0.31/0.46         => ( ! [A: list_com,B: state,Aa: list_com,Ba: state] :
% 0.31/0.46                ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A @ B ) ) @ ( transi1302705790_state @ R ) )
% 0.31/0.46               => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46                 => ( ( P @ A @ B )
% 0.31/0.46                   => ( P @ Aa @ Ba ) ) ) )
% 0.31/0.46           => ( P @ Bx @ By ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_induct2
% 0.31/0.46  thf(fact_15_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: list_P890094829_state,Xb: list_P890094829_state,Za: list_P890094829_state,Zb: list_P890094829_state,R: set_Pr1696918727_state] :
% 0.31/0.46        ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Xa @ Xb ) @ ( produc1354769367_state @ Za @ Zb ) ) @ ( transi445721450_state @ R ) )
% 0.31/0.46       => ( ( ( produc1354769367_state @ Xa @ Xb )
% 0.31/0.46           != ( produc1354769367_state @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: list_P890094829_state,B: list_P890094829_state] :
% 0.31/0.46                ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Xa @ Xb ) @ ( produc1354769367_state @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Za @ Zb ) ) @ ( transi445721450_state @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_16_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: list_P1040014977_state,Xb: list_P1040014977_state,Za: list_P1040014977_state,Zb: list_P1040014977_state,R: set_Pr1847866567_state] :
% 0.31/0.46        ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) )
% 0.31/0.46       => ( ( ( produc1298457559_state @ Xa @ Xb )
% 0.31/0.46           != ( produc1298457559_state @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: list_P1040014977_state,B: list_P1040014977_state] :
% 0.31/0.46                ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_17_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: list_com,Xb: list_com,Za: list_com,Zb: list_com,R: set_Pr2083163591st_com] :
% 0.31/0.46        ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/0.46       => ( ( ( produc1307105171st_com @ Xa @ Xb )
% 0.31/0.46           != ( produc1307105171st_com @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: list_com,B: list_com] :
% 0.31/0.46                ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_18_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: list_list_com,Xb: list_state,Za: list_list_com,Zb: list_state,R: set_Pr1419004359_state] :
% 0.31/0.46        ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) )
% 0.31/0.46       => ( ( ( produc1742567891_state @ Xa @ Xb )
% 0.31/0.46           != ( produc1742567891_state @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: list_list_com,B: list_state] :
% 0.31/0.46                ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_19_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: com > com > $o,Xb: list_com,Za: com > com > $o,Zb: list_com,R: set_Pr135335153st_com] :
% 0.31/0.46        ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/0.46       => ( ( ( produc1914379986st_com @ Xa @ Xb )
% 0.31/0.46           != ( produc1914379986st_com @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: com > com > $o,B: list_com] :
% 0.31/0.46                ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_20_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: produc410756839_state,Xb: produc410756839_state,Za: produc410756839_state,Zb: produc410756839_state,R: set_Pr541394119_state] :
% 0.31/0.46        ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) )
% 0.31/0.46       => ( ( ( produc2065881943_state @ Xa @ Xb )
% 0.31/0.46           != ( produc2065881943_state @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: produc410756839_state,B: produc410756839_state] :
% 0.31/0.46                ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_21_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 0.31/0.46        ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 0.31/0.46       => ( ( ( produc1909270103_state @ Xa @ Xb )
% 0.31/0.46           != ( produc1909270103_state @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: produc2041926651_state,B: produc2041926651_state] :
% 0.31/0.46                ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_22_converse__rtranclE2,axiom,
% 0.31/0.46      ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 0.31/0.46       => ( ( ( produc1204172211_state @ Xa @ Xb )
% 0.31/0.46           != ( produc1204172211_state @ Za @ Zb ) )
% 0.31/0.46         => ~ ! [A: list_com,B: state] :
% 0.31/0.46                ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A @ B ) ) @ R )
% 0.31/0.46               => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtranclE2
% 0.31/0.46  thf(fact_23_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_P890094829_state,Ay: list_P890094829_state,Bx: list_P890094829_state,By: list_P890094829_state,R: set_Pr1696918727_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.31/0.46        ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: list_P890094829_state,B: list_P890094829_state,Aa: list_P890094829_state,Ba: list_P890094829_state] :
% 0.31/0.46                ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Aa @ Ba ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_24_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.31/0.46        ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: list_P1040014977_state,B: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.31/0.46                ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Aa @ Ba ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_25_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.31/0.46        ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: list_com,B: list_com,Aa: list_com,Ba: list_com] :
% 0.31/0.46                ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Aa @ Ba ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_26_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.31/0.46        ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: list_list_com,B: list_state,Aa: list_list_com,Ba: list_state] :
% 0.31/0.46                ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Aa @ Ba ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_27_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.31/0.46        ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: com > com > $o,B: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.31/0.46                ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Aa @ Ba ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_28_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.31/0.46        ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: produc410756839_state,B: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.31/0.46                ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Aa @ Ba ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_29_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.31/0.46        ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: produc2041926651_state,B: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.31/0.46                ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_30_converse__rtrancl__induct2,axiom,
% 0.31/0.46      ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.31/0.46       => ( ( P @ Bx @ By )
% 0.31/0.46         => ( ! [A: list_com,B: state,Aa: list_com,Ba: state] :
% 0.31/0.46                ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.31/0.46               => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.31/0.46                 => ( ( P @ Aa @ Ba )
% 0.31/0.46                   => ( P @ A @ B ) ) ) )
% 0.31/0.46           => ( P @ Ax @ Ay ) ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % converse_rtrancl_induct2
% 0.31/0.46  thf(fact_31_exec1s__impl__execs,axiom,
% 0.31/0.46      ! [Cs2: list_com,S: state,T2: state] :
% 0.31/0.46        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ nil_com @ T2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/0.46       => ( pHoare259243732_execs @ S @ Cs2 @ T2 ) ) ).
% 0.31/0.46  
% 0.31/0.46  % exec1s_impl_execs
% 0.31/0.46  thf(fact_32_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr541394119_state] :
% 0.31/0.46        ( ( transi152726506_state @ ( transi152726506_state @ R ) )
% 0.31/0.46        = ( transi152726506_state @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_33_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr602326075st_com] :
% 0.31/0.46        ( ( transi436345274st_com @ ( transi436345274st_com @ R ) )
% 0.31/0.46        = ( transi436345274st_com @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_34_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr1325664839_state] :
% 0.31/0.46        ( ( transi1965148016_state @ ( transi1965148016_state @ R ) )
% 0.31/0.46        = ( transi1965148016_state @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_35_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr1142642759_state] :
% 0.31/0.46        ( ( transi339813252_state @ ( transi339813252_state @ R ) )
% 0.31/0.46        = ( transi339813252_state @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_36_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr1822651163om_com] :
% 0.31/0.46        ( ( transi863150634cl_com @ ( transi863150634cl_com @ R ) )
% 0.31/0.46        = ( transi863150634cl_com @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_37_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr1165141447_state] :
% 0.31/0.46        ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 0.31/0.46        = ( transi1302705790_state @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_38_rtrancl__idemp,axiom,
% 0.31/0.46      ! [R: set_Pr2096893127_state] :
% 0.31/0.46        ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 0.31/0.46        = ( transi463013610_state @ R ) ) ).
% 0.31/0.46  
% 0.31/0.46  % rtrancl_idemp
% 0.31/0.46  thf(fact_39_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: produc2046512871_state,R: set_Pr541394119_state] :
% 0.31/0.46        ( ( member284400400_state @ P2 @ R )
% 0.31/0.46       => ( member284400400_state @ P2 @ ( transi152726506_state @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_40_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: produc258871771st_com,R: set_Pr602326075st_com] :
% 0.31/0.46        ( ( member32358020st_com @ P2 @ R )
% 0.31/0.46       => ( member32358020st_com @ P2 @ ( transi436345274st_com @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_41_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: produc1586269031_state,R: set_Pr1325664839_state] :
% 0.31/0.46        ( ( member423306384_state @ P2 @ R )
% 0.31/0.46       => ( member423306384_state @ P2 @ ( transi1965148016_state @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_42_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: produc1225889383_state,R: set_Pr1142642759_state] :
% 0.31/0.46        ( ( member1267359376_state @ P2 @ R )
% 0.31/0.46       => ( member1267359376_state @ P2 @ ( transi339813252_state @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_43_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: product_prod_com_com,R: set_Pr1822651163om_com] :
% 0.31/0.46        ( ( member1333916004om_com @ P2 @ R )
% 0.31/0.46       => ( member1333916004om_com @ P2 @ ( transi863150634cl_com @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_44_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 0.31/0.46        ( ( member1069318160_state @ P2 @ R )
% 0.31/0.46       => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_45_r__into__rtrancl,axiom,
% 0.31/0.46      ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 0.31/0.46        ( ( member512523024_state @ P2 @ R )
% 0.31/0.46       => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % r_into_rtrancl
% 0.31/0.46  thf(fact_46_list_Oinject,axiom,
% 0.31/0.46      ! [X21: produc2041926651_state,X22: list_P1040014977_state,Y21: produc2041926651_state,Y22: list_P1040014977_state] :
% 0.31/0.46        ( ( ( cons_P465369265_state @ X21 @ X22 )
% 0.31/0.46          = ( cons_P465369265_state @ Y21 @ Y22 ) )
% 0.31/0.46        = ( ( X21 = Y21 )
% 0.31/0.46          & ( X22 = Y22 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % list.inject
% 0.31/0.46  thf(fact_47_list_Oinject,axiom,
% 0.31/0.46      ! [X21: state,X22: list_state,Y21: state,Y22: list_state] :
% 0.31/0.46        ( ( ( cons_state @ X21 @ X22 )
% 0.31/0.46          = ( cons_state @ Y21 @ Y22 ) )
% 0.31/0.46        = ( ( X21 = Y21 )
% 0.31/0.46          & ( X22 = Y22 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % list.inject
% 0.31/0.46  thf(fact_48_list_Oinject,axiom,
% 0.31/0.46      ! [X21: list_com,X22: list_list_com,Y21: list_com,Y22: list_list_com] :
% 0.31/0.46        ( ( ( cons_list_com @ X21 @ X22 )
% 0.31/0.46          = ( cons_list_com @ Y21 @ Y22 ) )
% 0.31/0.46        = ( ( X21 = Y21 )
% 0.31/0.46          & ( X22 = Y22 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % list.inject
% 0.31/0.46  thf(fact_49_list_Oinject,axiom,
% 0.31/0.46      ! [X21: produc410756839_state > nat,X22: list_P1627643054te_nat,Y21: produc410756839_state > nat,Y22: list_P1627643054te_nat] :
% 0.31/0.46        ( ( ( cons_P1631380062te_nat @ X21 @ X22 )
% 0.31/0.46          = ( cons_P1631380062te_nat @ Y21 @ Y22 ) )
% 0.31/0.46        = ( ( X21 = Y21 )
% 0.31/0.46          & ( X22 = Y22 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % list.inject
% 0.31/0.46  thf(fact_50_list_Oinject,axiom,
% 0.31/0.46      ! [X21: produc2041926651_state > nat,X22: list_P1178430914te_nat,Y21: produc2041926651_state > nat,Y22: list_P1178430914te_nat] :
% 0.31/0.46        ( ( ( cons_P1821701106te_nat @ X21 @ X22 )
% 0.31/0.46          = ( cons_P1821701106te_nat @ Y21 @ Y22 ) )
% 0.31/0.46        = ( ( X21 = Y21 )
% 0.31/0.46          & ( X22 = Y22 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % list.inject
% 0.31/0.46  thf(fact_51_list_Oinject,axiom,
% 0.31/0.46      ! [X21: com,X22: list_com,Y21: com,Y22: list_com] :
% 0.31/0.46        ( ( ( cons_com @ X21 @ X22 )
% 0.31/0.46          = ( cons_com @ Y21 @ Y22 ) )
% 0.31/0.46        = ( ( X21 = Y21 )
% 0.31/0.46          & ( X22 = Y22 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % list.inject
% 0.31/0.46  thf(fact_52_prod_Oinject,axiom,
% 0.31/0.46      ! [X1: list_com,X2: list_com,Y1: list_com,Y2: list_com] :
% 0.31/0.46        ( ( ( produc1307105171st_com @ X1 @ X2 )
% 0.31/0.46          = ( produc1307105171st_com @ Y1 @ Y2 ) )
% 0.31/0.46        = ( ( X1 = Y1 )
% 0.31/0.46          & ( X2 = Y2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod.inject
% 0.31/0.46  thf(fact_53_prod_Oinject,axiom,
% 0.31/0.46      ! [X1: list_list_com,X2: list_state,Y1: list_list_com,Y2: list_state] :
% 0.31/0.46        ( ( ( produc1742567891_state @ X1 @ X2 )
% 0.31/0.46          = ( produc1742567891_state @ Y1 @ Y2 ) )
% 0.31/0.46        = ( ( X1 = Y1 )
% 0.31/0.46          & ( X2 = Y2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod.inject
% 0.31/0.46  thf(fact_54_prod_Oinject,axiom,
% 0.31/0.46      ! [X1: com > com > $o,X2: list_com,Y1: com > com > $o,Y2: list_com] :
% 0.31/0.46        ( ( ( produc1914379986st_com @ X1 @ X2 )
% 0.31/0.46          = ( produc1914379986st_com @ Y1 @ Y2 ) )
% 0.31/0.46        = ( ( X1 = Y1 )
% 0.31/0.46          & ( X2 = Y2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod.inject
% 0.31/0.46  thf(fact_55_prod_Oinject,axiom,
% 0.31/0.46      ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y2: produc2041926651_state] :
% 0.31/0.46        ( ( ( produc1909270103_state @ X1 @ X2 )
% 0.31/0.46          = ( produc1909270103_state @ Y1 @ Y2 ) )
% 0.31/0.46        = ( ( X1 = Y1 )
% 0.31/0.46          & ( X2 = Y2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod.inject
% 0.31/0.46  thf(fact_56_prod_Oinject,axiom,
% 0.31/0.46      ! [X1: list_com,X2: state,Y1: list_com,Y2: state] :
% 0.31/0.46        ( ( ( produc1204172211_state @ X1 @ X2 )
% 0.31/0.46          = ( produc1204172211_state @ Y1 @ Y2 ) )
% 0.31/0.46        = ( ( X1 = Y1 )
% 0.31/0.46          & ( X2 = Y2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod.inject
% 0.31/0.46  thf(fact_57_prod_Oinject,axiom,
% 0.31/0.46      ! [X1: produc410756839_state,X2: produc410756839_state,Y1: produc410756839_state,Y2: produc410756839_state] :
% 0.31/0.46        ( ( ( produc2065881943_state @ X1 @ X2 )
% 0.31/0.46          = ( produc2065881943_state @ Y1 @ Y2 ) )
% 0.31/0.46        = ( ( X1 = Y1 )
% 0.31/0.46          & ( X2 = Y2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod.inject
% 0.31/0.46  thf(fact_58_old_Oprod_Oinject,axiom,
% 0.31/0.46      ! [A2: produc2041926651_state,B2: produc2041926651_state,A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.31/0.46        ( ( ( produc1909270103_state @ A2 @ B2 )
% 0.31/0.46          = ( produc1909270103_state @ A3 @ B3 ) )
% 0.31/0.46        = ( ( A2 = A3 )
% 0.31/0.46          & ( B2 = B3 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % old.prod.inject
% 0.31/0.46  thf(fact_59_old_Oprod_Oinject,axiom,
% 0.31/0.46      ! [A2: list_com,B2: state,A3: list_com,B3: state] :
% 0.31/0.46        ( ( ( produc1204172211_state @ A2 @ B2 )
% 0.31/0.46          = ( produc1204172211_state @ A3 @ B3 ) )
% 0.31/0.46        = ( ( A2 = A3 )
% 0.31/0.46          & ( B2 = B3 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % old.prod.inject
% 0.31/0.46  thf(fact_60_old_Oprod_Oinject,axiom,
% 0.31/0.46      ! [A2: produc410756839_state,B2: produc410756839_state,A3: produc410756839_state,B3: produc410756839_state] :
% 0.31/0.46        ( ( ( produc2065881943_state @ A2 @ B2 )
% 0.31/0.46          = ( produc2065881943_state @ A3 @ B3 ) )
% 0.31/0.46        = ( ( A2 = A3 )
% 0.31/0.46          & ( B2 = B3 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % old.prod.inject
% 0.31/0.46  thf(fact_61_prod__cases3,axiom,
% 0.31/0.46      ! [Y: produc410756839_state] :
% 0.31/0.46        ~ ! [A: produc2041926651_state,B: list_com,C2: state] :
% 0.31/0.46            ( Y
% 0.31/0.46           != ( produc1909270103_state @ A @ ( produc1204172211_state @ B @ C2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod_cases3
% 0.31/0.46  thf(fact_62_prod__cases3,axiom,
% 0.31/0.46      ! [Y: produc186437863_state] :
% 0.31/0.46        ~ ! [A: produc410756839_state,B: produc2041926651_state,C2: produc2041926651_state] :
% 0.31/0.46            ( Y
% 0.31/0.46           != ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ C2 ) ) ) ).
% 0.31/0.46  
% 0.31/0.46  % prod_cases3
% 0.31/0.46  thf(fact_63_prod__cases4,axiom,
% 0.31/0.46      ! [Y: produc186437863_state] :
% 0.31/0.46        ~ ! [A: produc410756839_state,B: produc2041926651_state,C2: list_com,D: state] :
% 0.31/0.46            ( Y
% 0.31/0.46           != ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ ( produc1204172211_state @ C2 @ D ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_cases4
% 0.31/0.47  thf(fact_64_successively_Ocases,axiom,
% 0.31/0.47      ! [X: produc2058209240st_com] :
% 0.31/0.47        ( ! [P3: com > com > $o] :
% 0.31/0.47            ( X
% 0.31/0.47           != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.31/0.47       => ( ! [P3: com > com > $o,X3: com] :
% 0.31/0.47              ( X
% 0.31/0.47             != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 0.31/0.47         => ~ ! [P3: com > com > $o,X3: com,Y3: com,Xs: list_com] :
% 0.31/0.47                ( X
% 0.31/0.47               != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % successively.cases
% 0.31/0.47  thf(fact_65_sorted__wrt_Ocases,axiom,
% 0.31/0.47      ! [X: produc2058209240st_com] :
% 0.31/0.47        ( ! [P3: com > com > $o] :
% 0.31/0.47            ( X
% 0.31/0.47           != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.31/0.47       => ~ ! [P3: com > com > $o,X3: com,Ys: list_com] :
% 0.31/0.47              ( X
% 0.31/0.47             != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % sorted_wrt.cases
% 0.31/0.47  thf(fact_66_shuffles_Ocases,axiom,
% 0.31/0.47      ! [X: produc258871771st_com] :
% 0.31/0.47        ( ! [Ys: list_com] :
% 0.31/0.47            ( X
% 0.31/0.47           != ( produc1307105171st_com @ nil_com @ Ys ) )
% 0.31/0.47       => ( ! [Xs: list_com] :
% 0.31/0.47              ( X
% 0.31/0.47             != ( produc1307105171st_com @ Xs @ nil_com ) )
% 0.31/0.47         => ~ ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.31/0.47                ( X
% 0.31/0.47               != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % shuffles.cases
% 0.31/0.47  thf(fact_67_splice_Ocases,axiom,
% 0.31/0.47      ! [X: produc258871771st_com] :
% 0.31/0.47        ( ! [Ys: list_com] :
% 0.31/0.47            ( X
% 0.31/0.47           != ( produc1307105171st_com @ nil_com @ Ys ) )
% 0.31/0.47       => ~ ! [X3: com,Xs: list_com,Ys: list_com] :
% 0.31/0.47              ( X
% 0.31/0.47             != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs ) @ Ys ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % splice.cases
% 0.31/0.47  thf(fact_68_execs_Ointros_I1_J,axiom,
% 0.31/0.47      ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 0.31/0.47  
% 0.31/0.47  % execs.intros(1)
% 0.31/0.47  thf(fact_69_old_Oprod_Oinducts,axiom,
% 0.31/0.47      ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 0.31/0.47        ( ! [A: produc2041926651_state,B: produc2041926651_state] : ( P @ ( produc1909270103_state @ A @ B ) )
% 0.31/0.47       => ( P @ Prod ) ) ).
% 0.31/0.47  
% 0.31/0.47  % old.prod.inducts
% 0.31/0.47  thf(fact_70_old_Oprod_Oinducts,axiom,
% 0.31/0.47      ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 0.31/0.47        ( ! [A: list_com,B: state] : ( P @ ( produc1204172211_state @ A @ B ) )
% 0.31/0.47       => ( P @ Prod ) ) ).
% 0.31/0.47  
% 0.31/0.47  % old.prod.inducts
% 0.31/0.47  thf(fact_71_old_Oprod_Oinducts,axiom,
% 0.31/0.47      ! [P: produc186437863_state > $o,Prod: produc186437863_state] :
% 0.31/0.47        ( ! [A: produc410756839_state,B: produc410756839_state] : ( P @ ( produc2065881943_state @ A @ B ) )
% 0.31/0.47       => ( P @ Prod ) ) ).
% 0.31/0.47  
% 0.31/0.47  % old.prod.inducts
% 0.31/0.47  thf(fact_72_old_Oprod_Oexhaust,axiom,
% 0.31/0.47      ! [Y: produc410756839_state] :
% 0.31/0.47        ~ ! [A: produc2041926651_state,B: produc2041926651_state] :
% 0.31/0.47            ( Y
% 0.31/0.47           != ( produc1909270103_state @ A @ B ) ) ).
% 0.31/0.47  
% 0.31/0.47  % old.prod.exhaust
% 0.31/0.47  thf(fact_73_old_Oprod_Oexhaust,axiom,
% 0.31/0.47      ! [Y: produc2041926651_state] :
% 0.31/0.47        ~ ! [A: list_com,B: state] :
% 0.31/0.47            ( Y
% 0.31/0.47           != ( produc1204172211_state @ A @ B ) ) ).
% 0.31/0.47  
% 0.31/0.47  % old.prod.exhaust
% 0.31/0.47  thf(fact_74_old_Oprod_Oexhaust,axiom,
% 0.31/0.47      ! [Y: produc186437863_state] :
% 0.31/0.47        ~ ! [A: produc410756839_state,B: produc410756839_state] :
% 0.31/0.47            ( Y
% 0.31/0.47           != ( produc2065881943_state @ A @ B ) ) ).
% 0.31/0.47  
% 0.31/0.47  % old.prod.exhaust
% 0.31/0.47  thf(fact_75_Pair__inject,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.31/0.47        ( ( ( produc1909270103_state @ A2 @ B2 )
% 0.31/0.47          = ( produc1909270103_state @ A3 @ B3 ) )
% 0.31/0.47       => ~ ( ( A2 = A3 )
% 0.31/0.47           => ( B2 != B3 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Pair_inject
% 0.31/0.47  thf(fact_76_Pair__inject,axiom,
% 0.31/0.47      ! [A2: list_com,B2: state,A3: list_com,B3: state] :
% 0.31/0.47        ( ( ( produc1204172211_state @ A2 @ B2 )
% 0.31/0.47          = ( produc1204172211_state @ A3 @ B3 ) )
% 0.31/0.47       => ~ ( ( A2 = A3 )
% 0.31/0.47           => ( B2 != B3 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Pair_inject
% 0.31/0.47  thf(fact_77_Pair__inject,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,A3: produc410756839_state,B3: produc410756839_state] :
% 0.31/0.47        ( ( ( produc2065881943_state @ A2 @ B2 )
% 0.31/0.47          = ( produc2065881943_state @ A3 @ B3 ) )
% 0.31/0.47       => ~ ( ( A2 = A3 )
% 0.31/0.47           => ( B2 != B3 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Pair_inject
% 0.31/0.47  thf(fact_78_prod__cases,axiom,
% 0.31/0.47      ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 0.31/0.47        ( ! [A: produc2041926651_state,B: produc2041926651_state] : ( P @ ( produc1909270103_state @ A @ B ) )
% 0.31/0.47       => ( P @ P2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_cases
% 0.31/0.47  thf(fact_79_prod__cases,axiom,
% 0.31/0.47      ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 0.31/0.47        ( ! [A: list_com,B: state] : ( P @ ( produc1204172211_state @ A @ B ) )
% 0.31/0.47       => ( P @ P2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_cases
% 0.31/0.47  thf(fact_80_prod__cases,axiom,
% 0.31/0.47      ! [P: produc186437863_state > $o,P2: produc186437863_state] :
% 0.31/0.47        ( ! [A: produc410756839_state,B: produc410756839_state] : ( P @ ( produc2065881943_state @ A @ B ) )
% 0.31/0.47       => ( P @ P2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_cases
% 0.31/0.47  thf(fact_81_surj__pair,axiom,
% 0.31/0.47      ! [P2: produc410756839_state] :
% 0.31/0.47      ? [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.31/0.47        ( P2
% 0.31/0.47        = ( produc1909270103_state @ X3 @ Y3 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % surj_pair
% 0.31/0.47  thf(fact_82_surj__pair,axiom,
% 0.31/0.47      ! [P2: produc2041926651_state] :
% 0.31/0.47      ? [X3: list_com,Y3: state] :
% 0.31/0.47        ( P2
% 0.31/0.47        = ( produc1204172211_state @ X3 @ Y3 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % surj_pair
% 0.31/0.47  thf(fact_83_surj__pair,axiom,
% 0.31/0.47      ! [P2: produc186437863_state] :
% 0.31/0.47      ? [X3: produc410756839_state,Y3: produc410756839_state] :
% 0.31/0.47        ( P2
% 0.31/0.47        = ( produc2065881943_state @ X3 @ Y3 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % surj_pair
% 0.31/0.47  thf(fact_84_not__Cons__self2,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com] :
% 0.31/0.47        ( ( cons_com @ X @ Xs2 )
% 0.31/0.47       != Xs2 ) ).
% 0.31/0.47  
% 0.31/0.47  % not_Cons_self2
% 0.31/0.47  thf(fact_85_execs_Ointros_I2_J,axiom,
% 0.31/0.47      ! [S: state,C: com,T2: state,Cs2: list_com,U: state] :
% 0.31/0.47        ( ( exec @ S @ C @ T2 )
% 0.31/0.47       => ( ( pHoare259243732_execs @ T2 @ Cs2 @ U )
% 0.31/0.47         => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs2 ) @ U ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % execs.intros(2)
% 0.31/0.47  thf(fact_86_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47      ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 0.31/0.47        ( ! [F: com > com,X_1: list_com] : ( P @ F @ nil_com @ X_1 )
% 0.31/0.47       => ( ! [F: com > com,A: com,As: list_com,Bs: list_com] :
% 0.31/0.47              ( ( P @ F @ As @ ( cons_com @ ( F @ A ) @ Bs ) )
% 0.31/0.47             => ( P @ F @ ( cons_com @ A @ As ) @ Bs ) )
% 0.31/0.47         => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % map_tailrec_rev.induct
% 0.31/0.47  thf(fact_87_list__nonempty__induct,axiom,
% 0.31/0.47      ! [Xs2: list_com,P: list_com > $o] :
% 0.31/0.47        ( ( Xs2 != nil_com )
% 0.31/0.47       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/0.47         => ( ! [X3: com,Xs: list_com] :
% 0.31/0.47                ( ( Xs != nil_com )
% 0.31/0.47               => ( ( P @ Xs )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ Xs ) ) ) )
% 0.31/0.47           => ( P @ Xs2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list_nonempty_induct
% 0.31/0.47  thf(fact_88_successively_Oinduct,axiom,
% 0.31/0.47      ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.31/0.47        ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.31/0.47       => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 0.31/0.47         => ( ! [P3: com > com > $o,X3: com,Y3: com,Xs: list_com] :
% 0.31/0.47                ( ( P @ P3 @ ( cons_com @ Y3 @ Xs ) )
% 0.31/0.47               => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) )
% 0.31/0.47           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % successively.induct
% 0.31/0.47  thf(fact_89_remdups__adj_Oinduct,axiom,
% 0.31/0.47      ! [P: list_com > $o,A0: list_com] :
% 0.31/0.47        ( ( P @ nil_com )
% 0.31/0.47       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/0.47         => ( ! [X3: com,Y3: com,Xs: list_com] :
% 0.31/0.47                ( ( ( X3 = Y3 )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ Xs ) ) )
% 0.31/0.47               => ( ( ( X3 != Y3 )
% 0.31/0.47                   => ( P @ ( cons_com @ Y3 @ Xs ) ) )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) )
% 0.31/0.47           => ( P @ A0 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % remdups_adj.induct
% 0.31/0.47  thf(fact_90_sorted__wrt_Oinduct,axiom,
% 0.31/0.47      ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.31/0.47        ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.31/0.47       => ( ! [P3: com > com > $o,X3: com,Ys: list_com] :
% 0.31/0.47              ( ( P @ P3 @ Ys )
% 0.31/0.47             => ( P @ P3 @ ( cons_com @ X3 @ Ys ) ) )
% 0.31/0.47         => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % sorted_wrt.induct
% 0.31/0.47  thf(fact_91_remdups__adj_Ocases,axiom,
% 0.31/0.47      ! [X: list_com] :
% 0.31/0.47        ( ( X != nil_com )
% 0.31/0.47       => ( ! [X3: com] :
% 0.31/0.47              ( X
% 0.31/0.47             != ( cons_com @ X3 @ nil_com ) )
% 0.31/0.47         => ~ ! [X3: com,Y3: com,Xs: list_com] :
% 0.31/0.47                ( X
% 0.31/0.47               != ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % remdups_adj.cases
% 0.31/0.47  thf(fact_92_transpose_Ocases,axiom,
% 0.31/0.47      ! [X: list_list_com] :
% 0.31/0.47        ( ( X != nil_list_com )
% 0.31/0.47       => ( ! [Xss: list_list_com] :
% 0.31/0.47              ( X
% 0.31/0.47             != ( cons_list_com @ nil_com @ Xss ) )
% 0.31/0.47         => ~ ! [X3: com,Xs: list_com,Xss: list_list_com] :
% 0.31/0.47                ( X
% 0.31/0.47               != ( cons_list_com @ ( cons_com @ X3 @ Xs ) @ Xss ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % transpose.cases
% 0.31/0.47  thf(fact_93_shuffles_Oinduct,axiom,
% 0.31/0.47      ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.31/0.47        ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.31/0.47       => ( ! [Xs: list_com] : ( P @ Xs @ nil_com )
% 0.31/0.47         => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.31/0.47                ( ( P @ Xs @ ( cons_com @ Y3 @ Ys ) )
% 0.31/0.47               => ( ( P @ ( cons_com @ X3 @ Xs ) @ Ys )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) )
% 0.31/0.47           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % shuffles.induct
% 0.31/0.47  thf(fact_94_mem__Collect__eq,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,P: produc410756839_state > $o] :
% 0.31/0.47        ( ( member1069318160_state @ A2 @ ( collec300063826_state @ P ) )
% 0.31/0.47        = ( P @ A2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % mem_Collect_eq
% 0.31/0.47  thf(fact_95_mem__Collect__eq,axiom,
% 0.31/0.47      ! [A2: state,P: state > $o] :
% 0.31/0.47        ( ( member_state @ A2 @ ( collect_state @ P ) )
% 0.31/0.47        = ( P @ A2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % mem_Collect_eq
% 0.31/0.47  thf(fact_96_mem__Collect__eq,axiom,
% 0.31/0.47      ! [A2: produc186437863_state,P: produc186437863_state > $o] :
% 0.31/0.47        ( ( member512523024_state @ A2 @ ( collec489924946_state @ P ) )
% 0.31/0.47        = ( P @ A2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % mem_Collect_eq
% 0.31/0.47  thf(fact_97_Collect__mem__eq,axiom,
% 0.31/0.47      ! [A4: set_Pr1165141447_state] :
% 0.31/0.47        ( ( collec300063826_state
% 0.31/0.47          @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 0.31/0.47        = A4 ) ).
% 0.31/0.47  
% 0.31/0.47  % Collect_mem_eq
% 0.31/0.47  thf(fact_98_Collect__mem__eq,axiom,
% 0.31/0.47      ! [A4: set_state] :
% 0.31/0.47        ( ( collect_state
% 0.31/0.47          @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 0.31/0.47        = A4 ) ).
% 0.31/0.47  
% 0.31/0.47  % Collect_mem_eq
% 0.31/0.47  thf(fact_99_Collect__mem__eq,axiom,
% 0.31/0.47      ! [A4: set_Pr2096893127_state] :
% 0.31/0.47        ( ( collec489924946_state
% 0.31/0.47          @ ^ [X4: produc186437863_state] : ( member512523024_state @ X4 @ A4 ) )
% 0.31/0.47        = A4 ) ).
% 0.31/0.47  
% 0.31/0.47  % Collect_mem_eq
% 0.31/0.47  thf(fact_100_induct__list012,axiom,
% 0.31/0.47      ! [P: list_com > $o,Xs2: list_com] :
% 0.31/0.47        ( ( P @ nil_com )
% 0.31/0.47       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/0.47         => ( ! [X3: com,Y3: com,Zs: list_com] :
% 0.31/0.47                ( ( P @ Zs )
% 0.31/0.47               => ( ( P @ ( cons_com @ Y3 @ Zs ) )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47           => ( P @ Xs2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % induct_list012
% 0.31/0.47  thf(fact_101_splice_Oinduct,axiom,
% 0.31/0.47      ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.31/0.47        ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.31/0.47       => ( ! [X3: com,Xs: list_com,Ys: list_com] :
% 0.31/0.47              ( ( P @ Ys @ Xs )
% 0.31/0.47             => ( P @ ( cons_com @ X3 @ Xs ) @ Ys ) )
% 0.31/0.47         => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % splice.induct
% 0.31/0.47  thf(fact_102_list__induct2_H,axiom,
% 0.31/0.47      ! [P: list_com > list_com > $o,Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( P @ nil_com @ nil_com )
% 0.31/0.47       => ( ! [X3: com,Xs: list_com] : ( P @ ( cons_com @ X3 @ Xs ) @ nil_com )
% 0.31/0.47         => ( ! [Y3: com,Ys: list_com] : ( P @ nil_com @ ( cons_com @ Y3 @ Ys ) )
% 0.31/0.47           => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.31/0.47                  ( ( P @ Xs @ Ys )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) )
% 0.31/0.47             => ( P @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list_induct2'
% 0.31/0.47  thf(fact_103_neq__Nil__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com] :
% 0.31/0.47        ( ( Xs2 != nil_com )
% 0.31/0.47        = ( ? [Y4: com,Ys3: list_com] :
% 0.31/0.47              ( Xs2
% 0.31/0.47              = ( cons_com @ Y4 @ Ys3 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % neq_Nil_conv
% 0.31/0.47  thf(fact_104_list_Oinducts,axiom,
% 0.31/0.47      ! [P: list_com > $o,List: list_com] :
% 0.31/0.47        ( ( P @ nil_com )
% 0.31/0.47       => ( ! [X12: com,X23: list_com] :
% 0.31/0.47              ( ( P @ X23 )
% 0.31/0.47             => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 0.31/0.47         => ( P @ List ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list.inducts
% 0.31/0.47  thf(fact_105_list_Oexhaust,axiom,
% 0.31/0.47      ! [Y: list_com] :
% 0.31/0.47        ( ( Y != nil_com )
% 0.31/0.47       => ~ ! [X212: com,X222: list_com] :
% 0.31/0.47              ( Y
% 0.31/0.47             != ( cons_com @ X212 @ X222 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list.exhaust
% 0.31/0.47  thf(fact_106_list_OdiscI,axiom,
% 0.31/0.47      ! [List: list_com,X21: com,X22: list_com] :
% 0.31/0.47        ( ( List
% 0.31/0.47          = ( cons_com @ X21 @ X22 ) )
% 0.31/0.47       => ( List != nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list.discI
% 0.31/0.47  thf(fact_107_list_Odistinct_I1_J,axiom,
% 0.31/0.47      ! [X21: com,X22: list_com] :
% 0.31/0.47        ( nil_com
% 0.31/0.47       != ( cons_com @ X21 @ X22 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list.distinct(1)
% 0.31/0.47  thf(fact_108_execs_Oinducts,axiom,
% 0.31/0.47      ! [X1: state,X2: list_com,X32: state,P: state > list_com > state > $o] :
% 0.31/0.47        ( ( pHoare259243732_execs @ X1 @ X2 @ X32 )
% 0.31/0.47       => ( ! [S3: state] : ( P @ S3 @ nil_com @ S3 )
% 0.31/0.47         => ( ! [S3: state,C2: com,T3: state,Cs3: list_com,U2: state] :
% 0.31/0.47                ( ( exec @ S3 @ C2 @ T3 )
% 0.31/0.47               => ( ( pHoare259243732_execs @ T3 @ Cs3 @ U2 )
% 0.31/0.47                 => ( ( P @ T3 @ Cs3 @ U2 )
% 0.31/0.47                   => ( P @ S3 @ ( cons_com @ C2 @ Cs3 ) @ U2 ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % execs.inducts
% 0.31/0.47  thf(fact_109_execs_Osimps,axiom,
% 0.31/0.47      ( pHoare259243732_execs
% 0.31/0.47      = ( ^ [A12: state,A23: list_com,A32: state] :
% 0.31/0.47            ( ? [S4: state] :
% 0.31/0.47                ( ( A12 = S4 )
% 0.31/0.47                & ( A23 = nil_com )
% 0.31/0.47                & ( A32 = S4 ) )
% 0.31/0.47            | ? [S4: state,C3: com,T: state,Cs4: list_com,U3: state] :
% 0.31/0.47                ( ( A12 = S4 )
% 0.31/0.47                & ( A23
% 0.31/0.47                  = ( cons_com @ C3 @ Cs4 ) )
% 0.31/0.47                & ( A32 = U3 )
% 0.31/0.47                & ( exec @ S4 @ C3 @ T )
% 0.31/0.47                & ( pHoare259243732_execs @ T @ Cs4 @ U3 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % execs.simps
% 0.31/0.47  thf(fact_110_execs_Ocases,axiom,
% 0.31/0.47      ! [A1: state,A22: list_com,A33: state] :
% 0.31/0.47        ( ( pHoare259243732_execs @ A1 @ A22 @ A33 )
% 0.31/0.47       => ( ( ( A22 = nil_com )
% 0.31/0.47           => ( A33 != A1 ) )
% 0.31/0.47         => ~ ! [C2: com,T3: state,Cs3: list_com] :
% 0.31/0.47                ( ( A22
% 0.31/0.47                  = ( cons_com @ C2 @ Cs3 ) )
% 0.31/0.47               => ( ( exec @ A1 @ C2 @ T3 )
% 0.31/0.47                 => ~ ( pHoare259243732_execs @ T3 @ Cs3 @ A33 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % execs.cases
% 0.31/0.47  thf(fact_111_converse__rtrancl__into__rtrancl,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.31/0.47       => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47         => ( member1069318160_state @ ( produc1909270103_state @ A2 @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % converse_rtrancl_into_rtrancl
% 0.31/0.47  thf(fact_112_converse__rtrancl__into__rtrancl,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.31/0.47       => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C ) @ ( transi463013610_state @ R ) )
% 0.31/0.47         => ( member512523024_state @ ( produc2065881943_state @ A2 @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % converse_rtrancl_into_rtrancl
% 0.31/0.47  thf(fact_113_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C ) @ R )
% 0.31/0.47         => ( member1069318160_state @ ( produc1909270103_state @ A2 @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.rtrancl_into_rtrancl
% 0.31/0.47  thf(fact_114_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C ) @ R )
% 0.31/0.47         => ( member512523024_state @ ( produc2065881943_state @ A2 @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.rtrancl_into_rtrancl
% 0.31/0.47  thf(fact_115_converse__rtrancl__induct,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( P @ B2 )
% 0.31/0.47         => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.31/0.47               => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47                 => ( ( P @ Z )
% 0.31/0.47                   => ( P @ Y3 ) ) ) )
% 0.31/0.47           => ( P @ A2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % converse_rtrancl_induct
% 0.31/0.47  thf(fact_116_converse__rtrancl__induct,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( P @ B2 )
% 0.31/0.47         => ( ! [Y3: produc410756839_state,Z: produc410756839_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z ) @ R )
% 0.31/0.47               => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47                 => ( ( P @ Z )
% 0.31/0.47                   => ( P @ Y3 ) ) ) )
% 0.31/0.47           => ( P @ A2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % converse_rtrancl_induct
% 0.31/0.47  thf(fact_117_rtrancl_Ortrancl__refl,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A2 @ A2 ) @ ( transi1302705790_state @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.rtrancl_refl
% 0.31/0.47  thf(fact_118_rtrancl_Ortrancl__refl,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,R: set_Pr2096893127_state] : ( member512523024_state @ ( produc2065881943_state @ A2 @ A2 ) @ ( transi463013610_state @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.rtrancl_refl
% 0.31/0.47  thf(fact_119_converse__rtranclE,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( X != Z2 )
% 0.31/0.47         => ~ ! [Y3: produc2041926651_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R )
% 0.31/0.47               => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % converse_rtranclE
% 0.31/0.47  thf(fact_120_converse__rtranclE,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( X != Z2 )
% 0.31/0.47         => ~ ! [Y3: produc410756839_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ X @ Y3 ) @ R )
% 0.31/0.47               => ~ ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % converse_rtranclE
% 0.31/0.47  thf(fact_121_rtrancl_Oinducts,axiom,
% 0.31/0.47      ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ! [A: produc2041926651_state] : ( P @ A @ A )
% 0.31/0.47         => ( ! [A: produc2041926651_state,B: produc2041926651_state,C2: produc2041926651_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47               => ( ( P @ A @ B )
% 0.31/0.47                 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C2 ) @ R )
% 0.31/0.47                   => ( P @ A @ C2 ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.inducts
% 0.31/0.47  thf(fact_122_rtrancl_Oinducts,axiom,
% 0.31/0.47      ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ! [A: produc410756839_state] : ( P @ A @ A )
% 0.31/0.47         => ( ! [A: produc410756839_state,B: produc410756839_state,C2: produc410756839_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.31/0.47               => ( ( P @ A @ B )
% 0.31/0.47                 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C2 ) @ R )
% 0.31/0.47                   => ( P @ A @ C2 ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.inducts
% 0.31/0.47  thf(fact_123_rtrancl__induct,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( P @ A2 )
% 0.31/0.47         => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47               => ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.31/0.47                 => ( ( P @ Y3 )
% 0.31/0.47                   => ( P @ Z ) ) ) )
% 0.31/0.47           => ( P @ B2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_induct
% 0.31/0.47  thf(fact_124_rtrancl__induct,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( P @ A2 )
% 0.31/0.47         => ( ! [Y3: produc410756839_state,Z: produc410756839_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ A2 @ Y3 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47               => ( ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z ) @ R )
% 0.31/0.47                 => ( ( P @ Y3 )
% 0.31/0.47                   => ( P @ Z ) ) ) )
% 0.31/0.47           => ( P @ B2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_induct
% 0.31/0.47  thf(fact_125_rtrancl__trans,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47         => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_trans
% 0.31/0.47  thf(fact_126_rtrancl__trans,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47         => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_trans
% 0.31/0.47  thf(fact_127_rtrancl_Osimps,axiom,
% 0.31/0.47      ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47        = ( ? [A5: produc2041926651_state] :
% 0.31/0.47              ( ( A1 = A5 )
% 0.31/0.47              & ( A22 = A5 ) )
% 0.31/0.47          | ? [A5: produc2041926651_state,B4: produc2041926651_state,C3: produc2041926651_state] :
% 0.31/0.47              ( ( A1 = A5 )
% 0.31/0.47              & ( A22 = C3 )
% 0.31/0.47              & ( member1069318160_state @ ( produc1909270103_state @ A5 @ B4 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47              & ( member1069318160_state @ ( produc1909270103_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.simps
% 0.31/0.47  thf(fact_128_rtrancl_Osimps,axiom,
% 0.31/0.47      ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47        = ( ? [A5: produc410756839_state] :
% 0.31/0.47              ( ( A1 = A5 )
% 0.31/0.47              & ( A22 = A5 ) )
% 0.31/0.47          | ? [A5: produc410756839_state,B4: produc410756839_state,C3: produc410756839_state] :
% 0.31/0.47              ( ( A1 = A5 )
% 0.31/0.47              & ( A22 = C3 )
% 0.31/0.47              & ( member512523024_state @ ( produc2065881943_state @ A5 @ B4 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47              & ( member512523024_state @ ( produc2065881943_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.simps
% 0.31/0.47  thf(fact_129_rtrancl_Ocases,axiom,
% 0.31/0.47      ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( A22 != A1 )
% 0.31/0.47         => ~ ! [B: produc2041926651_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47               => ~ ( member1069318160_state @ ( produc1909270103_state @ B @ A22 ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.cases
% 0.31/0.47  thf(fact_130_rtrancl_Ocases,axiom,
% 0.31/0.47      ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( A22 != A1 )
% 0.31/0.47         => ~ ! [B: produc410756839_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B ) @ ( transi463013610_state @ R ) )
% 0.31/0.47               => ~ ( member512523024_state @ ( produc2065881943_state @ B @ A22 ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl.cases
% 0.31/0.47  thf(fact_131_rtranclE,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( A2 != B2 )
% 0.31/0.47         => ~ ! [Y3: produc2041926651_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47               => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ B2 ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtranclE
% 0.31/0.47  thf(fact_132_rtranclE,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( A2 != B2 )
% 0.31/0.47         => ~ ! [Y3: produc410756839_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ A2 @ Y3 ) @ ( transi463013610_state @ R ) )
% 0.31/0.47               => ~ ( member512523024_state @ ( produc2065881943_state @ Y3 @ B2 ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtranclE
% 0.31/0.47  thf(fact_133_prod__induct4,axiom,
% 0.31/0.47      ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 0.31/0.47        ( ! [A: produc410756839_state,B: produc2041926651_state,C2: list_com,D: state] : ( P @ ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ ( produc1204172211_state @ C2 @ D ) ) ) )
% 0.31/0.47       => ( P @ X ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_induct4
% 0.31/0.47  thf(fact_134_prod__induct3,axiom,
% 0.31/0.47      ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 0.31/0.47        ( ! [A: produc2041926651_state,B: list_com,C2: state] : ( P @ ( produc1909270103_state @ A @ ( produc1204172211_state @ B @ C2 ) ) )
% 0.31/0.47       => ( P @ X ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_induct3
% 0.31/0.47  thf(fact_135_prod__induct3,axiom,
% 0.31/0.47      ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 0.31/0.47        ( ! [A: produc410756839_state,B: produc2041926651_state,C2: produc2041926651_state] : ( P @ ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ C2 ) ) )
% 0.31/0.47       => ( P @ X ) ) ).
% 0.31/0.47  
% 0.31/0.47  % prod_induct3
% 0.31/0.47  thf(fact_136_exec1_OSemi,axiom,
% 0.31/0.47      ! [C1: com,C22: com,Cs2: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs2 ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1.Semi
% 0.31/0.47  thf(fact_137_exec1E_I3_J,axiom,
% 0.31/0.47      ! [C1: com,C22: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/0.47       => ~ ( ( Cs
% 0.31/0.47              = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs2 ) ) )
% 0.31/0.47           => ( S2 != S ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1E(3)
% 0.31/0.47  thf(fact_138_exec1_ODo,axiom,
% 0.31/0.47      ! [T2: state,F2: state > set_state,S: state,Cs2: list_com] :
% 0.31/0.47        ( ( member_state @ T2 @ ( F2 @ S ) )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ T2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1.Do
% 0.31/0.47  thf(fact_139_exec1E_I2_J,axiom,
% 0.31/0.47      ! [F2: state > set_state,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/0.47       => ~ ( ( Cs = Cs2 )
% 0.31/0.47           => ~ ( member_state @ S2 @ ( F2 @ S ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1E(2)
% 0.31/0.47  thf(fact_140_exec1_OIfFalse,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C1: com,C22: com,Cs2: list_com] :
% 0.31/0.47        ( ~ ( B2 @ S )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs2 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1.IfFalse
% 0.31/0.47  thf(fact_141_exec1_OIfTrue,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C1: com,C22: com,Cs2: list_com] :
% 0.31/0.47        ( ( B2 @ S )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs2 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1.IfTrue
% 0.31/0.47  thf(fact_142_exec1E_I4_J,axiom,
% 0.31/0.47      ! [B2: state > $o,C1: com,C22: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/0.47       => ( ( ( Cs
% 0.31/0.47              = ( cons_com @ C1 @ Cs2 ) )
% 0.31/0.47           => ( ( S2 = S )
% 0.31/0.47             => ~ ( B2 @ S ) ) )
% 0.31/0.47         => ~ ( ( Cs
% 0.31/0.47                = ( cons_com @ C22 @ Cs2 ) )
% 0.31/0.47             => ( ( S2 = S )
% 0.31/0.47               => ( B2 @ S ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1E(4)
% 0.31/0.47  thf(fact_143_exec1_OWhileFalse,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C: com,Cs2: list_com] :
% 0.31/0.47        ( ~ ( B2 @ S )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1.WhileFalse
% 0.31/0.47  thf(fact_144_exec1_OWhileTrue,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C: com,Cs2: list_com] :
% 0.31/0.47        ( ( B2 @ S )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1.WhileTrue
% 0.31/0.47  thf(fact_145_while__termiE,axiom,
% 0.31/0.47      ! [B2: state > $o,C: com,S: state] :
% 0.31/0.47        ( ( termi @ ( while @ B2 @ C ) @ S )
% 0.31/0.47       => ( ( B2 @ S )
% 0.31/0.47         => ( termi @ C @ S ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % while_termiE
% 0.31/0.47  thf(fact_146_while__termiE2,axiom,
% 0.31/0.47      ! [B2: state > $o,C: com,S: state,T2: state] :
% 0.31/0.47        ( ( termi @ ( while @ B2 @ C ) @ S )
% 0.31/0.47       => ( ( B2 @ S )
% 0.31/0.47         => ( ( exec @ S @ C @ T2 )
% 0.31/0.47           => ( termi @ ( while @ B2 @ C ) @ T2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % while_termiE2
% 0.31/0.47  thf(fact_147_exec1E_I5_J,axiom,
% 0.31/0.47      ! [B2: state > $o,C: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/0.47       => ( ( ( Cs = Cs2 )
% 0.31/0.47           => ( ( S2 = S )
% 0.31/0.47             => ( B2 @ S ) ) )
% 0.31/0.47         => ~ ( ( Cs
% 0.31/0.47                = ( cons_com @ C @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) ) )
% 0.31/0.47             => ( ( S2 = S )
% 0.31/0.47               => ~ ( B2 @ S ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec1E(5)
% 0.31/0.47  thf(fact_148_termi_OSemi,axiom,
% 0.31/0.47      ! [C1: com,S0: state,C22: com] :
% 0.31/0.47        ( ( termi @ C1 @ S0 )
% 0.31/0.47       => ( ! [S1: state] :
% 0.31/0.47              ( ( exec @ S0 @ C1 @ S1 )
% 0.31/0.47             => ( termi @ C22 @ S1 ) )
% 0.31/0.47         => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % termi.Semi
% 0.31/0.47  thf(fact_149_termi_OWhileTrue,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C: com] :
% 0.31/0.47        ( ( B2 @ S )
% 0.31/0.47       => ( ( termi @ C @ S )
% 0.31/0.47         => ( ! [T3: state] :
% 0.31/0.47                ( ( exec @ S @ C @ T3 )
% 0.31/0.47               => ( termi @ ( while @ B2 @ C ) @ T3 ) )
% 0.31/0.47           => ( termi @ ( while @ B2 @ C ) @ S ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % termi.WhileTrue
% 0.31/0.47  thf(fact_150_com_Oinject_I2_J,axiom,
% 0.31/0.47      ! [X21: com,X22: com,Y21: com,Y22: com] :
% 0.31/0.47        ( ( ( semi @ X21 @ X22 )
% 0.31/0.47          = ( semi @ Y21 @ Y22 ) )
% 0.31/0.47        = ( ( X21 = Y21 )
% 0.31/0.47          & ( X22 = Y22 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.inject(2)
% 0.31/0.47  thf(fact_151_com_Oinject_I1_J,axiom,
% 0.31/0.47      ! [X1: state > set_state,Y1: state > set_state] :
% 0.31/0.47        ( ( ( do @ X1 )
% 0.31/0.47          = ( do @ Y1 ) )
% 0.31/0.47        = ( X1 = Y1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.inject(1)
% 0.31/0.47  thf(fact_152_com_Oinject_I3_J,axiom,
% 0.31/0.47      ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 0.31/0.47        ( ( ( cond @ X31 @ X322 @ X33 )
% 0.31/0.47          = ( cond @ Y31 @ Y32 @ Y33 ) )
% 0.31/0.47        = ( ( X31 = Y31 )
% 0.31/0.47          & ( X322 = Y32 )
% 0.31/0.47          & ( X33 = Y33 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.inject(3)
% 0.31/0.47  thf(fact_153_com_Oinject_I4_J,axiom,
% 0.31/0.47      ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.31/0.47        ( ( ( while @ X41 @ X42 )
% 0.31/0.47          = ( while @ Y41 @ Y42 ) )
% 0.31/0.47        = ( ( X41 = Y41 )
% 0.31/0.47          & ( X42 = Y42 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.inject(4)
% 0.31/0.47  thf(fact_154_exec_OWhileFalse,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C: com] :
% 0.31/0.47        ( ~ ( B2 @ S )
% 0.31/0.47       => ( exec @ S @ ( while @ B2 @ C ) @ S ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec.WhileFalse
% 0.31/0.47  thf(fact_155_exec_OWhileTrue,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C: com,T2: state,U: state] :
% 0.31/0.47        ( ( B2 @ S )
% 0.31/0.47       => ( ( exec @ S @ C @ T2 )
% 0.31/0.47         => ( ( exec @ T2 @ ( while @ B2 @ C ) @ U )
% 0.31/0.47           => ( exec @ S @ ( while @ B2 @ C ) @ U ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec.WhileTrue
% 0.31/0.47  thf(fact_156_com_Odistinct_I19_J,axiom,
% 0.31/0.47      ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 0.31/0.47        ( ( cond @ X31 @ X322 @ X33 )
% 0.31/0.47       != ( while @ X41 @ X42 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.distinct(19)
% 0.31/0.47  thf(fact_157_termi_OWhileFalse,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C: com] :
% 0.31/0.47        ( ~ ( B2 @ S )
% 0.31/0.47       => ( termi @ ( while @ B2 @ C ) @ S ) ) ).
% 0.31/0.47  
% 0.31/0.47  % termi.WhileFalse
% 0.31/0.47  thf(fact_158_com_Odistinct_I5_J,axiom,
% 0.31/0.47      ! [X1: state > set_state,X41: state > $o,X42: com] :
% 0.31/0.47        ( ( do @ X1 )
% 0.31/0.47       != ( while @ X41 @ X42 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.distinct(5)
% 0.31/0.47  thf(fact_159_exec_OIfFalse,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C22: com,T2: state,C1: com] :
% 0.31/0.47        ( ~ ( B2 @ S )
% 0.31/0.47       => ( ( exec @ S @ C22 @ T2 )
% 0.31/0.47         => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec.IfFalse
% 0.31/0.47  thf(fact_160_exec_OIfTrue,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C1: com,T2: state,C22: com] :
% 0.31/0.47        ( ( B2 @ S )
% 0.31/0.47       => ( ( exec @ S @ C1 @ T2 )
% 0.31/0.47         => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec.IfTrue
% 0.31/0.47  thf(fact_161_com_Odistinct_I13_J,axiom,
% 0.31/0.47      ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 0.31/0.47        ( ( semi @ X21 @ X22 )
% 0.31/0.47       != ( while @ X41 @ X42 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.distinct(13)
% 0.31/0.47  thf(fact_162_exec_ODo,axiom,
% 0.31/0.47      ! [T2: state,F2: state > set_state,S: state] :
% 0.31/0.47        ( ( member_state @ T2 @ ( F2 @ S ) )
% 0.31/0.47       => ( exec @ S @ ( do @ F2 ) @ T2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec.Do
% 0.31/0.47  thf(fact_163_exec_OSemi,axiom,
% 0.31/0.47      ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 0.31/0.47        ( ( exec @ S0 @ C1 @ S12 )
% 0.31/0.47       => ( ( exec @ S12 @ C22 @ S22 )
% 0.31/0.47         => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % exec.Semi
% 0.31/0.47  thf(fact_164_termi_OIfFalse,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C22: com,C1: com] :
% 0.31/0.47        ( ~ ( B2 @ S )
% 0.31/0.47       => ( ( termi @ C22 @ S )
% 0.31/0.47         => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % termi.IfFalse
% 0.31/0.47  thf(fact_165_termi_OIfTrue,axiom,
% 0.31/0.47      ! [B2: state > $o,S: state,C1: com,C22: com] :
% 0.31/0.47        ( ( B2 @ S )
% 0.31/0.47       => ( ( termi @ C1 @ S )
% 0.31/0.47         => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % termi.IfTrue
% 0.31/0.47  thf(fact_166_com_Odistinct_I3_J,axiom,
% 0.31/0.47      ! [X1: state > set_state,X31: state > $o,X322: com,X33: com] :
% 0.31/0.47        ( ( do @ X1 )
% 0.31/0.47       != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.distinct(3)
% 0.31/0.47  thf(fact_167_com_Odistinct_I11_J,axiom,
% 0.31/0.47      ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 0.31/0.47        ( ( semi @ X21 @ X22 )
% 0.31/0.47       != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.distinct(11)
% 0.31/0.47  thf(fact_168_com_Odistinct_I1_J,axiom,
% 0.31/0.47      ! [X1: state > set_state,X21: com,X22: com] :
% 0.31/0.47        ( ( do @ X1 )
% 0.31/0.47       != ( semi @ X21 @ X22 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % com.distinct(1)
% 0.31/0.47  thf(fact_169_product__lists_Osimps_I1_J,axiom,
% 0.31/0.47      ( ( product_lists_com @ nil_list_com )
% 0.31/0.47      = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % product_lists.simps(1)
% 0.31/0.47  thf(fact_170_subseqs_Osimps_I1_J,axiom,
% 0.31/0.47      ( ( subseqs_com @ nil_com )
% 0.31/0.47      = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % subseqs.simps(1)
% 0.31/0.47  thf(fact_171_app__execs,axiom,
% 0.31/0.47      ! [Cs2: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % app_execs
% 0.31/0.47  thf(fact_172_insert__Nil,axiom,
% 0.31/0.47      ! [X: com] :
% 0.31/0.47        ( ( insert_com @ X @ nil_com )
% 0.31/0.47        = ( cons_com @ X @ nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % insert_Nil
% 0.31/0.47  thf(fact_173_listrel_Oinducts,axiom,
% 0.31/0.47      ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 0.31/0.47       => ( ( P @ nil_com @ nil_com )
% 0.31/0.47         => ( ! [X3: com,Y3: com,Xs: list_com,Ys: list_com] :
% 0.31/0.47                ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.31/0.47               => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) )
% 0.31/0.47                 => ( ( P @ Xs @ Ys )
% 0.31/0.47                   => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.inducts
% 0.31/0.47  thf(fact_174_listrel_Oinducts,axiom,
% 0.31/0.47      ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 0.31/0.47       => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 0.31/0.47         => ( ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.31/0.47                ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.31/0.47               => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) )
% 0.31/0.47                 => ( ( P @ Xs @ Ys )
% 0.31/0.47                   => ( P @ ( cons_P465369265_state @ X3 @ Xs ) @ ( cons_P465369265_state @ Y3 @ Ys ) ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.inducts
% 0.31/0.47  thf(fact_175_listrel_Oinducts,axiom,
% 0.31/0.47      ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 0.31/0.47        ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47       => ( ( P @ nil_list_com @ nil_state )
% 0.31/0.47         => ( ! [X3: list_com,Y3: state,Xs: list_list_com,Ys: list_state] :
% 0.31/0.47                ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.31/0.47               => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47                 => ( ( P @ Xs @ Ys )
% 0.31/0.47                   => ( P @ ( cons_list_com @ X3 @ Xs ) @ ( cons_state @ Y3 @ Ys ) ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.inducts
% 0.31/0.47  thf(fact_176_listrel_Oinducts,axiom,
% 0.31/0.47      ! [X1: list_P890094829_state,X2: list_P890094829_state,R: set_Pr2096893127_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ X1 @ X2 ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47       => ( ( P @ nil_Pr1347322605_state @ nil_Pr1347322605_state )
% 0.31/0.47         => ( ! [X3: produc410756839_state,Y3: produc410756839_state,Xs: list_P890094829_state,Ys: list_P890094829_state] :
% 0.31/0.47                ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 0.31/0.47               => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47                 => ( ( P @ Xs @ Ys )
% 0.31/0.47                   => ( P @ ( cons_P438230685_state @ X3 @ Xs ) @ ( cons_P438230685_state @ Y3 @ Ys ) ) ) ) )
% 0.31/0.47           => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.inducts
% 0.31/0.47  thf(fact_177_append_Oassoc,axiom,
% 0.31/0.47      ! [A2: list_com,B2: list_com,C: list_com] :
% 0.31/0.47        ( ( append_com @ ( append_com @ A2 @ B2 ) @ C )
% 0.31/0.47        = ( append_com @ A2 @ ( append_com @ B2 @ C ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append.assoc
% 0.31/0.47  thf(fact_178_append__assoc,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( append_com @ ( append_com @ Xs2 @ Ys2 ) @ Zs2 )
% 0.31/0.47        = ( append_com @ Xs2 @ ( append_com @ Ys2 @ Zs2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_assoc
% 0.31/0.47  thf(fact_179_append__same__eq,axiom,
% 0.31/0.47      ! [Ys2: list_com,Xs2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Ys2 @ Xs2 )
% 0.31/0.47          = ( append_com @ Zs2 @ Xs2 ) )
% 0.31/0.47        = ( Ys2 = Zs2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_same_eq
% 0.31/0.47  thf(fact_180_same__append__eq,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ Ys2 )
% 0.31/0.47          = ( append_com @ Xs2 @ Zs2 ) )
% 0.31/0.47        = ( Ys2 = Zs2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % same_append_eq
% 0.31/0.47  thf(fact_181_append__Nil2,axiom,
% 0.31/0.47      ! [Xs2: list_com] :
% 0.31/0.47        ( ( append_com @ Xs2 @ nil_com )
% 0.31/0.47        = Xs2 ) ).
% 0.31/0.47  
% 0.31/0.47  % append_Nil2
% 0.31/0.47  thf(fact_182_append__self__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ Ys2 )
% 0.31/0.47          = Xs2 )
% 0.31/0.47        = ( Ys2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_self_conv
% 0.31/0.47  thf(fact_183_self__append__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( Xs2
% 0.31/0.47          = ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47        = ( Ys2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % self_append_conv
% 0.31/0.47  thf(fact_184_append__self__conv2,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ Ys2 )
% 0.31/0.47          = Ys2 )
% 0.31/0.47        = ( Xs2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_self_conv2
% 0.31/0.47  thf(fact_185_self__append__conv2,axiom,
% 0.31/0.47      ! [Ys2: list_com,Xs2: list_com] :
% 0.31/0.47        ( ( Ys2
% 0.31/0.47          = ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47        = ( Xs2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % self_append_conv2
% 0.31/0.47  thf(fact_186_Nil__is__append__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( nil_com
% 0.31/0.47          = ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47        = ( ( Xs2 = nil_com )
% 0.31/0.47          & ( Ys2 = nil_com ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Nil_is_append_conv
% 0.31/0.47  thf(fact_187_append__is__Nil__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ Ys2 )
% 0.31/0.47          = nil_com )
% 0.31/0.47        = ( ( Xs2 = nil_com )
% 0.31/0.47          & ( Ys2 = nil_com ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_is_Nil_conv
% 0.31/0.47  thf(fact_188_append_Oright__neutral,axiom,
% 0.31/0.47      ! [A2: list_com] :
% 0.31/0.47        ( ( append_com @ A2 @ nil_com )
% 0.31/0.47        = A2 ) ).
% 0.31/0.47  
% 0.31/0.47  % append.right_neutral
% 0.31/0.47  thf(fact_189_append1__eq__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com,Ys2: list_com,Y: com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) )
% 0.31/0.47          = ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) )
% 0.31/0.47        = ( ( Xs2 = Ys2 )
% 0.31/0.47          & ( X = Y ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append1_eq_conv
% 0.31/0.47  thf(fact_190_listrel__rtrancl__refl,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_rtrancl_refl
% 0.31/0.47  thf(fact_191_listrel__rtrancl__refl,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,R: set_Pr2096893127_state] : ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_rtrancl_refl
% 0.31/0.47  thf(fact_192_append__Cons,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( append_com @ ( cons_com @ X @ Xs2 ) @ Ys2 )
% 0.31/0.47        = ( cons_com @ X @ ( append_com @ Xs2 @ Ys2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_Cons
% 0.31/0.47  thf(fact_193_Cons__eq__appendI,axiom,
% 0.31/0.47      ! [X: com,Xs1: list_com,Ys2: list_com,Xs2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( ( cons_com @ X @ Xs1 )
% 0.31/0.47          = Ys2 )
% 0.31/0.47       => ( ( Xs2
% 0.31/0.47            = ( append_com @ Xs1 @ Zs2 ) )
% 0.31/0.47         => ( ( cons_com @ X @ Xs2 )
% 0.31/0.47            = ( append_com @ Ys2 @ Zs2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_eq_appendI
% 0.31/0.47  thf(fact_194_append_Oleft__neutral,axiom,
% 0.31/0.47      ! [A2: list_com] :
% 0.31/0.47        ( ( append_com @ nil_com @ A2 )
% 0.31/0.47        = A2 ) ).
% 0.31/0.47  
% 0.31/0.47  % append.left_neutral
% 0.31/0.47  thf(fact_195_append__Nil,axiom,
% 0.31/0.47      ! [Ys2: list_com] :
% 0.31/0.47        ( ( append_com @ nil_com @ Ys2 )
% 0.31/0.47        = Ys2 ) ).
% 0.31/0.47  
% 0.31/0.47  % append_Nil
% 0.31/0.47  thf(fact_196_eq__Nil__appendI,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( Xs2 = Ys2 )
% 0.31/0.47       => ( Xs2
% 0.31/0.47          = ( append_com @ nil_com @ Ys2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % eq_Nil_appendI
% 0.31/0.47  thf(fact_197_append__eq__appendI,axiom,
% 0.31/0.47      ! [Xs2: list_com,Xs1: list_com,Zs2: list_com,Ys2: list_com,Us: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ Xs1 )
% 0.31/0.47          = Zs2 )
% 0.31/0.47       => ( ( Ys2
% 0.31/0.47            = ( append_com @ Xs1 @ Us ) )
% 0.31/0.47         => ( ( append_com @ Xs2 @ Ys2 )
% 0.31/0.47            = ( append_com @ Zs2 @ Us ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_eq_appendI
% 0.31/0.47  thf(fact_198_append__eq__append__conv2,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com,Ts: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ Ys2 )
% 0.31/0.47          = ( append_com @ Zs2 @ Ts ) )
% 0.31/0.47        = ( ? [Us2: list_com] :
% 0.31/0.47              ( ( ( Xs2
% 0.31/0.47                  = ( append_com @ Zs2 @ Us2 ) )
% 0.31/0.47                & ( ( append_com @ Us2 @ Ys2 )
% 0.31/0.47                  = Ts ) )
% 0.31/0.47              | ( ( ( append_com @ Xs2 @ Us2 )
% 0.31/0.47                  = Zs2 )
% 0.31/0.47                & ( Ys2
% 0.31/0.47                  = ( append_com @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_eq_append_conv2
% 0.31/0.47  thf(fact_199_rev__induct,axiom,
% 0.31/0.47      ! [P: list_com > $o,Xs2: list_com] :
% 0.31/0.47        ( ( P @ nil_com )
% 0.31/0.47       => ( ! [X3: com,Xs: list_com] :
% 0.31/0.47              ( ( P @ Xs )
% 0.31/0.47             => ( P @ ( append_com @ Xs @ ( cons_com @ X3 @ nil_com ) ) ) )
% 0.31/0.47         => ( P @ Xs2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rev_induct
% 0.31/0.47  thf(fact_200_rev__exhaust,axiom,
% 0.31/0.47      ! [Xs2: list_com] :
% 0.31/0.47        ( ( Xs2 != nil_com )
% 0.31/0.47       => ~ ! [Ys: list_com,Y3: com] :
% 0.31/0.47              ( Xs2
% 0.31/0.47             != ( append_com @ Ys @ ( cons_com @ Y3 @ nil_com ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rev_exhaust
% 0.31/0.47  thf(fact_201_Cons__eq__append__conv,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( ( cons_com @ X @ Xs2 )
% 0.31/0.47          = ( append_com @ Ys2 @ Zs2 ) )
% 0.31/0.47        = ( ( ( Ys2 = nil_com )
% 0.31/0.47            & ( ( cons_com @ X @ Xs2 )
% 0.31/0.47              = Zs2 ) )
% 0.31/0.47          | ? [Ys4: list_com] :
% 0.31/0.47              ( ( ( cons_com @ X @ Ys4 )
% 0.31/0.47                = Ys2 )
% 0.31/0.47              & ( Xs2
% 0.31/0.47                = ( append_com @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_eq_append_conv
% 0.31/0.47  thf(fact_202_append__eq__Cons__conv,axiom,
% 0.31/0.47      ! [Ys2: list_com,Zs2: list_com,X: com,Xs2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Ys2 @ Zs2 )
% 0.31/0.47          = ( cons_com @ X @ Xs2 ) )
% 0.31/0.47        = ( ( ( Ys2 = nil_com )
% 0.31/0.47            & ( Zs2
% 0.31/0.47              = ( cons_com @ X @ Xs2 ) ) )
% 0.31/0.47          | ? [Ys4: list_com] :
% 0.31/0.47              ( ( Ys2
% 0.31/0.47                = ( cons_com @ X @ Ys4 ) )
% 0.31/0.47              & ( ( append_com @ Ys4 @ Zs2 )
% 0.31/0.47                = Xs2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_eq_Cons_conv
% 0.31/0.47  thf(fact_203_rev__nonempty__induct,axiom,
% 0.31/0.47      ! [Xs2: list_com,P: list_com > $o] :
% 0.31/0.47        ( ( Xs2 != nil_com )
% 0.31/0.47       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.31/0.47         => ( ! [X3: com,Xs: list_com] :
% 0.31/0.47                ( ( Xs != nil_com )
% 0.31/0.47               => ( ( P @ Xs )
% 0.31/0.47                 => ( P @ ( append_com @ Xs @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 0.31/0.47           => ( P @ Xs2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rev_nonempty_induct
% 0.31/0.47  thf(fact_204_listrel__Nil2,axiom,
% 0.31/0.47      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( listrel_com_com @ R ) )
% 0.31/0.47       => ( Xs2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Nil2
% 0.31/0.47  thf(fact_205_listrel__Nil1,axiom,
% 0.31/0.47      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs2 ) @ ( listrel_com_com @ R ) )
% 0.31/0.47       => ( Xs2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Nil1
% 0.31/0.47  thf(fact_206_listrel_ONil,axiom,
% 0.31/0.47      ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.Nil
% 0.31/0.47  thf(fact_207_listrel__rtrancl__trans,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state,Zs2: list_P1040014977_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.31/0.47       => ( ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.31/0.47         => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_rtrancl_trans
% 0.31/0.47  thf(fact_208_listrel__rtrancl__trans,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state,Zs2: list_P890094829_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 0.31/0.47       => ( ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 0.31/0.47         => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_rtrancl_trans
% 0.31/0.47  thf(fact_209_listrel_OCons,axiom,
% 0.31/0.47      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/0.47       => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel_com_com @ R ) )
% 0.31/0.47         => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.Cons
% 0.31/0.47  thf(fact_210_listrel_OCons,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/0.47       => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) )
% 0.31/0.47         => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.Cons
% 0.31/0.47  thf(fact_211_listrel_OCons,axiom,
% 0.31/0.47      ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs2: list_list_com,Ys2: list_state] :
% 0.31/0.47        ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 0.31/0.47       => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47         => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs2 ) @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.Cons
% 0.31/0.47  thf(fact_212_listrel_OCons,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.31/0.47       => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47         => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.Cons
% 0.31/0.47  thf(fact_213_listrel__Cons1,axiom,
% 0.31/0.47      ! [Y: com,Ys2: list_com,Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys2 ) @ Xs2 ) @ ( listrel_com_com @ R ) )
% 0.31/0.47       => ~ ! [Y3: com,Ys: list_com] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_com @ Y3 @ Ys ) )
% 0.31/0.47             => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y3 ) @ R )
% 0.31/0.47               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons1
% 0.31/0.47  thf(fact_214_listrel__Cons1,axiom,
% 0.31/0.47      ! [Y: produc2041926651_state,Ys2: list_P1040014977_state,Xs2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys2 ) @ Xs2 ) @ ( listre194873521_state @ R ) )
% 0.31/0.47       => ~ ! [Y3: produc2041926651_state,Ys: list_P1040014977_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_P465369265_state @ Y3 @ Ys ) )
% 0.31/0.47             => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y3 ) @ R )
% 0.31/0.47               => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons1
% 0.31/0.47  thf(fact_215_listrel__Cons1,axiom,
% 0.31/0.47      ! [Y: list_com,Ys2: list_list_com,Xs2: list_state,R: set_Pr849496667_state] :
% 0.31/0.47        ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys2 ) @ Xs2 ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47       => ~ ! [Y3: state,Ys: list_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_state @ Y3 @ Ys ) )
% 0.31/0.47             => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y3 ) @ R )
% 0.31/0.47               => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys2 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons1
% 0.31/0.47  thf(fact_216_listrel__Cons1,axiom,
% 0.31/0.47      ! [Y: produc410756839_state,Ys2: list_P890094829_state,Xs2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ Y @ Ys2 ) @ Xs2 ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47       => ~ ! [Y3: produc410756839_state,Ys: list_P890094829_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_P438230685_state @ Y3 @ Ys ) )
% 0.31/0.47             => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Y3 ) @ R )
% 0.31/0.47               => ~ ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons1
% 0.31/0.47  thf(fact_217_listrel__Cons2,axiom,
% 0.31/0.47      ! [Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) )
% 0.31/0.47       => ~ ! [X3: com,Xs: list_com] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_com @ X3 @ Xs ) )
% 0.31/0.47             => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 0.31/0.47               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons2
% 0.31/0.47  thf(fact_218_listrel__Cons2,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) )
% 0.31/0.47       => ~ ! [X3: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_P465369265_state @ X3 @ Xs ) )
% 0.31/0.47             => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 0.31/0.47               => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons2
% 0.31/0.47  thf(fact_219_listrel__Cons2,axiom,
% 0.31/0.47      ! [Xs2: list_list_com,Y: state,Ys2: list_state,R: set_Pr849496667_state] :
% 0.31/0.47        ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47       => ~ ! [X3: list_com,Xs: list_list_com] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_list_com @ X3 @ Xs ) )
% 0.31/0.47             => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 0.31/0.47               => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys2 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons2
% 0.31/0.47  thf(fact_220_listrel__Cons2,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47       => ~ ! [X3: produc410756839_state,Xs: list_P890094829_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_P438230685_state @ X3 @ Xs ) )
% 0.31/0.47             => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R )
% 0.31/0.47               => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_Cons2
% 0.31/0.47  thf(fact_221_app__exec,axiom,
% 0.31/0.47      ! [Cs2: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % app_exec
% 0.31/0.47  thf(fact_222_listrel_Ocases,axiom,
% 0.31/0.47      ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.31/0.47       => ( ( ( A1 = nil_com )
% 0.31/0.47           => ( A22 != nil_com ) )
% 0.31/0.47         => ~ ! [X3: com,Y3: com,Xs: list_com] :
% 0.31/0.47                ( ( A1
% 0.31/0.47                  = ( cons_com @ X3 @ Xs ) )
% 0.31/0.47               => ! [Ys: list_com] :
% 0.31/0.47                    ( ( A22
% 0.31/0.47                      = ( cons_com @ Y3 @ Ys ) )
% 0.31/0.47                   => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.31/0.47                     => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.cases
% 0.31/0.47  thf(fact_223_listrel_Ocases,axiom,
% 0.31/0.47      ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.31/0.47       => ( ( ( A1 = nil_Pr1844458753_state )
% 0.31/0.47           => ( A22 != nil_Pr1844458753_state ) )
% 0.31/0.47         => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.31/0.47                ( ( A1
% 0.31/0.47                  = ( cons_P465369265_state @ X3 @ Xs ) )
% 0.31/0.47               => ! [Ys: list_P1040014977_state] :
% 0.31/0.47                    ( ( A22
% 0.31/0.47                      = ( cons_P465369265_state @ Y3 @ Ys ) )
% 0.31/0.47                   => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.31/0.47                     => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.cases
% 0.31/0.47  thf(fact_224_listrel_Ocases,axiom,
% 0.31/0.47      ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.31/0.47        ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47       => ( ( ( A1 = nil_list_com )
% 0.31/0.47           => ( A22 != nil_state ) )
% 0.31/0.47         => ~ ! [X3: list_com,Y3: state,Xs: list_list_com] :
% 0.31/0.47                ( ( A1
% 0.31/0.47                  = ( cons_list_com @ X3 @ Xs ) )
% 0.31/0.47               => ! [Ys: list_state] :
% 0.31/0.47                    ( ( A22
% 0.31/0.47                      = ( cons_state @ Y3 @ Ys ) )
% 0.31/0.47                   => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.31/0.47                     => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.cases
% 0.31/0.47  thf(fact_225_listrel_Ocases,axiom,
% 0.31/0.47      ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47       => ( ( ( A1 = nil_Pr1347322605_state )
% 0.31/0.47           => ( A22 != nil_Pr1347322605_state ) )
% 0.31/0.47         => ~ ! [X3: produc410756839_state,Y3: produc410756839_state,Xs: list_P890094829_state] :
% 0.31/0.47                ( ( A1
% 0.31/0.47                  = ( cons_P438230685_state @ X3 @ Xs ) )
% 0.31/0.47               => ! [Ys: list_P890094829_state] :
% 0.31/0.47                    ( ( A22
% 0.31/0.47                      = ( cons_P438230685_state @ Y3 @ Ys ) )
% 0.31/0.47                   => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 0.31/0.47                     => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.cases
% 0.31/0.47  thf(fact_226_listrel_Osimps,axiom,
% 0.31/0.47      ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.31/0.47        = ( ( ( A1 = nil_com )
% 0.31/0.47            & ( A22 = nil_com ) )
% 0.31/0.47          | ? [X4: com,Y4: com,Xs3: list_com,Ys3: list_com] :
% 0.31/0.47              ( ( A1
% 0.31/0.47                = ( cons_com @ X4 @ Xs3 ) )
% 0.31/0.47              & ( A22
% 0.31/0.47                = ( cons_com @ Y4 @ Ys3 ) )
% 0.31/0.47              & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y4 ) @ R )
% 0.31/0.47              & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.simps
% 0.31/0.47  thf(fact_227_listrel_Osimps,axiom,
% 0.31/0.47      ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.31/0.47        = ( ( ( A1 = nil_Pr1844458753_state )
% 0.31/0.47            & ( A22 = nil_Pr1844458753_state ) )
% 0.31/0.47          | ? [X4: produc2041926651_state,Y4: produc2041926651_state,Xs3: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 0.31/0.47              ( ( A1
% 0.31/0.47                = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 0.31/0.47              & ( A22
% 0.31/0.47                = ( cons_P465369265_state @ Y4 @ Ys3 ) )
% 0.31/0.47              & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y4 ) @ R )
% 0.31/0.47              & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.simps
% 0.31/0.47  thf(fact_228_listrel_Osimps,axiom,
% 0.31/0.47      ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.31/0.47        ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47        = ( ( ( A1 = nil_list_com )
% 0.31/0.47            & ( A22 = nil_state ) )
% 0.31/0.47          | ? [X4: list_com,Y4: state,Xs3: list_list_com,Ys3: list_state] :
% 0.31/0.47              ( ( A1
% 0.31/0.47                = ( cons_list_com @ X4 @ Xs3 ) )
% 0.31/0.47              & ( A22
% 0.31/0.47                = ( cons_state @ Y4 @ Ys3 ) )
% 0.31/0.47              & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y4 ) @ R )
% 0.31/0.47              & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.simps
% 0.31/0.47  thf(fact_229_listrel_Osimps,axiom,
% 0.31/0.47      ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47        = ( ( ( A1 = nil_Pr1347322605_state )
% 0.31/0.47            & ( A22 = nil_Pr1347322605_state ) )
% 0.31/0.47          | ? [X4: produc410756839_state,Y4: produc410756839_state,Xs3: list_P890094829_state,Ys3: list_P890094829_state] :
% 0.31/0.47              ( ( A1
% 0.31/0.47                = ( cons_P438230685_state @ X4 @ Xs3 ) )
% 0.31/0.47              & ( A22
% 0.31/0.47                = ( cons_P438230685_state @ Y4 @ Ys3 ) )
% 0.31/0.47              & ( member512523024_state @ ( produc2065881943_state @ X4 @ Y4 ) @ R )
% 0.31/0.47              & ( member423306384_state @ ( produc1354769367_state @ Xs3 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel.simps
% 0.31/0.47  thf(fact_230_bind__simps_I2_J,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com,F2: com > list_com] :
% 0.31/0.47        ( ( bind_com_com @ ( cons_com @ X @ Xs2 ) @ F2 )
% 0.31/0.47        = ( append_com @ ( F2 @ X ) @ ( bind_com_com @ Xs2 @ F2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % bind_simps(2)
% 0.31/0.47  thf(fact_231_snoc__listrel1__snoc__iff,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com,Ys2: list_com,Y: com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 0.31/0.47        = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.31/0.47            & ( X = Y ) )
% 0.31/0.47          | ( ( Xs2 = Ys2 )
% 0.31/0.47            & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % snoc_listrel1_snoc_iff
% 0.31/0.47  thf(fact_232_snoc__listrel1__snoc__iff,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,X: produc2041926651_state,Ys2: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys2 @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47        = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47            & ( X = Y ) )
% 0.31/0.47          | ( ( Xs2 = Ys2 )
% 0.31/0.47            & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % snoc_listrel1_snoc_iff
% 0.31/0.47  thf(fact_233_snoc__listrel1__snoc__iff,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,X: produc410756839_state,Ys2: list_P890094829_state,Y: produc410756839_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ ( cons_P438230685_state @ X @ nil_Pr1347322605_state ) ) @ ( append221843330_state @ Ys2 @ ( cons_P438230685_state @ Y @ nil_Pr1347322605_state ) ) ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47        = ( ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47            & ( X = Y ) )
% 0.31/0.47          | ( ( Xs2 = Ys2 )
% 0.31/0.47            & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % snoc_listrel1_snoc_iff
% 0.31/0.47  thf(fact_234_maps__simps_I1_J,axiom,
% 0.31/0.47      ! [F2: com > list_com,X: com,Xs2: list_com] :
% 0.31/0.47        ( ( maps_com_com @ F2 @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47        = ( append_com @ ( F2 @ X ) @ ( maps_com_com @ F2 @ Xs2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % maps_simps(1)
% 0.31/0.47  thf(fact_235_concat__eq__append__conv,axiom,
% 0.31/0.47      ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( ( concat_com @ Xss2 )
% 0.31/0.47          = ( append_com @ Ys2 @ Zs2 ) )
% 0.31/0.47        = ( ( ( Xss2 = nil_list_com )
% 0.31/0.47           => ( ( Ys2 = nil_com )
% 0.31/0.47              & ( Zs2 = nil_com ) ) )
% 0.31/0.47          & ( ( Xss2 != nil_list_com )
% 0.31/0.47           => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 0.31/0.47                ( ( Xss2
% 0.31/0.47                  = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.31/0.47                & ( Ys2
% 0.31/0.47                  = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 0.31/0.47                & ( Zs2
% 0.31/0.47                  = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % concat_eq_append_conv
% 0.31/0.47  thf(fact_236_bind__simps_I1_J,axiom,
% 0.31/0.47      ! [F2: com > list_com] :
% 0.31/0.47        ( ( bind_com_com @ nil_com @ F2 )
% 0.31/0.47        = nil_com ) ).
% 0.31/0.47  
% 0.31/0.47  % bind_simps(1)
% 0.31/0.47  thf(fact_237_concat__append,axiom,
% 0.31/0.47      ! [Xs2: list_list_com,Ys2: list_list_com] :
% 0.31/0.47        ( ( concat_com @ ( append_list_com @ Xs2 @ Ys2 ) )
% 0.31/0.47        = ( append_com @ ( concat_com @ Xs2 ) @ ( concat_com @ Ys2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % concat_append
% 0.31/0.47  thf(fact_238_Cons__listrel1__Cons,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 0.31/0.47        = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/0.47            & ( Xs2 = Ys2 ) )
% 0.31/0.47          | ( ( X = Y )
% 0.31/0.47            & ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1_Cons
% 0.31/0.47  thf(fact_239_Cons__listrel1__Cons,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47        = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/0.47            & ( Xs2 = Ys2 ) )
% 0.31/0.47          | ( ( X = Y )
% 0.31/0.47            & ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1_Cons
% 0.31/0.47  thf(fact_240_Cons__listrel1__Cons,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47        = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.31/0.47            & ( Xs2 = Ys2 ) )
% 0.31/0.47          | ( ( X = Y )
% 0.31/0.47            & ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1_Cons
% 0.31/0.47  thf(fact_241_listrel1I2,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ X @ Ys2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I2
% 0.31/0.47  thf(fact_242_rtrancl__listrel1__ConsI1,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ X @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_listrel1_ConsI1
% 0.31/0.47  thf(fact_243_not__Nil__listrel1,axiom,
% 0.31/0.47      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs2 ) @ ( listrel1_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % not_Nil_listrel1
% 0.31/0.47  thf(fact_244_not__listrel1__Nil,axiom,
% 0.31/0.47      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % not_listrel1_Nil
% 0.31/0.47  thf(fact_245_append__listrel1I,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Us: list_com,Vs: list_com] :
% 0.31/0.47        ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.31/0.47            & ( Us = Vs ) )
% 0.31/0.47          | ( ( Xs2 = Ys2 )
% 0.31/0.47            & ( member32358020st_com @ ( produc1307105171st_com @ Us @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Us ) @ ( append_com @ Ys2 @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_listrel1I
% 0.31/0.47  thf(fact_246_concat_Osimps_I1_J,axiom,
% 0.31/0.47      ( ( concat_com @ nil_list_com )
% 0.31/0.47      = nil_com ) ).
% 0.31/0.47  
% 0.31/0.47  % concat.simps(1)
% 0.31/0.47  thf(fact_247_concat_Osimps_I2_J,axiom,
% 0.31/0.47      ! [X: list_com,Xs2: list_list_com] :
% 0.31/0.47        ( ( concat_com @ ( cons_list_com @ X @ Xs2 ) )
% 0.31/0.47        = ( append_com @ X @ ( concat_com @ Xs2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % concat.simps(2)
% 0.31/0.47  thf(fact_248_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.31/0.47      ! [R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 0.31/0.47        = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_rtrancl_eq_rtrancl_listrel1
% 0.31/0.47  thf(fact_249_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.31/0.47      ! [R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( listre1244407729_state @ ( transi463013610_state @ R ) )
% 0.31/0.47        = ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_rtrancl_eq_rtrancl_listrel1
% 0.31/0.47  thf(fact_250_maps__simps_I2_J,axiom,
% 0.31/0.47      ! [F2: com > list_com] :
% 0.31/0.47        ( ( maps_com_com @ F2 @ nil_com )
% 0.31/0.47        = nil_com ) ).
% 0.31/0.47  
% 0.31/0.47  % maps_simps(2)
% 0.31/0.47  thf(fact_251_Cons__listrel1E2,axiom,
% 0.31/0.47      ! [Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 0.31/0.47       => ( ! [X3: com] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_com @ X3 @ Ys2 ) )
% 0.31/0.47             => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 0.31/0.47         => ~ ! [Zs: list_com] :
% 0.31/0.47                ( ( Xs2
% 0.31/0.47                  = ( cons_com @ Y @ Zs ) )
% 0.31/0.47               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1E2
% 0.31/0.47  thf(fact_252_Cons__listrel1E2,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47       => ( ! [X3: produc2041926651_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_P465369265_state @ X3 @ Ys2 ) )
% 0.31/0.47             => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 0.31/0.47         => ~ ! [Zs: list_P1040014977_state] :
% 0.31/0.47                ( ( Xs2
% 0.31/0.47                  = ( cons_P465369265_state @ Y @ Zs ) )
% 0.31/0.47               => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1E2
% 0.31/0.47  thf(fact_253_Cons__listrel1E2,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47       => ( ! [X3: produc410756839_state] :
% 0.31/0.47              ( ( Xs2
% 0.31/0.47                = ( cons_P438230685_state @ X3 @ Ys2 ) )
% 0.31/0.47             => ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R ) )
% 0.31/0.47         => ~ ! [Zs: list_P890094829_state] :
% 0.31/0.47                ( ( Xs2
% 0.31/0.47                  = ( cons_P438230685_state @ Y @ Zs ) )
% 0.31/0.47               => ~ ( member423306384_state @ ( produc1354769367_state @ Zs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1E2
% 0.31/0.47  thf(fact_254_Cons__listrel1E1,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.31/0.47       => ( ! [Y3: com] :
% 0.31/0.47              ( ( Ys2
% 0.31/0.47                = ( cons_com @ Y3 @ Xs2 ) )
% 0.31/0.47             => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y3 ) @ R ) )
% 0.31/0.47         => ~ ! [Zs: list_com] :
% 0.31/0.47                ( ( Ys2
% 0.31/0.47                  = ( cons_com @ X @ Zs ) )
% 0.31/0.47               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Zs ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1E1
% 0.31/0.47  thf(fact_255_Cons__listrel1E1,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47       => ( ! [Y3: produc2041926651_state] :
% 0.31/0.47              ( ( Ys2
% 0.31/0.47                = ( cons_P465369265_state @ Y3 @ Xs2 ) )
% 0.31/0.47             => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R ) )
% 0.31/0.47         => ~ ! [Zs: list_P1040014977_state] :
% 0.31/0.47                ( ( Ys2
% 0.31/0.47                  = ( cons_P465369265_state @ X @ Zs ) )
% 0.31/0.47               => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Zs ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1E1
% 0.31/0.47  thf(fact_256_Cons__listrel1E1,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47       => ( ! [Y3: produc410756839_state] :
% 0.31/0.47              ( ( Ys2
% 0.31/0.47                = ( cons_P438230685_state @ Y3 @ Xs2 ) )
% 0.31/0.47             => ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y3 ) @ R ) )
% 0.31/0.47         => ~ ! [Zs: list_P890094829_state] :
% 0.31/0.47                ( ( Ys2
% 0.31/0.47                  = ( cons_P438230685_state @ X @ Zs ) )
% 0.31/0.47               => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Zs ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_listrel1E1
% 0.31/0.47  thf(fact_257_listrel1I1,axiom,
% 0.31/0.47      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com] :
% 0.31/0.47        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Xs2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I1
% 0.31/0.47  thf(fact_258_listrel1I1,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/0.47       => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Xs2 ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I1
% 0.31/0.47  thf(fact_259_listrel1I1,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.31/0.47       => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Xs2 ) ) @ ( listre1725776070_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I1
% 0.31/0.47  thf(fact_260_listrel__reflcl__if__listrel1,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47       => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_reflcl_if_listrel1
% 0.31/0.47  thf(fact_261_listrel__reflcl__if__listrel1,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47       => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_reflcl_if_listrel1
% 0.31/0.47  thf(fact_262_concat__eq__appendD,axiom,
% 0.31/0.47      ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( ( concat_com @ Xss2 )
% 0.31/0.47          = ( append_com @ Ys2 @ Zs2 ) )
% 0.31/0.47       => ( ( Xss2 != nil_list_com )
% 0.31/0.47         => ? [Xss12: list_list_com,Xs: list_com,Xs5: list_com,Xss23: list_list_com] :
% 0.31/0.47              ( ( Xss2
% 0.31/0.47                = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs @ Xs5 ) @ Xss23 ) ) )
% 0.31/0.47              & ( Ys2
% 0.31/0.47                = ( append_com @ ( concat_com @ Xss12 ) @ Xs ) )
% 0.31/0.47              & ( Zs2
% 0.31/0.47                = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % concat_eq_appendD
% 0.31/0.47  thf(fact_263_listrel1I,axiom,
% 0.31/0.47      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Us: list_com,Vs: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/0.47       => ( ( Xs2
% 0.31/0.47            = ( append_com @ Us @ ( cons_com @ X @ Vs ) ) )
% 0.31/0.47         => ( ( Ys2
% 0.31/0.47              = ( append_com @ Us @ ( cons_com @ Y @ Vs ) ) )
% 0.31/0.47           => ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I
% 0.31/0.47  thf(fact_264_listrel1I,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Us: list_P1040014977_state,Vs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/0.47       => ( ( Xs2
% 0.31/0.47            = ( append982487830_state @ Us @ ( cons_P465369265_state @ X @ Vs ) ) )
% 0.31/0.47         => ( ( Ys2
% 0.31/0.47              = ( append982487830_state @ Us @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 0.31/0.47           => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I
% 0.31/0.47  thf(fact_265_listrel1I,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Us: list_P890094829_state,Vs: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.31/0.47       => ( ( Xs2
% 0.31/0.47            = ( append221843330_state @ Us @ ( cons_P438230685_state @ X @ Vs ) ) )
% 0.31/0.47         => ( ( Ys2
% 0.31/0.47              = ( append221843330_state @ Us @ ( cons_P438230685_state @ Y @ Vs ) ) )
% 0.31/0.47           => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1I
% 0.31/0.47  thf(fact_266_listrel1E,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.31/0.47       => ~ ! [X3: com,Y3: com] :
% 0.31/0.47              ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.31/0.47             => ! [Us3: list_com,Vs2: list_com] :
% 0.31/0.47                  ( ( Xs2
% 0.31/0.47                    = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 0.31/0.47                 => ( Ys2
% 0.31/0.47                   != ( append_com @ Us3 @ ( cons_com @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1E
% 0.31/0.47  thf(fact_267_listrel1E,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47       => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.31/0.47              ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.31/0.47             => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 0.31/0.47                  ( ( Xs2
% 0.31/0.47                    = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 0.31/0.47                 => ( Ys2
% 0.31/0.47                   != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1E
% 0.31/0.47  thf(fact_268_listrel1E,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47       => ~ ! [X3: produc410756839_state,Y3: produc410756839_state] :
% 0.31/0.47              ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 0.31/0.47             => ! [Us3: list_P890094829_state,Vs2: list_P890094829_state] :
% 0.31/0.47                  ( ( Xs2
% 0.31/0.47                    = ( append221843330_state @ Us3 @ ( cons_P438230685_state @ X3 @ Vs2 ) ) )
% 0.31/0.47                 => ( Ys2
% 0.31/0.47                   != ( append221843330_state @ Us3 @ ( cons_P438230685_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1E
% 0.31/0.47  thf(fact_269_rtrancl__listrel1__ConsI2,axiom,
% 0.31/0.47      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 0.31/0.47       => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.31/0.47         => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_listrel1_ConsI2
% 0.31/0.47  thf(fact_270_rtrancl__listrel1__ConsI2,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.31/0.47       => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 0.31/0.47         => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_listrel1_ConsI2
% 0.31/0.47  thf(fact_271_rtrancl__listrel1__ConsI2,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.31/0.47       => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) )
% 0.31/0.47         => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rtrancl_listrel1_ConsI2
% 0.31/0.47  thf(fact_272_lexord__append__left__rightI,axiom,
% 0.31/0.47      ! [A2: com,B2: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 0.31/0.47        ( ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ B2 ) @ R )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A2 @ X ) ) @ ( append_com @ U @ ( cons_com @ B2 @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_left_rightI
% 0.31/0.47  thf(fact_273_lexord__append__left__rightI,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.31/0.47       => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A2 @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B2 @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_left_rightI
% 0.31/0.47  thf(fact_274_lexord__append__left__rightI,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,U: list_P890094829_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.31/0.47       => ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ U @ ( cons_P438230685_state @ A2 @ X ) ) @ ( append221843330_state @ U @ ( cons_P438230685_state @ B2 @ Y ) ) ) @ ( lexord1893203674_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_left_rightI
% 0.31/0.47  thf(fact_275_rotate1_Osimps_I2_J,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com] :
% 0.31/0.47        ( ( rotate1_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47        = ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rotate1.simps(2)
% 0.31/0.47  thf(fact_276_butlast__snoc,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com] :
% 0.31/0.47        ( ( butlast_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) )
% 0.31/0.47        = Xs2 ) ).
% 0.31/0.47  
% 0.31/0.47  % butlast_snoc
% 0.31/0.47  thf(fact_277_rotate1__is__Nil__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com] :
% 0.31/0.47        ( ( ( rotate1_com @ Xs2 )
% 0.31/0.47          = nil_com )
% 0.31/0.47        = ( Xs2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % rotate1_is_Nil_conv
% 0.31/0.47  thf(fact_278_lexord__cons__cons,axiom,
% 0.31/0.47      ! [A2: com,X: list_com,B2: com,Y: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A2 @ X ) @ ( cons_com @ B2 @ Y ) ) @ ( lexord_com @ R ) )
% 0.31/0.47        = ( ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ B2 ) @ R )
% 0.31/0.47          | ( ( A2 = B2 )
% 0.31/0.47            & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_cons_cons
% 0.31/0.47  thf(fact_279_lexord__cons__cons,axiom,
% 0.31/0.47      ! [A2: produc2041926651_state,X: list_P1040014977_state,B2: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A2 @ X ) @ ( cons_P465369265_state @ B2 @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 0.31/0.47        = ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.31/0.47          | ( ( A2 = B2 )
% 0.31/0.47            & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_cons_cons
% 0.31/0.47  thf(fact_280_lexord__cons__cons,axiom,
% 0.31/0.47      ! [A2: produc410756839_state,X: list_P890094829_state,B2: produc410756839_state,Y: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ A2 @ X ) @ ( cons_P438230685_state @ B2 @ Y ) ) @ ( lexord1893203674_state @ R ) )
% 0.31/0.47        = ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.31/0.47          | ( ( A2 = B2 )
% 0.31/0.47            & ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_cons_cons
% 0.31/0.47  thf(fact_281_lexord__Nil__left,axiom,
% 0.31/0.47      ! [Y: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 0.31/0.47        = ( ? [A5: com,X4: list_com] :
% 0.31/0.47              ( Y
% 0.31/0.47              = ( cons_com @ A5 @ X4 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_Nil_left
% 0.31/0.47  thf(fact_282_butlast_Osimps_I1_J,axiom,
% 0.31/0.47      ( ( butlast_com @ nil_com )
% 0.31/0.47      = nil_com ) ).
% 0.31/0.47  
% 0.31/0.47  % butlast.simps(1)
% 0.31/0.47  thf(fact_283_rotate1_Osimps_I1_J,axiom,
% 0.31/0.47      ( ( rotate1_com @ nil_com )
% 0.31/0.47      = nil_com ) ).
% 0.31/0.47  
% 0.31/0.47  % rotate1.simps(1)
% 0.31/0.47  thf(fact_284_lexord__linear,axiom,
% 0.31/0.47      ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.31/0.47        ( ! [A: produc2041926651_state,B: produc2041926651_state] :
% 0.31/0.47            ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.31/0.47            | ( A = B )
% 0.31/0.47            | ( member1069318160_state @ ( produc1909270103_state @ B @ A ) @ R ) )
% 0.31/0.47       => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 0.31/0.47          | ( X = Y )
% 0.31/0.47          | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_linear
% 0.31/0.47  thf(fact_285_lexord__linear,axiom,
% 0.31/0.47      ! [R: set_Pr2096893127_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 0.31/0.47        ( ! [A: produc410756839_state,B: produc410756839_state] :
% 0.31/0.47            ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.31/0.47            | ( A = B )
% 0.31/0.47            | ( member512523024_state @ ( produc2065881943_state @ B @ A ) @ R ) )
% 0.31/0.47       => ( ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) )
% 0.31/0.47          | ( X = Y )
% 0.31/0.47          | ( member423306384_state @ ( produc1354769367_state @ Y @ X ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_linear
% 0.31/0.47  thf(fact_286_lexord__irreflexive,axiom,
% 0.31/0.47      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 0.31/0.47        ( ! [X3: produc2041926651_state] :
% 0.31/0.47            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_irreflexive
% 0.31/0.47  thf(fact_287_lexord__irreflexive,axiom,
% 0.31/0.47      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 0.31/0.47        ( ! [X3: produc410756839_state] :
% 0.31/0.47            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( lexord1893203674_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_irreflexive
% 0.31/0.47  thf(fact_288_butlast_Osimps_I2_J,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com] :
% 0.31/0.47        ( ( ( Xs2 = nil_com )
% 0.31/0.47         => ( ( butlast_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47            = nil_com ) )
% 0.31/0.47        & ( ( Xs2 != nil_com )
% 0.31/0.47         => ( ( butlast_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47            = ( cons_com @ X @ ( butlast_com @ Xs2 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % butlast.simps(2)
% 0.31/0.47  thf(fact_289_lexord__Nil__right,axiom,
% 0.31/0.47      ! [X: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_Nil_right
% 0.31/0.47  thf(fact_290_butlast__append,axiom,
% 0.31/0.47      ! [Ys2: list_com,Xs2: list_com] :
% 0.31/0.47        ( ( ( Ys2 = nil_com )
% 0.31/0.47         => ( ( butlast_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47            = ( butlast_com @ Xs2 ) ) )
% 0.31/0.47        & ( ( Ys2 != nil_com )
% 0.31/0.47         => ( ( butlast_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47            = ( append_com @ Xs2 @ ( butlast_com @ Ys2 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % butlast_append
% 0.31/0.47  thf(fact_291_lexord__append__leftI,axiom,
% 0.31/0.47      ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_leftI
% 0.31/0.47  thf(fact_292_lexord__append__leftD,axiom,
% 0.31/0.47      ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 0.31/0.47       => ( ! [A: com] :
% 0.31/0.47              ~ ( member1333916004om_com @ ( product_Pair_com_com @ A @ A ) @ R )
% 0.31/0.47         => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_leftD
% 0.31/0.47  thf(fact_293_lexord__append__leftD,axiom,
% 0.31/0.47      ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 0.31/0.47       => ( ! [A: produc2041926651_state] :
% 0.31/0.47              ~ ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ R )
% 0.31/0.47         => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_leftD
% 0.31/0.47  thf(fact_294_lexord__append__leftD,axiom,
% 0.31/0.47      ! [X: list_P890094829_state,U: list_P890094829_state,V: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ X @ U ) @ ( append221843330_state @ X @ V ) ) @ ( lexord1893203674_state @ R ) )
% 0.31/0.47       => ( ! [A: produc410756839_state] :
% 0.31/0.47              ~ ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ R )
% 0.31/0.47         => ( member423306384_state @ ( produc1354769367_state @ U @ V ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_leftD
% 0.31/0.47  thf(fact_295_lexord__append__rightI,axiom,
% 0.31/0.47      ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ? [B5: com,Z3: list_com] :
% 0.31/0.47            ( Y
% 0.31/0.47            = ( cons_com @ B5 @ Z3 ) )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_append_rightI
% 0.31/0.47  thf(fact_296_lexord__same__pref__if__irrefl,axiom,
% 0.31/0.47      ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ( irrefl_com @ R )
% 0.31/0.47       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lexord_com @ R ) )
% 0.31/0.47          = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lexord_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_same_pref_if_irrefl
% 0.31/0.47  thf(fact_297_append__butlast__last__id,axiom,
% 0.31/0.47      ! [Xs2: list_com] :
% 0.31/0.47        ( ( Xs2 != nil_com )
% 0.31/0.47       => ( ( append_com @ ( butlast_com @ Xs2 ) @ ( cons_com @ ( last_com @ Xs2 ) @ nil_com ) )
% 0.31/0.47          = Xs2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_butlast_last_id
% 0.31/0.47  thf(fact_298_snoc__eq__iff__butlast,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com,Ys2: list_com] :
% 0.31/0.47        ( ( ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) )
% 0.31/0.47          = Ys2 )
% 0.31/0.47        = ( ( Ys2 != nil_com )
% 0.31/0.47          & ( ( butlast_com @ Ys2 )
% 0.31/0.47            = Xs2 )
% 0.31/0.47          & ( ( last_com @ Ys2 )
% 0.31/0.47            = X ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % snoc_eq_iff_butlast
% 0.31/0.47  thf(fact_299_last__appendR,axiom,
% 0.31/0.47      ! [Ys2: list_com,Xs2: list_com] :
% 0.31/0.47        ( ( Ys2 != nil_com )
% 0.31/0.47       => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47          = ( last_com @ Ys2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % last_appendR
% 0.31/0.47  thf(fact_300_last__appendL,axiom,
% 0.31/0.47      ! [Ys2: list_com,Xs2: list_com] :
% 0.31/0.47        ( ( Ys2 = nil_com )
% 0.31/0.47       => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47          = ( last_com @ Xs2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % last_appendL
% 0.31/0.47  thf(fact_301_last__snoc,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com] :
% 0.31/0.47        ( ( last_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) )
% 0.31/0.47        = X ) ).
% 0.31/0.47  
% 0.31/0.47  % last_snoc
% 0.31/0.47  thf(fact_302_last__ConsR,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com] :
% 0.31/0.47        ( ( Xs2 != nil_com )
% 0.31/0.47       => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47          = ( last_com @ Xs2 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % last_ConsR
% 0.31/0.47  thf(fact_303_last__ConsL,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com] :
% 0.31/0.47        ( ( Xs2 = nil_com )
% 0.31/0.47       => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47          = X ) ) ).
% 0.31/0.47  
% 0.31/0.47  % last_ConsL
% 0.31/0.47  thf(fact_304_last_Osimps,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com] :
% 0.31/0.47        ( ( ( Xs2 = nil_com )
% 0.31/0.47         => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47            = X ) )
% 0.31/0.47        & ( ( Xs2 != nil_com )
% 0.31/0.47         => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.31/0.47            = ( last_com @ Xs2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % last.simps
% 0.31/0.47  thf(fact_305_longest__common__suffix,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47      ? [Ss: list_com,Xs5: list_com,Ys5: list_com] :
% 0.31/0.47        ( ( Xs2
% 0.31/0.47          = ( append_com @ Xs5 @ Ss ) )
% 0.31/0.47        & ( Ys2
% 0.31/0.47          = ( append_com @ Ys5 @ Ss ) )
% 0.31/0.47        & ( ( Xs5 = nil_com )
% 0.31/0.47          | ( Ys5 = nil_com )
% 0.31/0.47          | ( ( last_com @ Xs5 )
% 0.31/0.47           != ( last_com @ Ys5 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % longest_common_suffix
% 0.31/0.47  thf(fact_306_last__append,axiom,
% 0.31/0.47      ! [Ys2: list_com,Xs2: list_com] :
% 0.31/0.47        ( ( ( Ys2 = nil_com )
% 0.31/0.47         => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47            = ( last_com @ Xs2 ) ) )
% 0.31/0.47        & ( ( Ys2 != nil_com )
% 0.31/0.47         => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.31/0.47            = ( last_com @ Ys2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % last_append
% 0.31/0.47  thf(fact_307_irreflI,axiom,
% 0.31/0.47      ! [R2: set_Pr1165141447_state] :
% 0.31/0.47        ( ! [A: produc2041926651_state] :
% 0.31/0.47            ~ ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ R2 )
% 0.31/0.47       => ( irrefl654089520_state @ R2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % irreflI
% 0.31/0.47  thf(fact_308_irreflI,axiom,
% 0.31/0.47      ! [R2: set_Pr2096893127_state] :
% 0.31/0.47        ( ! [A: produc410756839_state] :
% 0.31/0.47            ~ ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ R2 )
% 0.31/0.47       => ( irrefl1358048924_state @ R2 ) ) ).
% 0.31/0.47  
% 0.31/0.47  % irreflI
% 0.31/0.47  thf(fact_309_irrefl__def,axiom,
% 0.31/0.47      ( irrefl654089520_state
% 0.31/0.47      = ( ^ [R3: set_Pr1165141447_state] :
% 0.31/0.47          ! [A5: produc2041926651_state] :
% 0.31/0.47            ~ ( member1069318160_state @ ( produc1909270103_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % irrefl_def
% 0.31/0.47  thf(fact_310_irrefl__def,axiom,
% 0.31/0.47      ( irrefl1358048924_state
% 0.31/0.47      = ( ^ [R3: set_Pr2096893127_state] :
% 0.31/0.47          ! [A5: produc410756839_state] :
% 0.31/0.47            ~ ( member512523024_state @ ( produc2065881943_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % irrefl_def
% 0.31/0.47  thf(fact_311_lenlex__append2,axiom,
% 0.31/0.47      ! [R2: set_Pr1822651163om_com,Us: list_com,Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( irrefl_com @ R2 )
% 0.31/0.47       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us @ Xs2 ) @ ( append_com @ Us @ Ys2 ) ) @ ( lenlex_com @ R2 ) )
% 0.31/0.47          = ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lenlex_append2
% 0.31/0.47  thf(fact_312_Nil__lenlex__iff1,axiom,
% 0.31/0.47      ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ns ) @ ( lenlex_com @ R ) )
% 0.31/0.47        = ( Ns != nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Nil_lenlex_iff1
% 0.31/0.47  thf(fact_313_Nil__notin__lex,axiom,
% 0.31/0.47      ! [Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ys2 ) @ ( lex_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Nil_notin_lex
% 0.31/0.47  thf(fact_314_Nil2__notin__lex,axiom,
% 0.31/0.47      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( lex_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Nil2_notin_lex
% 0.31/0.47  thf(fact_315_lex__append__leftI,axiom,
% 0.31/0.47      ! [Ys2: list_com,Zs2: list_com,R: set_Pr1822651163om_com,Xs2: list_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) )
% 0.31/0.47       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_leftI
% 0.31/0.47  thf(fact_316_lenlex__irreflexive,axiom,
% 0.31/0.47      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 0.31/0.47        ( ! [X3: produc2041926651_state] :
% 0.31/0.47            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( lenlex295247238_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lenlex_irreflexive
% 0.31/0.47  thf(fact_317_lenlex__irreflexive,axiom,
% 0.31/0.47      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 0.31/0.47        ( ! [X3: produc410756839_state] :
% 0.31/0.47            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( lenlex1401983474_state @ R ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lenlex_irreflexive
% 0.31/0.47  thf(fact_318_Nil__lenlex__iff2,axiom,
% 0.31/0.47      ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ~ ( member32358020st_com @ ( produc1307105171st_com @ Ns @ nil_com ) @ ( lenlex_com @ R ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Nil_lenlex_iff2
% 0.31/0.47  thf(fact_319_lex__append__leftD,axiom,
% 0.31/0.47      ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ! [X3: com] :
% 0.31/0.47            ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.31/0.47       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) )
% 0.31/0.47         => ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_leftD
% 0.31/0.47  thf(fact_320_lex__append__leftD,axiom,
% 0.31/0.47      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,Zs2: list_P1040014977_state] :
% 0.31/0.47        ( ! [X3: produc2041926651_state] :
% 0.31/0.47            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ Ys2 ) @ ( append982487830_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/0.47         => ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_leftD
% 0.31/0.47  thf(fact_321_lex__append__leftD,axiom,
% 0.31/0.47      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,Zs2: list_P890094829_state] :
% 0.31/0.47        ( ! [X3: produc410756839_state] :
% 0.31/0.47            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ Ys2 ) @ ( append221843330_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 0.31/0.47         => ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_leftD
% 0.31/0.47  thf(fact_322_lex__append__left__iff,axiom,
% 0.31/0.47      ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.31/0.47        ( ! [X3: com] :
% 0.31/0.47            ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.31/0.47       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) )
% 0.31/0.47          = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_left_iff
% 0.31/0.47  thf(fact_323_lex__append__left__iff,axiom,
% 0.31/0.47      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,Zs2: list_P1040014977_state] :
% 0.31/0.47        ( ! [X3: produc2041926651_state] :
% 0.31/0.47            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ Ys2 ) @ ( append982487830_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/0.47          = ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_left_iff
% 0.31/0.47  thf(fact_324_lex__append__left__iff,axiom,
% 0.31/0.47      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,Zs2: list_P890094829_state] :
% 0.31/0.47        ( ! [X3: produc410756839_state] :
% 0.31/0.47            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.31/0.47       => ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ Ys2 ) @ ( append221843330_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 0.31/0.47          = ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_left_iff
% 0.31/0.47  thf(fact_325_Cons__in__lex,axiom,
% 0.31/0.47      ! [X: com,Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( lex_com @ R ) )
% 0.31/0.47        = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.31/0.47            & ( ( size_size_list_com @ Xs2 )
% 0.31/0.47              = ( size_size_list_com @ Ys2 ) ) )
% 0.31/0.47          | ( ( X = Y )
% 0.31/0.47            & ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lex_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_in_lex
% 0.31/0.47  thf(fact_326_Cons__in__lex,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/0.47        = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.31/0.47            & ( ( size_s213202669_state @ Xs2 )
% 0.31/0.47              = ( size_s213202669_state @ Ys2 ) ) )
% 0.31/0.47          | ( ( X = Y )
% 0.31/0.47            & ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_in_lex
% 0.31/0.47  thf(fact_327_Cons__in__lex,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 0.31/0.47        = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.31/0.47            & ( ( size_s837829465_state @ Xs2 )
% 0.31/0.47              = ( size_s837829465_state @ Ys2 ) ) )
% 0.31/0.47          | ( ( X = Y )
% 0.31/0.47            & ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_in_lex
% 0.31/0.47  thf(fact_328_append__eq__append__conv,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,Us: list_com,Vs: list_com] :
% 0.31/0.47        ( ( ( ( size_size_list_com @ Xs2 )
% 0.31/0.47            = ( size_size_list_com @ Ys2 ) )
% 0.31/0.47          | ( ( size_size_list_com @ Us )
% 0.31/0.47            = ( size_size_list_com @ Vs ) ) )
% 0.31/0.47       => ( ( ( append_com @ Xs2 @ Us )
% 0.31/0.47            = ( append_com @ Ys2 @ Vs ) )
% 0.31/0.47          = ( ( Xs2 = Ys2 )
% 0.31/0.47            & ( Us = Vs ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % append_eq_append_conv
% 0.31/0.47  thf(fact_329_list__induct3,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com,P: list_com > list_com > list_com > $o] :
% 0.31/0.47        ( ( ( size_size_list_com @ Xs2 )
% 0.31/0.47          = ( size_size_list_com @ Ys2 ) )
% 0.31/0.47       => ( ( ( size_size_list_com @ Ys2 )
% 0.31/0.47            = ( size_size_list_com @ Zs2 ) )
% 0.31/0.47         => ( ( P @ nil_com @ nil_com @ nil_com )
% 0.31/0.47           => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com,Z: com,Zs: list_com] :
% 0.31/0.47                  ( ( ( size_size_list_com @ Xs )
% 0.31/0.47                    = ( size_size_list_com @ Ys ) )
% 0.31/0.47                 => ( ( ( size_size_list_com @ Ys )
% 0.31/0.47                      = ( size_size_list_com @ Zs ) )
% 0.31/0.47                   => ( ( P @ Xs @ Ys @ Zs )
% 0.31/0.47                     => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) @ ( cons_com @ Z @ Zs ) ) ) ) )
% 0.31/0.47             => ( P @ Xs2 @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list_induct3
% 0.31/0.47  thf(fact_330_list__induct2,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,P: list_com > list_com > $o] :
% 0.31/0.47        ( ( ( size_size_list_com @ Xs2 )
% 0.31/0.47          = ( size_size_list_com @ Ys2 ) )
% 0.31/0.47       => ( ( P @ nil_com @ nil_com )
% 0.31/0.47         => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.31/0.47                ( ( ( size_size_list_com @ Xs )
% 0.31/0.47                  = ( size_size_list_com @ Ys ) )
% 0.31/0.47               => ( ( P @ Xs @ Ys )
% 0.31/0.47                 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) )
% 0.31/0.47           => ( P @ Xs2 @ Ys2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list_induct2
% 0.31/0.47  thf(fact_331_same__length__different,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( Xs2 != Ys2 )
% 0.31/0.47       => ( ( ( size_size_list_com @ Xs2 )
% 0.31/0.47            = ( size_size_list_com @ Ys2 ) )
% 0.31/0.47         => ? [Pre: list_com,X3: com,Xs5: list_com,Y3: com,Ys5: list_com] :
% 0.31/0.47              ( ( X3 != Y3 )
% 0.31/0.47              & ( Xs2
% 0.31/0.47                = ( append_com @ Pre @ ( append_com @ ( cons_com @ X3 @ nil_com ) @ Xs5 ) ) )
% 0.31/0.47              & ( Ys2
% 0.31/0.47                = ( append_com @ Pre @ ( append_com @ ( cons_com @ Y3 @ nil_com ) @ Ys5 ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % same_length_different
% 0.31/0.47  thf(fact_332_lexord__sufE,axiom,
% 0.31/0.47      ! [Xs2: list_com,Zs2: list_com,Ys2: list_com,Qs: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Zs2 ) @ ( append_com @ Ys2 @ Qs ) ) @ ( lexord_com @ R ) )
% 0.31/0.47       => ( ( Xs2 != Ys2 )
% 0.31/0.47         => ( ( ( size_size_list_com @ Xs2 )
% 0.31/0.47              = ( size_size_list_com @ Ys2 ) )
% 0.31/0.47           => ( ( ( size_size_list_com @ Zs2 )
% 0.31/0.47                = ( size_size_list_com @ Qs ) )
% 0.31/0.47             => ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lexord_com @ R ) ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lexord_sufE
% 0.31/0.47  thf(fact_333_lex__append__rightI,axiom,
% 0.31/0.47      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Vs: list_com,Us: list_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lex_com @ R ) )
% 0.31/0.47       => ( ( ( size_size_list_com @ Vs )
% 0.31/0.47            = ( size_size_list_com @ Us ) )
% 0.31/0.47         => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Us ) @ ( append_com @ Ys2 @ Vs ) ) @ ( lex_com @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_append_rightI
% 0.31/0.47  thf(fact_334_lenlex__append1,axiom,
% 0.31/0.47      ! [Us: list_com,Xs2: list_com,R2: set_Pr1822651163om_com,Vs: list_com,Ys2: list_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ Us @ Xs2 ) @ ( lenlex_com @ R2 ) )
% 0.31/0.47       => ( ( ( size_size_list_com @ Vs )
% 0.31/0.47            = ( size_size_list_com @ Ys2 ) )
% 0.31/0.47         => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us @ Vs ) @ ( append_com @ Xs2 @ Ys2 ) ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lenlex_append1
% 0.31/0.47  thf(fact_335_Cons__lenlex__iff,axiom,
% 0.31/0.47      ! [M: com,Ms: list_com,N: com,Ns: list_com,R: set_Pr1822651163om_com] :
% 0.31/0.47        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ M @ Ms ) @ ( cons_com @ N @ Ns ) ) @ ( lenlex_com @ R ) )
% 0.31/0.47        = ( ( ord_less_nat @ ( size_size_list_com @ Ms ) @ ( size_size_list_com @ Ns ) )
% 0.31/0.47          | ( ( ( size_size_list_com @ Ms )
% 0.31/0.47              = ( size_size_list_com @ Ns ) )
% 0.31/0.47            & ( member1333916004om_com @ ( product_Pair_com_com @ M @ N ) @ R ) )
% 0.31/0.47          | ( ( M = N )
% 0.31/0.47            & ( member32358020st_com @ ( produc1307105171st_com @ Ms @ Ns ) @ ( lenlex_com @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_lenlex_iff
% 0.31/0.47  thf(fact_336_Cons__lenlex__iff,axiom,
% 0.31/0.47      ! [M: produc2041926651_state,Ms: list_P1040014977_state,N: produc2041926651_state,Ns: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ M @ Ms ) @ ( cons_P465369265_state @ N @ Ns ) ) @ ( lenlex295247238_state @ R ) )
% 0.31/0.47        = ( ( ord_less_nat @ ( size_s213202669_state @ Ms ) @ ( size_s213202669_state @ Ns ) )
% 0.31/0.47          | ( ( ( size_s213202669_state @ Ms )
% 0.31/0.47              = ( size_s213202669_state @ Ns ) )
% 0.31/0.47            & ( member1069318160_state @ ( produc1909270103_state @ M @ N ) @ R ) )
% 0.31/0.47          | ( ( M = N )
% 0.31/0.47            & ( member1267359376_state @ ( produc1298457559_state @ Ms @ Ns ) @ ( lenlex295247238_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_lenlex_iff
% 0.31/0.47  thf(fact_337_Cons__lenlex__iff,axiom,
% 0.31/0.47      ! [M: produc410756839_state,Ms: list_P890094829_state,N: produc410756839_state,Ns: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ M @ Ms ) @ ( cons_P438230685_state @ N @ Ns ) ) @ ( lenlex1401983474_state @ R ) )
% 0.31/0.47        = ( ( ord_less_nat @ ( size_s837829465_state @ Ms ) @ ( size_s837829465_state @ Ns ) )
% 0.31/0.47          | ( ( ( size_s837829465_state @ Ms )
% 0.31/0.47              = ( size_s837829465_state @ Ns ) )
% 0.31/0.47            & ( member512523024_state @ ( produc2065881943_state @ M @ N ) @ R ) )
% 0.31/0.47          | ( ( M = N )
% 0.31/0.47            & ( member423306384_state @ ( produc1354769367_state @ Ms @ Ns ) @ ( lenlex1401983474_state @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % Cons_lenlex_iff
% 0.31/0.47  thf(fact_338_list__ex1__simps_I1_J,axiom,
% 0.31/0.47      ! [P: com > $o] :
% 0.31/0.47        ~ ( list_ex1_com @ P @ nil_com ) ).
% 0.31/0.47  
% 0.31/0.47  % list_ex1_simps(1)
% 0.31/0.47  thf(fact_339_in__measures_I2_J,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state,F2: produc2041926651_state > nat,Fs: list_P1178430914te_nat] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ ( cons_P1821701106te_nat @ F2 @ Fs ) ) )
% 0.31/0.47        = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.31/0.47          | ( ( ( F2 @ X )
% 0.31/0.47              = ( F2 @ Y ) )
% 0.31/0.47            & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ Fs ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % in_measures(2)
% 0.31/0.47  thf(fact_340_in__measures_I2_J,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state,F2: produc410756839_state > nat,Fs: list_P1627643054te_nat] :
% 0.31/0.47        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ ( cons_P1631380062te_nat @ F2 @ Fs ) ) )
% 0.31/0.47        = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.31/0.47          | ( ( ( F2 @ X )
% 0.31/0.47              = ( F2 @ Y ) )
% 0.31/0.47            & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ Fs ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % in_measures(2)
% 0.31/0.47  thf(fact_341_listrel__iff__nth,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) )
% 0.31/0.47        = ( ( ( size_s213202669_state @ Xs2 )
% 0.31/0.47            = ( size_s213202669_state @ Ys2 ) )
% 0.31/0.47          & ! [N2: nat] :
% 0.31/0.47              ( ( ord_less_nat @ N2 @ ( size_s213202669_state @ Xs2 ) )
% 0.31/0.47             => ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ N2 ) @ ( nth_Pr553241858_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_iff_nth
% 0.31/0.47  thf(fact_342_listrel__iff__nth,axiom,
% 0.31/0.47      ! [Xs2: list_list_com,Ys2: list_state,R: set_Pr849496667_state] :
% 0.31/0.47        ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 0.31/0.47        = ( ( ( size_s318434721st_com @ Xs2 )
% 0.31/0.47            = ( size_size_list_state @ Ys2 ) )
% 0.31/0.47          & ! [N2: nat] :
% 0.31/0.47              ( ( ord_less_nat @ N2 @ ( size_s318434721st_com @ Xs2 ) )
% 0.31/0.47             => ( member64234660_state @ ( produc1204172211_state @ ( nth_list_com @ Xs2 @ N2 ) @ ( nth_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_iff_nth
% 0.31/0.47  thf(fact_343_listrel__iff__nth,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 0.31/0.47        = ( ( ( size_s837829465_state @ Xs2 )
% 0.31/0.47            = ( size_s837829465_state @ Ys2 ) )
% 0.31/0.47          & ! [N2: nat] :
% 0.31/0.47              ( ( ord_less_nat @ N2 @ ( size_s837829465_state @ Xs2 ) )
% 0.31/0.47             => ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ N2 ) @ ( nth_Pr526167918_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel_iff_nth
% 0.31/0.47  thf(fact_344_in__measures_I1_J,axiom,
% 0.31/0.47      ! [X: produc2041926651_state,Y: produc2041926651_state] :
% 0.31/0.47        ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ nil_Pr1876916290te_nat ) ) ).
% 0.31/0.47  
% 0.31/0.47  % in_measures(1)
% 0.31/0.47  thf(fact_345_in__measures_I1_J,axiom,
% 0.31/0.47      ! [X: produc410756839_state,Y: produc410756839_state] :
% 0.31/0.47        ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ nil_Pr164089518te_nat ) ) ).
% 0.31/0.47  
% 0.31/0.47  % in_measures(1)
% 0.31/0.47  thf(fact_346_nth__append__length,axiom,
% 0.31/0.47      ! [Xs2: list_com,X: com,Ys2: list_com] :
% 0.31/0.47        ( ( nth_com @ ( append_com @ Xs2 @ ( cons_com @ X @ Ys2 ) ) @ ( size_size_list_com @ Xs2 ) )
% 0.31/0.47        = X ) ).
% 0.31/0.47  
% 0.31/0.47  % nth_append_length
% 0.31/0.47  thf(fact_347_measures__less,axiom,
% 0.31/0.47      ! [F2: produc2041926651_state > nat,X: produc2041926651_state,Y: produc2041926651_state,Fs: list_P1178430914te_nat] :
% 0.31/0.47        ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.31/0.47       => ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ ( cons_P1821701106te_nat @ F2 @ Fs ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % measures_less
% 0.31/0.47  thf(fact_348_measures__less,axiom,
% 0.31/0.47      ! [F2: produc410756839_state > nat,X: produc410756839_state,Y: produc410756839_state,Fs: list_P1627643054te_nat] :
% 0.31/0.47        ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.31/0.47       => ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ ( cons_P1631380062te_nat @ F2 @ Fs ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % measures_less
% 0.31/0.47  thf(fact_349_listrel1__iff__update,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.31/0.47        = ( ? [Y4: produc2041926651_state,N2: nat] :
% 0.31/0.47              ( ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ N2 ) @ Y4 ) @ R )
% 0.31/0.47              & ( ord_less_nat @ N2 @ ( size_s213202669_state @ Xs2 ) )
% 0.31/0.47              & ( Ys2
% 0.31/0.47                = ( list_u737668969_state @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1_iff_update
% 0.31/0.47  thf(fact_350_listrel1__iff__update,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.31/0.47        = ( ? [Y4: produc410756839_state,N2: nat] :
% 0.31/0.47              ( ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ N2 ) @ Y4 ) @ R )
% 0.31/0.47              & ( ord_less_nat @ N2 @ ( size_s837829465_state @ Xs2 ) )
% 0.31/0.47              & ( Ys2
% 0.31/0.47                = ( list_u364351829_state @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % listrel1_iff_update
% 0.31/0.47  thf(fact_351_lex__take__index,axiom,
% 0.31/0.47      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.31/0.47        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( lex_Pr570247525_state @ R ) )
% 0.31/0.47       => ~ ! [I: nat] :
% 0.31/0.47              ( ( ord_less_nat @ I @ ( size_s213202669_state @ Xs2 ) )
% 0.31/0.47             => ( ( ord_less_nat @ I @ ( size_s213202669_state @ Ys2 ) )
% 0.31/0.47               => ( ( ( take_P558217449_state @ I @ Xs2 )
% 0.31/0.47                    = ( take_P558217449_state @ I @ Ys2 ) )
% 0.31/0.47                 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ I ) @ ( nth_Pr553241858_state @ Ys2 @ I ) ) @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_take_index
% 0.31/0.47  thf(fact_352_lex__take__index,axiom,
% 0.31/0.47      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.31/0.47        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( lex_Pr1762629969_state @ R ) )
% 0.31/0.47       => ~ ! [I: nat] :
% 0.31/0.47              ( ( ord_less_nat @ I @ ( size_s837829465_state @ Xs2 ) )
% 0.31/0.47             => ( ( ord_less_nat @ I @ ( size_s837829465_state @ Ys2 ) )
% 0.31/0.47               => ( ( ( take_P1852316373_state @ I @ Xs2 )
% 0.31/0.47                    = ( take_P1852316373_state @ I @ Ys2 ) )
% 0.31/0.47                 => ~ ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ I ) @ ( nth_Pr526167918_state @ Ys2 @ I ) ) @ R ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  % lex_take_index
% 0.31/0.47  thf(fact_353_list__update__nonempty,axiom,
% 0.31/0.47      ! [Xs2: list_com,K: nat,X: com] :
% 0.31/0.47        ( ( ( list_update_com @ Xs2 @ K @ X )
% 0.31/0.47          = nil_com )
% 0.31/0.47        = ( Xs2 = nil_com ) ) ).
% 0.31/0.47  
% 0.31/0.47  % list_update_nonempty
% 0.31/0.47  
% 0.31/0.47  % Conjectures (4)
% 0.31/0.47  thf(conj_0,hypothesis,
% 0.31/0.47      member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 0.31/0.47  
% 0.31/0.47  thf(conj_1,hypothesis,
% 0.31/0.47      termi @ c @ s ).
% 0.31/0.47  
% 0.31/0.47  thf(conj_2,hypothesis,
% 0.31/0.47      ! [S5: state,S6: state] :
% 0.31/0.47        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ S5 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ S6 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.31/0.47       => ( ( termi @ c @ S5 )
% 0.31/0.47         => ( ( termi @ c2 @ S6 )
% 0.31/0.47            & ! [T4: state] :
% 0.31/0.47                ( ( exec @ S6 @ c2 @ T4 )
% 0.31/0.47               => ( pHoare806997636termis @ cs @ T4 ) ) ) ) ) ).
% 0.31/0.47  
% 0.31/0.47  thf(conj_3,conjecture,
% 0.31/0.47      termi @ c2 @ s2 ).
% 0.31/0.47  
% 0.31/0.47  %------------------------------------------------------------------------------
% 0.31/0.47  ------------------------
% 3.03/1.63  ---- Embedded in THF ---
% 3.03/1.63  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.03/1.63  %%% Generated on Tue Feb 24 08:27:40 EST 2026
% 3.03/1.63  %%% using '$$dhol' embedding, version 1.3.0.
% 3.03/1.63  %%% Logic specification used:
% 3.03/1.63  %%% thf(spec, logic, $$dhol).
% 3.03/1.63  
% 3.03/1.63  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2DTF11910.p
% See solution above
% 3.03/1.63  ------------------------
% 3.03/1.68  ---- Cleaned THF ---
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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_Mt__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_J,type,
% 3.03/1.68      set_Pr1696918727_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_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_Mt__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,
% 3.03/1.68      produc270545127_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      set_Pr541394119_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc2046512871_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J_J,type,
% 3.03/1.68      set_Pr1847866567_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 3.03/1.68      produc1519776487_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      set_Pr1325664839_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc1586269031_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      set_Pr2096893127_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc186437863_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J_J,type,
% 3.03/1.68      set_Pr1419004359_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J_J,type,
% 3.03/1.68      set_Pr135335153st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 3.03/1.68      produc392316135_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 3.03/1.68      produc1440412305st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      set_Pr1142642759_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J_J,type,
% 3.03/1.68      set_Pr2083163591st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__List__Olist_I_062_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__Nat__Onat_J_J,type,
% 3.03/1.68      list_P1627643054te_nat: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc1225889383_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 3.03/1.68      produc1762014951st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      list_P890094829_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      set_Pr1165141447_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc410756839_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      set_Pr391631483_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__List__Olist_I_062_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.68      list_P1178430914te_nat: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc1393453339_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      produc2058209240st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 3.03/1.68      set_Pr602326075st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 3.03/1.68      list_P1040014977_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 3.03/1.68      set_Pr849496667_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 3.03/1.68      produc258871771st_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      produc2041926651_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J_J,type,
% 3.03/1.68      set_Pr1822651163om_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 3.03/1.68      product_prod_com_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J,type,
% 3.03/1.68      list_list_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__List__Olist_It__PLang__Ostate_J,type,
% 3.03/1.68      list_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Set__Oset_It__PLang__Ostate_J,type,
% 3.03/1.68      set_state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      list_com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__PLang__Ostate,type,
% 3.03/1.68      state: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__PLang__Ocom,type,
% 3.03/1.68      com: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(ty_n_t__Nat__Onat,type,
% 3.03/1.68      nat: $tType ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oappend_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      append_list_com: list_list_com > list_list_com > list_list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oappend_001t__PLang__Ocom,type,
% 3.03/1.68      append_com: list_com > list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oappend_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,
% 3.03/1.68      append221843330_state: list_P890094829_state > list_P890094829_state > list_P890094829_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Obind_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 3.03/1.68      bind_com_com: list_com > ( com > list_com ) > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Obutlast_001t__PLang__Ocom,type,
% 3.03/1.68      butlast_com: list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oconcat_001t__PLang__Ocom,type,
% 3.03/1.68      concat_com: list_list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oinsert_001t__PLang__Ocom,type,
% 3.03/1.68      insert_com: com > list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olast_001t__PLang__Ocom,type,
% 3.03/1.68      last_com: list_com > com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olenlex_001t__PLang__Ocom,type,
% 3.03/1.68      lenlex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olenlex_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      lenlex295247238_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olenlex_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,
% 3.03/1.68      lenlex1401983474_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olex_001t__PLang__Ocom,type,
% 3.03/1.68      lex_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      lex_Pr570247525_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olex_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,
% 3.03/1.68      lex_Pr1762629969_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olexord_001t__PLang__Ocom,type,
% 3.03/1.68      lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olexord_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olexord_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,
% 3.03/1.68      lexord1893203674_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_001_062_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Nat__Onat_J,type,
% 3.03/1.68      cons_P1821701106te_nat: ( produc2041926651_state > nat ) > list_P1178430914te_nat > list_P1178430914te_nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_001_062_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__Nat__Onat_J,type,
% 3.03/1.68      cons_P1631380062te_nat: ( produc410756839_state > nat ) > list_P1627643054te_nat > list_P1627643054te_nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      cons_list_com: list_com > list_list_com > list_list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_001t__PLang__Ocom,type,
% 3.03/1.68      cons_com: com > list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_001t__PLang__Ostate,type,
% 3.03/1.68      cons_state: state > list_state > list_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_OCons_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,
% 3.03/1.68      cons_P438230685_state: produc410756839_state > list_P890094829_state > list_P890094829_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_001_062_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Nat__Onat_J,type,
% 3.03/1.68      nil_Pr1876916290te_nat: list_P1178430914te_nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_001_062_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__Nat__Onat_J,type,
% 3.03/1.68      nil_Pr164089518te_nat: list_P1627643054te_nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      nil_list_com: list_list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_001t__PLang__Ocom,type,
% 3.03/1.68      nil_com: list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_001t__PLang__Ostate,type,
% 3.03/1.68      nil_state: list_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      nil_Pr1844458753_state: list_P1040014977_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist_ONil_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,
% 3.03/1.68      nil_Pr1347322605_state: list_P890094829_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist__ex1_001t__PLang__Ocom,type,
% 3.03/1.68      list_ex1_com: ( com > $o ) > list_com > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist__update_001t__PLang__Ocom,type,
% 3.03/1.68      list_update_com: list_com > nat > com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      list_u737668969_state: list_P1040014977_state > nat > produc2041926651_state > list_P1040014977_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olist__update_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,
% 3.03/1.68      list_u364351829_state: list_P890094829_state > nat > produc410756839_state > list_P890094829_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel1_001t__PLang__Ocom,type,
% 3.03/1.68      listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel1_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel1_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,
% 3.03/1.68      listre1725776070_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel_001t__List__Olist_It__PLang__Ocom_J_001t__PLang__Ostate,type,
% 3.03/1.68      listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 3.03/1.68      listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Olistrel_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_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,
% 3.03/1.68      listre1244407729_state: set_Pr2096893127_state > set_Pr1325664839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Omaps_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 3.03/1.68      maps_com_com: ( com > list_com ) > list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Omeasures_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      measur1071343867_state: list_P1178430914te_nat > set_Pr1165141447_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Omeasures_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,
% 3.03/1.68      measur768621543_state: list_P1627643054te_nat > set_Pr2096893127_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Onth_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      nth_list_com: list_list_com > nat > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Onth_001t__PLang__Ocom,type,
% 3.03/1.68      nth_com: list_com > nat > com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Onth_001t__PLang__Ostate,type,
% 3.03/1.68      nth_state: list_state > nat > state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      nth_Pr553241858_state: list_P1040014977_state > nat > produc2041926651_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Onth_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,
% 3.03/1.68      nth_Pr526167918_state: list_P890094829_state > nat > produc410756839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Oproduct__lists_001t__PLang__Ocom,type,
% 3.03/1.68      product_lists_com: list_list_com > list_list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Orotate1_001t__PLang__Ocom,type,
% 3.03/1.68      rotate1_com: list_com > list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Osubseqs_001t__PLang__Ocom,type,
% 3.03/1.68      subseqs_com: list_com > list_list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Otake_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      take_P558217449_state: nat > list_P1040014977_state > list_P1040014977_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_List_Otake_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,
% 3.03/1.68      take_P1852316373_state: nat > list_P890094829_state > list_P890094829_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J,type,
% 3.03/1.68      size_s318434721st_com: list_list_com > nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      size_size_list_com: list_com > nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__PLang__Ostate_J,type,
% 3.03/1.68      size_size_list_state: list_state > nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 3.03/1.68      size_s213202669_state: list_P1040014977_state > nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Nat_Osize__class_Osize_001t__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,
% 3.03/1.68      size_s837829465_state: list_P890094829_state > nat ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 3.03/1.68      ord_less_nat: nat > nat > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Oexec1,type,
% 3.03/1.68      pHoare259243666_exec1: set_Pr1165141447_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Oexecs,type,
% 3.03/1.68      pHoare259243732_execs: state > list_com > state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Otermis,type,
% 3.03/1.68      pHoare806997636termis: list_com > state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PLang_Ocom_OCond,type,
% 3.03/1.68      cond: ( state > $o ) > com > com > com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PLang_Ocom_ODo,type,
% 3.03/1.68      do: ( state > set_state ) > com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PLang_Ocom_OSemi,type,
% 3.03/1.68      semi: com > com > com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PLang_Ocom_OWhile,type,
% 3.03/1.68      while: ( state > $o ) > com > com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PLang_Oexec,type,
% 3.03/1.68      exec: state > com > state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_PTermi_Otermi,type,
% 3.03/1.68      termi: com > state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      produc1914379986st_com: ( com > com > $o ) > list_com > produc2058209240st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_001t__List__Olist_It__PLang__Ostate_J,type,
% 3.03/1.68      produc1742567891_state: list_list_com > list_state > produc1393453339_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__PLang__Ocom_J_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      produc1307105171st_com: list_com > list_com > produc258871771st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__PLang__Ocom_J_001t__PLang__Ostate,type,
% 3.03/1.68      produc1204172211_state: list_com > state > produc2041926651_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 3.03/1.68      produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__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_001t__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,
% 3.03/1.68      produc1354769367_state: list_P890094829_state > list_P890094829_state > produc1586269031_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__PLang__Ocom_001t__PLang__Ocom,type,
% 3.03/1.68      product_Pair_com_com: com > com > product_prod_com_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__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_001t__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,
% 3.03/1.68      produc67337417st_com: produc2058209240st_com > produc2058209240st_com > produc1440412305st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 3.03/1.68      produc67381847_state: produc1393453339_state > produc1393453339_state > produc392316135_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 3.03/1.68      produc313736791st_com: produc258871771st_com > produc258871771st_com > produc1762014951st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_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_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,
% 3.03/1.68      produc984060759_state: produc1225889383_state > produc1225889383_state > produc1519776487_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_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_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,
% 3.03/1.68      produc1576663895_state: produc1586269031_state > produc1586269031_state > produc270545127_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_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_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,
% 3.03/1.68      produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Product__Type_OPair_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_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,
% 3.03/1.68      produc2049704791_state: produc186437863_state > produc186437863_state > produc2046512871_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Relation_Oirrefl_001t__PLang__Ocom,type,
% 3.03/1.68      irrefl_com: set_Pr1822651163om_com > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Relation_Oirrefl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      irrefl654089520_state: set_Pr1165141447_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Relation_Oirrefl_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,
% 3.03/1.68      irrefl1358048924_state: set_Pr2096893127_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Set_OCollect_001t__PLang__Ostate,type,
% 3.03/1.68      collect_state: ( state > $o ) > set_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Set_OCollect_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,
% 3.03/1.68      collec300063826_state: ( produc410756839_state > $o ) > set_Pr1165141447_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Set_OCollect_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,
% 3.03/1.68      collec489924946_state: ( produc186437863_state > $o ) > set_Pr2096893127_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__PLang__Ocom_J,type,
% 3.03/1.68      transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 3.03/1.68      transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__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,
% 3.03/1.68      transi1965148016_state: set_Pr1325664839_state > set_Pr1325664839_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__PLang__Ocom,type,
% 3.03/1.68      transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__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,
% 3.03/1.68      transi1592315797st_com: set_Pr135335153st_com > set_Pr135335153st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J,type,
% 3.03/1.68      transi89280670_state: set_Pr1419004359_state > set_Pr1419004359_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 3.03/1.68      transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J,type,
% 3.03/1.68      transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_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,
% 3.03/1.68      transi445721450_state: set_Pr1696918727_state > set_Pr1696918727_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J,type,
% 3.03/1.68      transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_Transitive__Closure_Ortrancl_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,
% 3.03/1.68      transi152726506_state: set_Pr541394119_state > set_Pr541394119_state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__PLang__Ostate,type,
% 3.03/1.68      member_state: state > set_state > $o ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J,type,
% 3.03/1.68      member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J,type,
% 3.03/1.68      member64234660_state: produc2041926651_state > set_Pr849496667_state > $o ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ocom_Mt__PLang__Ocom_J,type,
% 3.03/1.68      member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_I_062_It__PLang__Ocom_M_062_It__PLang__Ocom_M_Eo_J_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 3.03/1.68      member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__PLang__Ocom_J_J_Mt__List__Olist_It__PLang__Ostate_J_J_J,type,
% 3.03/1.68      member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__List__Olist_It__PLang__Ocom_J_J_J,type,
% 3.03/1.68      member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 3.03/1.68      member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__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,
% 3.03/1.68      member1642814224_state: produc270545127_state > set_Pr1696918727_state > $o ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
% 3.03/1.68  
% 3.03/1.68  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,
% 3.03/1.68      member284400400_state: produc2046512871_state > set_Pr541394119_state > $o ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_v_c,type,
% 3.03/1.68      c: com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_v_c_H,type,
% 3.03/1.68      c2: com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_v_cs_H,type,
% 3.03/1.68      cs: list_com ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_v_s,type,
% 3.03/1.68      s: state ).
% 3.03/1.68  
% 3.03/1.68  thf(sy_v_s_H,type,
% 3.03/1.68      s2: state ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_0_exec1E_I1_J,axiom,
% 3.03/1.68      ! [S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ nil_com @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_1_termis_Osimps_I2_J,axiom,
% 3.03/1.68      ! [C: com,Cs2: list_com,S: state] :
% 3.03/1.68        ( ( pHoare806997636termis @ ( cons_com @ C @ Cs2 ) @ S )
% 3.03/1.68        = ( ( termi @ C @ S )
% 3.03/1.68          & ! [T: state] :
% 3.03/1.68              ( ( exec @ S @ C @ T )
% 3.03/1.68             => ( pHoare806997636termis @ Cs2 @ T ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_2_termis_Osimps_I1_J,axiom,
% 3.03/1.68      ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_3_exec__impl__execs,axiom,
% 3.03/1.68      ! [S: state,C: com,S2: state,Cs2: list_com] :
% 3.03/1.68        ( ( exec @ S @ C @ S2 )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_4_exec1s__impl__exec,axiom,
% 3.03/1.68      ! [C: com,S: state,T2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 3.03/1.68       => ( exec @ S @ C @ T2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_5_exec1__pres__termis,axiom,
% 3.03/1.68      ! [Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 3.03/1.68       => ( ( pHoare806997636termis @ Cs2 @ S )
% 3.03/1.68         => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_6_execs__pres__termis,axiom,
% 3.03/1.68      ! [Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 3.03/1.68       => ( ( pHoare806997636termis @ Cs2 @ S )
% 3.03/1.68         => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_7_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_P890094829_state,Ay: list_P890094829_state,Bx: list_P890094829_state,By: list_P890094829_state,R: set_Pr1696918727_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 3.03/1.68        ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: list_P890094829_state,B: list_P890094829_state,Aa: list_P890094829_state,Ba: list_P890094829_state] :
% 3.03/1.68                ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ A @ B ) ) @ ( transi445721450_state @ R ) )
% 3.03/1.68               => ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_8_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 3.03/1.68        ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: list_P1040014977_state,B: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 3.03/1.68                ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ A @ B ) ) @ ( transi1428749162_state @ R ) )
% 3.03/1.68               => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_9_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 3.03/1.68        ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: list_com,B: list_com,Aa: list_com,Ba: list_com] :
% 3.03/1.68                ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ A @ B ) ) @ ( transi1782245470st_com @ R ) )
% 3.03/1.68               => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_10_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 3.03/1.68        ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: list_list_com,B: list_state,Aa: list_list_com,Ba: list_state] :
% 3.03/1.68                ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ A @ B ) ) @ ( transi89280670_state @ R ) )
% 3.03/1.68               => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_11_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 3.03/1.68        ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: com > com > $o,B: list_com,Aa: com > com > $o,Ba: list_com] :
% 3.03/1.68                ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ A @ B ) ) @ ( transi1592315797st_com @ R ) )
% 3.03/1.68               => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_12_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 3.03/1.68        ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: produc410756839_state,B: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 3.03/1.68                ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A @ B ) ) @ ( transi152726506_state @ R ) )
% 3.03/1.68               => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_13_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: produc2041926651_state,B: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A @ B ) ) @ ( transi463013610_state @ R ) )
% 3.03/1.68               => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_14_rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( P @ Ax @ Ay )
% 3.03/1.68         => ( ! [A: list_com,B: state,Aa: list_com,Ba: state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A @ B ) ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68               => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68                 => ( ( P @ A @ B )
% 3.03/1.68                   => ( P @ Aa @ Ba ) ) ) )
% 3.03/1.68           => ( P @ Bx @ By ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_15_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: list_P890094829_state,Xb: list_P890094829_state,Za: list_P890094829_state,Zb: list_P890094829_state,R: set_Pr1696918727_state] :
% 3.03/1.68        ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Xa @ Xb ) @ ( produc1354769367_state @ Za @ Zb ) ) @ ( transi445721450_state @ R ) )
% 3.03/1.68       => ( ( ( produc1354769367_state @ Xa @ Xb )
% 3.03/1.68           != ( produc1354769367_state @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: list_P890094829_state,B: list_P890094829_state] :
% 3.03/1.68                ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Xa @ Xb ) @ ( produc1354769367_state @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Za @ Zb ) ) @ ( transi445721450_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_16_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: list_P1040014977_state,Xb: list_P1040014977_state,Za: list_P1040014977_state,Zb: list_P1040014977_state,R: set_Pr1847866567_state] :
% 3.03/1.68        ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) )
% 3.03/1.68       => ( ( ( produc1298457559_state @ Xa @ Xb )
% 3.03/1.68           != ( produc1298457559_state @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: list_P1040014977_state,B: list_P1040014977_state] :
% 3.03/1.68                ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_17_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: list_com,Xb: list_com,Za: list_com,Zb: list_com,R: set_Pr2083163591st_com] :
% 3.03/1.68        ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) )
% 3.03/1.68       => ( ( ( produc1307105171st_com @ Xa @ Xb )
% 3.03/1.68           != ( produc1307105171st_com @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: list_com,B: list_com] :
% 3.03/1.68                ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_18_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: list_list_com,Xb: list_state,Za: list_list_com,Zb: list_state,R: set_Pr1419004359_state] :
% 3.03/1.68        ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) )
% 3.03/1.68       => ( ( ( produc1742567891_state @ Xa @ Xb )
% 3.03/1.68           != ( produc1742567891_state @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: list_list_com,B: list_state] :
% 3.03/1.68                ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_19_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: com > com > $o,Xb: list_com,Za: com > com > $o,Zb: list_com,R: set_Pr135335153st_com] :
% 3.03/1.68        ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) )
% 3.03/1.68       => ( ( ( produc1914379986st_com @ Xa @ Xb )
% 3.03/1.68           != ( produc1914379986st_com @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: com > com > $o,B: list_com] :
% 3.03/1.68                ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_20_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: produc410756839_state,Xb: produc410756839_state,Za: produc410756839_state,Zb: produc410756839_state,R: set_Pr541394119_state] :
% 3.03/1.68        ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) )
% 3.03/1.68       => ( ( ( produc2065881943_state @ Xa @ Xb )
% 3.03/1.68           != ( produc2065881943_state @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: produc410756839_state,B: produc410756839_state] :
% 3.03/1.68                ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_21_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( ( produc1909270103_state @ Xa @ Xb )
% 3.03/1.68           != ( produc1909270103_state @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: produc2041926651_state,B: produc2041926651_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_22_converse__rtranclE2,axiom,
% 3.03/1.68      ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( ( produc1204172211_state @ Xa @ Xb )
% 3.03/1.68           != ( produc1204172211_state @ Za @ Zb ) )
% 3.03/1.68         => ~ ! [A: list_com,B: state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A @ B ) ) @ R )
% 3.03/1.68               => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_23_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_P890094829_state,Ay: list_P890094829_state,Bx: list_P890094829_state,By: list_P890094829_state,R: set_Pr1696918727_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 3.03/1.68        ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: list_P890094829_state,B: list_P890094829_state,Aa: list_P890094829_state,Ba: list_P890094829_state] :
% 3.03/1.68                ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Aa @ Ba ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_24_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 3.03/1.68        ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: list_P1040014977_state,B: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 3.03/1.68                ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Aa @ Ba ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_25_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 3.03/1.68        ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: list_com,B: list_com,Aa: list_com,Ba: list_com] :
% 3.03/1.68                ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Aa @ Ba ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_26_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 3.03/1.68        ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: list_list_com,B: list_state,Aa: list_list_com,Ba: list_state] :
% 3.03/1.68                ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Aa @ Ba ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_27_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 3.03/1.68        ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: com > com > $o,B: list_com,Aa: com > com > $o,Ba: list_com] :
% 3.03/1.68                ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Aa @ Ba ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_28_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 3.03/1.68        ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: produc410756839_state,B: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 3.03/1.68                ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Aa @ Ba ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_29_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: produc2041926651_state,B: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_30_converse__rtrancl__induct2,axiom,
% 3.03/1.68      ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( P @ Bx @ By )
% 3.03/1.68         => ( ! [A: list_com,B: state,Aa: list_com,Ba: state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 3.03/1.68               => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68                 => ( ( P @ Aa @ Ba )
% 3.03/1.68                   => ( P @ A @ B ) ) ) )
% 3.03/1.68           => ( P @ Ax @ Ay ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_31_exec1s__impl__execs,axiom,
% 3.03/1.68      ! [Cs2: list_com,S: state,T2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ nil_com @ T2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 3.03/1.68       => ( pHoare259243732_execs @ S @ Cs2 @ T2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_32_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr541394119_state] :
% 3.03/1.68        ( ( transi152726506_state @ ( transi152726506_state @ R ) )
% 3.03/1.68        = ( transi152726506_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_33_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr602326075st_com] :
% 3.03/1.68        ( ( transi436345274st_com @ ( transi436345274st_com @ R ) )
% 3.03/1.68        = ( transi436345274st_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_34_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr1325664839_state] :
% 3.03/1.68        ( ( transi1965148016_state @ ( transi1965148016_state @ R ) )
% 3.03/1.68        = ( transi1965148016_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_35_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr1142642759_state] :
% 3.03/1.68        ( ( transi339813252_state @ ( transi339813252_state @ R ) )
% 3.03/1.68        = ( transi339813252_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_36_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( transi863150634cl_com @ ( transi863150634cl_com @ R ) )
% 3.03/1.68        = ( transi863150634cl_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_37_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 3.03/1.68        = ( transi1302705790_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_38_rtrancl__idemp,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 3.03/1.68        = ( transi463013610_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_39_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: produc2046512871_state,R: set_Pr541394119_state] :
% 3.03/1.68        ( ( member284400400_state @ P2 @ R )
% 3.03/1.68       => ( member284400400_state @ P2 @ ( transi152726506_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_40_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: produc258871771st_com,R: set_Pr602326075st_com] :
% 3.03/1.68        ( ( member32358020st_com @ P2 @ R )
% 3.03/1.68       => ( member32358020st_com @ P2 @ ( transi436345274st_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_41_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: produc1586269031_state,R: set_Pr1325664839_state] :
% 3.03/1.68        ( ( member423306384_state @ P2 @ R )
% 3.03/1.68       => ( member423306384_state @ P2 @ ( transi1965148016_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_42_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: produc1225889383_state,R: set_Pr1142642759_state] :
% 3.03/1.68        ( ( member1267359376_state @ P2 @ R )
% 3.03/1.68       => ( member1267359376_state @ P2 @ ( transi339813252_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_43_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: product_prod_com_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member1333916004om_com @ P2 @ R )
% 3.03/1.68       => ( member1333916004om_com @ P2 @ ( transi863150634cl_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_44_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1069318160_state @ P2 @ R )
% 3.03/1.68       => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_45_r__into__rtrancl,axiom,
% 3.03/1.68      ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member512523024_state @ P2 @ R )
% 3.03/1.68       => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_46_list_Oinject,axiom,
% 3.03/1.68      ! [X21: produc2041926651_state,X22: list_P1040014977_state,Y21: produc2041926651_state,Y22: list_P1040014977_state] :
% 3.03/1.68        ( ( ( cons_P465369265_state @ X21 @ X22 )
% 3.03/1.68          = ( cons_P465369265_state @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_47_list_Oinject,axiom,
% 3.03/1.68      ! [X21: state,X22: list_state,Y21: state,Y22: list_state] :
% 3.03/1.68        ( ( ( cons_state @ X21 @ X22 )
% 3.03/1.68          = ( cons_state @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_48_list_Oinject,axiom,
% 3.03/1.68      ! [X21: list_com,X22: list_list_com,Y21: list_com,Y22: list_list_com] :
% 3.03/1.68        ( ( ( cons_list_com @ X21 @ X22 )
% 3.03/1.68          = ( cons_list_com @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_49_list_Oinject,axiom,
% 3.03/1.68      ! [X21: produc410756839_state > nat,X22: list_P1627643054te_nat,Y21: produc410756839_state > nat,Y22: list_P1627643054te_nat] :
% 3.03/1.68        ( ( ( cons_P1631380062te_nat @ X21 @ X22 )
% 3.03/1.68          = ( cons_P1631380062te_nat @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_50_list_Oinject,axiom,
% 3.03/1.68      ! [X21: produc2041926651_state > nat,X22: list_P1178430914te_nat,Y21: produc2041926651_state > nat,Y22: list_P1178430914te_nat] :
% 3.03/1.68        ( ( ( cons_P1821701106te_nat @ X21 @ X22 )
% 3.03/1.68          = ( cons_P1821701106te_nat @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_51_list_Oinject,axiom,
% 3.03/1.68      ! [X21: com,X22: list_com,Y21: com,Y22: list_com] :
% 3.03/1.68        ( ( ( cons_com @ X21 @ X22 )
% 3.03/1.68          = ( cons_com @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_52_prod_Oinject,axiom,
% 3.03/1.68      ! [X1: list_com,X2: list_com,Y1: list_com,Y2: list_com] :
% 3.03/1.68        ( ( ( produc1307105171st_com @ X1 @ X2 )
% 3.03/1.68          = ( produc1307105171st_com @ Y1 @ Y2 ) )
% 3.03/1.68        = ( ( X1 = Y1 )
% 3.03/1.68          & ( X2 = Y2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_53_prod_Oinject,axiom,
% 3.03/1.68      ! [X1: list_list_com,X2: list_state,Y1: list_list_com,Y2: list_state] :
% 3.03/1.68        ( ( ( produc1742567891_state @ X1 @ X2 )
% 3.03/1.68          = ( produc1742567891_state @ Y1 @ Y2 ) )
% 3.03/1.68        = ( ( X1 = Y1 )
% 3.03/1.68          & ( X2 = Y2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_54_prod_Oinject,axiom,
% 3.03/1.68      ! [X1: com > com > $o,X2: list_com,Y1: com > com > $o,Y2: list_com] :
% 3.03/1.68        ( ( ( produc1914379986st_com @ X1 @ X2 )
% 3.03/1.68          = ( produc1914379986st_com @ Y1 @ Y2 ) )
% 3.03/1.68        = ( ( X1 = Y1 )
% 3.03/1.68          & ( X2 = Y2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_55_prod_Oinject,axiom,
% 3.03/1.68      ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y2: produc2041926651_state] :
% 3.03/1.68        ( ( ( produc1909270103_state @ X1 @ X2 )
% 3.03/1.68          = ( produc1909270103_state @ Y1 @ Y2 ) )
% 3.03/1.68        = ( ( X1 = Y1 )
% 3.03/1.68          & ( X2 = Y2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_56_prod_Oinject,axiom,
% 3.03/1.68      ! [X1: list_com,X2: state,Y1: list_com,Y2: state] :
% 3.03/1.68        ( ( ( produc1204172211_state @ X1 @ X2 )
% 3.03/1.68          = ( produc1204172211_state @ Y1 @ Y2 ) )
% 3.03/1.68        = ( ( X1 = Y1 )
% 3.03/1.68          & ( X2 = Y2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_57_prod_Oinject,axiom,
% 3.03/1.68      ! [X1: produc410756839_state,X2: produc410756839_state,Y1: produc410756839_state,Y2: produc410756839_state] :
% 3.03/1.68        ( ( ( produc2065881943_state @ X1 @ X2 )
% 3.03/1.68          = ( produc2065881943_state @ Y1 @ Y2 ) )
% 3.03/1.68        = ( ( X1 = Y1 )
% 3.03/1.68          & ( X2 = Y2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_58_old_Oprod_Oinject,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,A3: produc2041926651_state,B3: produc2041926651_state] :
% 3.03/1.68        ( ( ( produc1909270103_state @ A2 @ B2 )
% 3.03/1.68          = ( produc1909270103_state @ A3 @ B3 ) )
% 3.03/1.68        = ( ( A2 = A3 )
% 3.03/1.68          & ( B2 = B3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_59_old_Oprod_Oinject,axiom,
% 3.03/1.68      ! [A2: list_com,B2: state,A3: list_com,B3: state] :
% 3.03/1.68        ( ( ( produc1204172211_state @ A2 @ B2 )
% 3.03/1.68          = ( produc1204172211_state @ A3 @ B3 ) )
% 3.03/1.68        = ( ( A2 = A3 )
% 3.03/1.68          & ( B2 = B3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_60_old_Oprod_Oinject,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,A3: produc410756839_state,B3: produc410756839_state] :
% 3.03/1.68        ( ( ( produc2065881943_state @ A2 @ B2 )
% 3.03/1.68          = ( produc2065881943_state @ A3 @ B3 ) )
% 3.03/1.68        = ( ( A2 = A3 )
% 3.03/1.68          & ( B2 = B3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_61_prod__cases3,axiom,
% 3.03/1.68      ! [Y: produc410756839_state] :
% 3.03/1.68        ~ ! [A: produc2041926651_state,B: list_com,C2: state] :
% 3.03/1.68            ( Y
% 3.03/1.68           != ( produc1909270103_state @ A @ ( produc1204172211_state @ B @ C2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_62_prod__cases3,axiom,
% 3.03/1.68      ! [Y: produc186437863_state] :
% 3.03/1.68        ~ ! [A: produc410756839_state,B: produc2041926651_state,C2: produc2041926651_state] :
% 3.03/1.68            ( Y
% 3.03/1.68           != ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ C2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_63_prod__cases4,axiom,
% 3.03/1.68      ! [Y: produc186437863_state] :
% 3.03/1.68        ~ ! [A: produc410756839_state,B: produc2041926651_state,C2: list_com,D: state] :
% 3.03/1.68            ( Y
% 3.03/1.68           != ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ ( produc1204172211_state @ C2 @ D ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_64_successively_Ocases,axiom,
% 3.03/1.68      ! [X: produc2058209240st_com] :
% 3.03/1.68        ( ! [P3: com > com > $o] :
% 3.03/1.68            ( X
% 3.03/1.68           != ( produc1914379986st_com @ P3 @ nil_com ) )
% 3.03/1.68       => ( ! [P3: com > com > $o,X3: com] :
% 3.03/1.68              ( X
% 3.03/1.68             != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 3.03/1.68         => ~ ! [P3: com > com > $o,X3: com,Y3: com,Xs: list_com] :
% 3.03/1.68                ( X
% 3.03/1.68               != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_65_sorted__wrt_Ocases,axiom,
% 3.03/1.68      ! [X: produc2058209240st_com] :
% 3.03/1.68        ( ! [P3: com > com > $o] :
% 3.03/1.68            ( X
% 3.03/1.68           != ( produc1914379986st_com @ P3 @ nil_com ) )
% 3.03/1.68       => ~ ! [P3: com > com > $o,X3: com,Ys: list_com] :
% 3.03/1.68              ( X
% 3.03/1.68             != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_66_shuffles_Ocases,axiom,
% 3.03/1.68      ! [X: produc258871771st_com] :
% 3.03/1.68        ( ! [Ys: list_com] :
% 3.03/1.68            ( X
% 3.03/1.68           != ( produc1307105171st_com @ nil_com @ Ys ) )
% 3.03/1.68       => ( ! [Xs: list_com] :
% 3.03/1.68              ( X
% 3.03/1.68             != ( produc1307105171st_com @ Xs @ nil_com ) )
% 3.03/1.68         => ~ ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 3.03/1.68                ( X
% 3.03/1.68               != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_67_splice_Ocases,axiom,
% 3.03/1.68      ! [X: produc258871771st_com] :
% 3.03/1.68        ( ! [Ys: list_com] :
% 3.03/1.68            ( X
% 3.03/1.68           != ( produc1307105171st_com @ nil_com @ Ys ) )
% 3.03/1.68       => ~ ! [X3: com,Xs: list_com,Ys: list_com] :
% 3.03/1.68              ( X
% 3.03/1.68             != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs ) @ Ys ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_68_execs_Ointros_I1_J,axiom,
% 3.03/1.68      ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_69_old_Oprod_Oinducts,axiom,
% 3.03/1.68      ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 3.03/1.68        ( ! [A: produc2041926651_state,B: produc2041926651_state] : ( P @ ( produc1909270103_state @ A @ B ) )
% 3.03/1.68       => ( P @ Prod ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_70_old_Oprod_Oinducts,axiom,
% 3.03/1.68      ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 3.03/1.68        ( ! [A: list_com,B: state] : ( P @ ( produc1204172211_state @ A @ B ) )
% 3.03/1.68       => ( P @ Prod ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_71_old_Oprod_Oinducts,axiom,
% 3.03/1.68      ! [P: produc186437863_state > $o,Prod: produc186437863_state] :
% 3.03/1.68        ( ! [A: produc410756839_state,B: produc410756839_state] : ( P @ ( produc2065881943_state @ A @ B ) )
% 3.03/1.68       => ( P @ Prod ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_72_old_Oprod_Oexhaust,axiom,
% 3.03/1.68      ! [Y: produc410756839_state] :
% 3.03/1.68        ~ ! [A: produc2041926651_state,B: produc2041926651_state] :
% 3.03/1.68            ( Y
% 3.03/1.68           != ( produc1909270103_state @ A @ B ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_73_old_Oprod_Oexhaust,axiom,
% 3.03/1.68      ! [Y: produc2041926651_state] :
% 3.03/1.68        ~ ! [A: list_com,B: state] :
% 3.03/1.68            ( Y
% 3.03/1.68           != ( produc1204172211_state @ A @ B ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_74_old_Oprod_Oexhaust,axiom,
% 3.03/1.68      ! [Y: produc186437863_state] :
% 3.03/1.68        ~ ! [A: produc410756839_state,B: produc410756839_state] :
% 3.03/1.68            ( Y
% 3.03/1.68           != ( produc2065881943_state @ A @ B ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_75_Pair__inject,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,A3: produc2041926651_state,B3: produc2041926651_state] :
% 3.03/1.68        ( ( ( produc1909270103_state @ A2 @ B2 )
% 3.03/1.68          = ( produc1909270103_state @ A3 @ B3 ) )
% 3.03/1.68       => ~ ( ( A2 = A3 )
% 3.03/1.68           => ( B2 != B3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_76_Pair__inject,axiom,
% 3.03/1.68      ! [A2: list_com,B2: state,A3: list_com,B3: state] :
% 3.03/1.68        ( ( ( produc1204172211_state @ A2 @ B2 )
% 3.03/1.68          = ( produc1204172211_state @ A3 @ B3 ) )
% 3.03/1.68       => ~ ( ( A2 = A3 )
% 3.03/1.68           => ( B2 != B3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_77_Pair__inject,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,A3: produc410756839_state,B3: produc410756839_state] :
% 3.03/1.68        ( ( ( produc2065881943_state @ A2 @ B2 )
% 3.03/1.68          = ( produc2065881943_state @ A3 @ B3 ) )
% 3.03/1.68       => ~ ( ( A2 = A3 )
% 3.03/1.68           => ( B2 != B3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_78_prod__cases,axiom,
% 3.03/1.68      ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 3.03/1.68        ( ! [A: produc2041926651_state,B: produc2041926651_state] : ( P @ ( produc1909270103_state @ A @ B ) )
% 3.03/1.68       => ( P @ P2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_79_prod__cases,axiom,
% 3.03/1.68      ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 3.03/1.68        ( ! [A: list_com,B: state] : ( P @ ( produc1204172211_state @ A @ B ) )
% 3.03/1.68       => ( P @ P2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_80_prod__cases,axiom,
% 3.03/1.68      ! [P: produc186437863_state > $o,P2: produc186437863_state] :
% 3.03/1.68        ( ! [A: produc410756839_state,B: produc410756839_state] : ( P @ ( produc2065881943_state @ A @ B ) )
% 3.03/1.68       => ( P @ P2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_81_surj__pair,axiom,
% 3.03/1.68      ! [P2: produc410756839_state] :
% 3.03/1.68      ? [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 3.03/1.68        ( P2
% 3.03/1.68        = ( produc1909270103_state @ X3 @ Y3 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_82_surj__pair,axiom,
% 3.03/1.68      ! [P2: produc2041926651_state] :
% 3.03/1.68      ? [X3: list_com,Y3: state] :
% 3.03/1.68        ( P2
% 3.03/1.68        = ( produc1204172211_state @ X3 @ Y3 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_83_surj__pair,axiom,
% 3.03/1.68      ! [P2: produc186437863_state] :
% 3.03/1.68      ? [X3: produc410756839_state,Y3: produc410756839_state] :
% 3.03/1.68        ( P2
% 3.03/1.68        = ( produc2065881943_state @ X3 @ Y3 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_84_not__Cons__self2,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com] :
% 3.03/1.68        ( ( cons_com @ X @ Xs2 )
% 3.03/1.68       != Xs2 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_85_execs_Ointros_I2_J,axiom,
% 3.03/1.68      ! [S: state,C: com,T2: state,Cs2: list_com,U: state] :
% 3.03/1.68        ( ( exec @ S @ C @ T2 )
% 3.03/1.68       => ( ( pHoare259243732_execs @ T2 @ Cs2 @ U )
% 3.03/1.68         => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs2 ) @ U ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_86_map__tailrec__rev_Oinduct,axiom,
% 3.03/1.68      ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 3.03/1.68        ( ! [F: com > com,X_1: list_com] : ( P @ F @ nil_com @ X_1 )
% 3.03/1.68       => ( ! [F: com > com,A: com,As: list_com,Bs: list_com] :
% 3.03/1.68              ( ( P @ F @ As @ ( cons_com @ ( F @ A ) @ Bs ) )
% 3.03/1.68             => ( P @ F @ ( cons_com @ A @ As ) @ Bs ) )
% 3.03/1.68         => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_87_list__nonempty__induct,axiom,
% 3.03/1.68      ! [Xs2: list_com,P: list_com > $o] :
% 3.03/1.68        ( ( Xs2 != nil_com )
% 3.03/1.68       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 3.03/1.68         => ( ! [X3: com,Xs: list_com] :
% 3.03/1.68                ( ( Xs != nil_com )
% 3.03/1.68               => ( ( P @ Xs )
% 3.03/1.68                 => ( P @ ( cons_com @ X3 @ Xs ) ) ) )
% 3.03/1.68           => ( P @ Xs2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_88_successively_Oinduct,axiom,
% 3.03/1.68      ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 3.03/1.68        ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 3.03/1.68       => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 3.03/1.68         => ( ! [P3: com > com > $o,X3: com,Y3: com,Xs: list_com] :
% 3.03/1.68                ( ( P @ P3 @ ( cons_com @ Y3 @ Xs ) )
% 3.03/1.68               => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) )
% 3.03/1.68           => ( P @ A0 @ A1 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_89_remdups__adj_Oinduct,axiom,
% 3.03/1.68      ! [P: list_com > $o,A0: list_com] :
% 3.03/1.68        ( ( P @ nil_com )
% 3.03/1.68       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 3.03/1.68         => ( ! [X3: com,Y3: com,Xs: list_com] :
% 3.03/1.68                ( ( ( X3 = Y3 )
% 3.03/1.68                 => ( P @ ( cons_com @ X3 @ Xs ) ) )
% 3.03/1.68               => ( ( ( X3 != Y3 )
% 3.03/1.68                   => ( P @ ( cons_com @ Y3 @ Xs ) ) )
% 3.03/1.68                 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) )
% 3.03/1.68           => ( P @ A0 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_90_sorted__wrt_Oinduct,axiom,
% 3.03/1.68      ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 3.03/1.68        ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 3.03/1.68       => ( ! [P3: com > com > $o,X3: com,Ys: list_com] :
% 3.03/1.68              ( ( P @ P3 @ Ys )
% 3.03/1.68             => ( P @ P3 @ ( cons_com @ X3 @ Ys ) ) )
% 3.03/1.68         => ( P @ A0 @ A1 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_91_remdups__adj_Ocases,axiom,
% 3.03/1.68      ! [X: list_com] :
% 3.03/1.68        ( ( X != nil_com )
% 3.03/1.68       => ( ! [X3: com] :
% 3.03/1.68              ( X
% 3.03/1.68             != ( cons_com @ X3 @ nil_com ) )
% 3.03/1.68         => ~ ! [X3: com,Y3: com,Xs: list_com] :
% 3.03/1.68                ( X
% 3.03/1.68               != ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_92_transpose_Ocases,axiom,
% 3.03/1.68      ! [X: list_list_com] :
% 3.03/1.68        ( ( X != nil_list_com )
% 3.03/1.68       => ( ! [Xss: list_list_com] :
% 3.03/1.68              ( X
% 3.03/1.68             != ( cons_list_com @ nil_com @ Xss ) )
% 3.03/1.68         => ~ ! [X3: com,Xs: list_com,Xss: list_list_com] :
% 3.03/1.68                ( X
% 3.03/1.68               != ( cons_list_com @ ( cons_com @ X3 @ Xs ) @ Xss ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_93_shuffles_Oinduct,axiom,
% 3.03/1.68      ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 3.03/1.68        ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 3.03/1.68       => ( ! [Xs: list_com] : ( P @ Xs @ nil_com )
% 3.03/1.68         => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 3.03/1.68                ( ( P @ Xs @ ( cons_com @ Y3 @ Ys ) )
% 3.03/1.68               => ( ( P @ ( cons_com @ X3 @ Xs ) @ Ys )
% 3.03/1.68                 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) )
% 3.03/1.68           => ( P @ A0 @ A1 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_94_mem__Collect__eq,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,P: produc410756839_state > $o] :
% 3.03/1.68        ( ( member1069318160_state @ A2 @ ( collec300063826_state @ P ) )
% 3.03/1.68        = ( P @ A2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_95_mem__Collect__eq,axiom,
% 3.03/1.68      ! [A2: state,P: state > $o] :
% 3.03/1.68        ( ( member_state @ A2 @ ( collect_state @ P ) )
% 3.03/1.68        = ( P @ A2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_96_mem__Collect__eq,axiom,
% 3.03/1.68      ! [A2: produc186437863_state,P: produc186437863_state > $o] :
% 3.03/1.68        ( ( member512523024_state @ A2 @ ( collec489924946_state @ P ) )
% 3.03/1.68        = ( P @ A2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_97_Collect__mem__eq,axiom,
% 3.03/1.68      ! [A4: set_Pr1165141447_state] :
% 3.03/1.68        ( ( collec300063826_state
% 3.03/1.68          @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 3.03/1.68        = A4 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_98_Collect__mem__eq,axiom,
% 3.03/1.68      ! [A4: set_state] :
% 3.03/1.68        ( ( collect_state
% 3.03/1.68          @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 3.03/1.68        = A4 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_99_Collect__mem__eq,axiom,
% 3.03/1.68      ! [A4: set_Pr2096893127_state] :
% 3.03/1.68        ( ( collec489924946_state
% 3.03/1.68          @ ^ [X4: produc186437863_state] : ( member512523024_state @ X4 @ A4 ) )
% 3.03/1.68        = A4 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_100_induct__list012,axiom,
% 3.03/1.68      ! [P: list_com > $o,Xs2: list_com] :
% 3.03/1.68        ( ( P @ nil_com )
% 3.03/1.68       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 3.03/1.68         => ( ! [X3: com,Y3: com,Zs: list_com] :
% 3.03/1.68                ( ( P @ Zs )
% 3.03/1.68               => ( ( P @ ( cons_com @ Y3 @ Zs ) )
% 3.03/1.68                 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Zs ) ) ) ) )
% 3.03/1.68           => ( P @ Xs2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_101_splice_Oinduct,axiom,
% 3.03/1.68      ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 3.03/1.68        ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 3.03/1.68       => ( ! [X3: com,Xs: list_com,Ys: list_com] :
% 3.03/1.68              ( ( P @ Ys @ Xs )
% 3.03/1.68             => ( P @ ( cons_com @ X3 @ Xs ) @ Ys ) )
% 3.03/1.68         => ( P @ A0 @ A1 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_102_list__induct2_H,axiom,
% 3.03/1.68      ! [P: list_com > list_com > $o,Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( P @ nil_com @ nil_com )
% 3.03/1.68       => ( ! [X3: com,Xs: list_com] : ( P @ ( cons_com @ X3 @ Xs ) @ nil_com )
% 3.03/1.68         => ( ! [Y3: com,Ys: list_com] : ( P @ nil_com @ ( cons_com @ Y3 @ Ys ) )
% 3.03/1.68           => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 3.03/1.68                  ( ( P @ Xs @ Ys )
% 3.03/1.68                 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) )
% 3.03/1.68             => ( P @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_103_neq__Nil__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com] :
% 3.03/1.68        ( ( Xs2 != nil_com )
% 3.03/1.68        = ( ? [Y4: com,Ys3: list_com] :
% 3.03/1.68              ( Xs2
% 3.03/1.68              = ( cons_com @ Y4 @ Ys3 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_104_list_Oinducts,axiom,
% 3.03/1.68      ! [P: list_com > $o,List: list_com] :
% 3.03/1.68        ( ( P @ nil_com )
% 3.03/1.68       => ( ! [X12: com,X23: list_com] :
% 3.03/1.68              ( ( P @ X23 )
% 3.03/1.68             => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 3.03/1.68         => ( P @ List ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_105_list_Oexhaust,axiom,
% 3.03/1.68      ! [Y: list_com] :
% 3.03/1.68        ( ( Y != nil_com )
% 3.03/1.68       => ~ ! [X212: com,X222: list_com] :
% 3.03/1.68              ( Y
% 3.03/1.68             != ( cons_com @ X212 @ X222 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_106_list_OdiscI,axiom,
% 3.03/1.68      ! [List: list_com,X21: com,X22: list_com] :
% 3.03/1.68        ( ( List
% 3.03/1.68          = ( cons_com @ X21 @ X22 ) )
% 3.03/1.68       => ( List != nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_107_list_Odistinct_I1_J,axiom,
% 3.03/1.68      ! [X21: com,X22: list_com] :
% 3.03/1.68        ( nil_com
% 3.03/1.68       != ( cons_com @ X21 @ X22 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_108_execs_Oinducts,axiom,
% 3.03/1.68      ! [X1: state,X2: list_com,X32: state,P: state > list_com > state > $o] :
% 3.03/1.68        ( ( pHoare259243732_execs @ X1 @ X2 @ X32 )
% 3.03/1.68       => ( ! [S3: state] : ( P @ S3 @ nil_com @ S3 )
% 3.03/1.68         => ( ! [S3: state,C2: com,T3: state,Cs3: list_com,U2: state] :
% 3.03/1.68                ( ( exec @ S3 @ C2 @ T3 )
% 3.03/1.68               => ( ( pHoare259243732_execs @ T3 @ Cs3 @ U2 )
% 3.03/1.68                 => ( ( P @ T3 @ Cs3 @ U2 )
% 3.03/1.68                   => ( P @ S3 @ ( cons_com @ C2 @ Cs3 ) @ U2 ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_109_execs_Osimps,axiom,
% 3.03/1.68      ( pHoare259243732_execs
% 3.03/1.68      = ( ^ [A12: state,A23: list_com,A32: state] :
% 3.03/1.68            ( ? [S4: state] :
% 3.03/1.68                ( ( A12 = S4 )
% 3.03/1.68                & ( A23 = nil_com )
% 3.03/1.68                & ( A32 = S4 ) )
% 3.03/1.68            | ? [S4: state,C3: com,T: state,Cs4: list_com,U3: state] :
% 3.03/1.68                ( ( A12 = S4 )
% 3.03/1.68                & ( A23
% 3.03/1.68                  = ( cons_com @ C3 @ Cs4 ) )
% 3.03/1.68                & ( A32 = U3 )
% 3.03/1.68                & ( exec @ S4 @ C3 @ T )
% 3.03/1.68                & ( pHoare259243732_execs @ T @ Cs4 @ U3 ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_110_execs_Ocases,axiom,
% 3.03/1.68      ! [A1: state,A22: list_com,A33: state] :
% 3.03/1.68        ( ( pHoare259243732_execs @ A1 @ A22 @ A33 )
% 3.03/1.68       => ( ( ( A22 = nil_com )
% 3.03/1.68           => ( A33 != A1 ) )
% 3.03/1.68         => ~ ! [C2: com,T3: state,Cs3: list_com] :
% 3.03/1.68                ( ( A22
% 3.03/1.68                  = ( cons_com @ C2 @ Cs3 ) )
% 3.03/1.68               => ( ( exec @ A1 @ C2 @ T3 )
% 3.03/1.68                 => ~ ( pHoare259243732_execs @ T3 @ Cs3 @ A33 ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_111_converse__rtrancl__into__rtrancl,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 3.03/1.68       => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68         => ( member1069318160_state @ ( produc1909270103_state @ A2 @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_112_converse__rtrancl__into__rtrancl,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 3.03/1.68       => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C ) @ ( transi463013610_state @ R ) )
% 3.03/1.68         => ( member512523024_state @ ( produc2065881943_state @ A2 @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_113_rtrancl_Ortrancl__into__rtrancl,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C ) @ R )
% 3.03/1.68         => ( member1069318160_state @ ( produc1909270103_state @ A2 @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_114_rtrancl_Ortrancl__into__rtrancl,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C ) @ R )
% 3.03/1.68         => ( member512523024_state @ ( produc2065881943_state @ A2 @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_115_converse__rtrancl__induct,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( P @ B2 )
% 3.03/1.68         => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 3.03/1.68               => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68                 => ( ( P @ Z )
% 3.03/1.68                   => ( P @ Y3 ) ) ) )
% 3.03/1.68           => ( P @ A2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_116_converse__rtrancl__induct,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( P @ B2 )
% 3.03/1.68         => ( ! [Y3: produc410756839_state,Z: produc410756839_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z ) @ R )
% 3.03/1.68               => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68                 => ( ( P @ Z )
% 3.03/1.68                   => ( P @ Y3 ) ) ) )
% 3.03/1.68           => ( P @ A2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_117_rtrancl_Ortrancl__refl,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A2 @ A2 ) @ ( transi1302705790_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_118_rtrancl_Ortrancl__refl,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,R: set_Pr2096893127_state] : ( member512523024_state @ ( produc2065881943_state @ A2 @ A2 ) @ ( transi463013610_state @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_119_converse__rtranclE,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( X != Z2 )
% 3.03/1.68         => ~ ! [Y3: produc2041926651_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R )
% 3.03/1.68               => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_120_converse__rtranclE,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( X != Z2 )
% 3.03/1.68         => ~ ! [Y3: produc410756839_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ X @ Y3 ) @ R )
% 3.03/1.68               => ~ ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_121_rtrancl_Oinducts,axiom,
% 3.03/1.68      ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ! [A: produc2041926651_state] : ( P @ A @ A )
% 3.03/1.68         => ( ! [A: produc2041926651_state,B: produc2041926651_state,C2: produc2041926651_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68               => ( ( P @ A @ B )
% 3.03/1.68                 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C2 ) @ R )
% 3.03/1.68                   => ( P @ A @ C2 ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_122_rtrancl_Oinducts,axiom,
% 3.03/1.68      ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ! [A: produc410756839_state] : ( P @ A @ A )
% 3.03/1.68         => ( ! [A: produc410756839_state,B: produc410756839_state,C2: produc410756839_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 3.03/1.68               => ( ( P @ A @ B )
% 3.03/1.68                 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C2 ) @ R )
% 3.03/1.68                   => ( P @ A @ C2 ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_123_rtrancl__induct,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( P @ A2 )
% 3.03/1.68         => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ Y3 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68               => ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 3.03/1.68                 => ( ( P @ Y3 )
% 3.03/1.68                   => ( P @ Z ) ) ) )
% 3.03/1.68           => ( P @ B2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_124_rtrancl__induct,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( P @ A2 )
% 3.03/1.68         => ( ! [Y3: produc410756839_state,Z: produc410756839_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ A2 @ Y3 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68               => ( ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z ) @ R )
% 3.03/1.68                 => ( ( P @ Y3 )
% 3.03/1.68                   => ( P @ Z ) ) ) )
% 3.03/1.68           => ( P @ B2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_125_rtrancl__trans,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68         => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_126_rtrancl__trans,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68         => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_127_rtrancl_Osimps,axiom,
% 3.03/1.68      ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68        = ( ? [A5: produc2041926651_state] :
% 3.03/1.68              ( ( A1 = A5 )
% 3.03/1.68              & ( A22 = A5 ) )
% 3.03/1.68          | ? [A5: produc2041926651_state,B4: produc2041926651_state,C3: produc2041926651_state] :
% 3.03/1.68              ( ( A1 = A5 )
% 3.03/1.68              & ( A22 = C3 )
% 3.03/1.68              & ( member1069318160_state @ ( produc1909270103_state @ A5 @ B4 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68              & ( member1069318160_state @ ( produc1909270103_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_128_rtrancl_Osimps,axiom,
% 3.03/1.68      ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68        = ( ? [A5: produc410756839_state] :
% 3.03/1.68              ( ( A1 = A5 )
% 3.03/1.68              & ( A22 = A5 ) )
% 3.03/1.68          | ? [A5: produc410756839_state,B4: produc410756839_state,C3: produc410756839_state] :
% 3.03/1.68              ( ( A1 = A5 )
% 3.03/1.68              & ( A22 = C3 )
% 3.03/1.68              & ( member512523024_state @ ( produc2065881943_state @ A5 @ B4 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68              & ( member512523024_state @ ( produc2065881943_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_129_rtrancl_Ocases,axiom,
% 3.03/1.68      ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( A22 != A1 )
% 3.03/1.68         => ~ ! [B: produc2041926651_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68               => ~ ( member1069318160_state @ ( produc1909270103_state @ B @ A22 ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_130_rtrancl_Ocases,axiom,
% 3.03/1.68      ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( A22 != A1 )
% 3.03/1.68         => ~ ! [B: produc410756839_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B ) @ ( transi463013610_state @ R ) )
% 3.03/1.68               => ~ ( member512523024_state @ ( produc2065881943_state @ B @ A22 ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_131_rtranclE,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( A2 != B2 )
% 3.03/1.68         => ~ ! [Y3: produc2041926651_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ Y3 ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68               => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ B2 ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_132_rtranclE,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( A2 != B2 )
% 3.03/1.68         => ~ ! [Y3: produc410756839_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ A2 @ Y3 ) @ ( transi463013610_state @ R ) )
% 3.03/1.68               => ~ ( member512523024_state @ ( produc2065881943_state @ Y3 @ B2 ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_133_prod__induct4,axiom,
% 3.03/1.68      ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 3.03/1.68        ( ! [A: produc410756839_state,B: produc2041926651_state,C2: list_com,D: state] : ( P @ ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ ( produc1204172211_state @ C2 @ D ) ) ) )
% 3.03/1.68       => ( P @ X ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_134_prod__induct3,axiom,
% 3.03/1.68      ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 3.03/1.68        ( ! [A: produc2041926651_state,B: list_com,C2: state] : ( P @ ( produc1909270103_state @ A @ ( produc1204172211_state @ B @ C2 ) ) )
% 3.03/1.68       => ( P @ X ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_135_prod__induct3,axiom,
% 3.03/1.68      ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 3.03/1.68        ( ! [A: produc410756839_state,B: produc2041926651_state,C2: produc2041926651_state] : ( P @ ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ C2 ) ) )
% 3.03/1.68       => ( P @ X ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_136_exec1_OSemi,axiom,
% 3.03/1.68      ! [C1: com,C22: com,Cs2: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs2 ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_137_exec1E_I3_J,axiom,
% 3.03/1.68      ! [C1: com,C22: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 3.03/1.68       => ~ ( ( Cs
% 3.03/1.68              = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs2 ) ) )
% 3.03/1.68           => ( S2 != S ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_138_exec1_ODo,axiom,
% 3.03/1.68      ! [T2: state,F2: state > set_state,S: state,Cs2: list_com] :
% 3.03/1.68        ( ( member_state @ T2 @ ( F2 @ S ) )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ T2 ) ) @ pHoare259243666_exec1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_139_exec1E_I2_J,axiom,
% 3.03/1.68      ! [F2: state > set_state,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 3.03/1.68       => ~ ( ( Cs = Cs2 )
% 3.03/1.68           => ~ ( member_state @ S2 @ ( F2 @ S ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_140_exec1_OIfFalse,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C1: com,C22: com,Cs2: list_com] :
% 3.03/1.68        ( ~ ( B2 @ S )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs2 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_141_exec1_OIfTrue,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C1: com,C22: com,Cs2: list_com] :
% 3.03/1.68        ( ( B2 @ S )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs2 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_142_exec1E_I4_J,axiom,
% 3.03/1.68      ! [B2: state > $o,C1: com,C22: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 3.03/1.68       => ( ( ( Cs
% 3.03/1.68              = ( cons_com @ C1 @ Cs2 ) )
% 3.03/1.68           => ( ( S2 = S )
% 3.03/1.68             => ~ ( B2 @ S ) ) )
% 3.03/1.68         => ~ ( ( Cs
% 3.03/1.68                = ( cons_com @ C22 @ Cs2 ) )
% 3.03/1.68             => ( ( S2 = S )
% 3.03/1.68               => ( B2 @ S ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_143_exec1_OWhileFalse,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C: com,Cs2: list_com] :
% 3.03/1.68        ( ~ ( B2 @ S )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_144_exec1_OWhileTrue,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C: com,Cs2: list_com] :
% 3.03/1.68        ( ( B2 @ S )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_145_while__termiE,axiom,
% 3.03/1.68      ! [B2: state > $o,C: com,S: state] :
% 3.03/1.68        ( ( termi @ ( while @ B2 @ C ) @ S )
% 3.03/1.68       => ( ( B2 @ S )
% 3.03/1.68         => ( termi @ C @ S ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_146_while__termiE2,axiom,
% 3.03/1.68      ! [B2: state > $o,C: com,S: state,T2: state] :
% 3.03/1.68        ( ( termi @ ( while @ B2 @ C ) @ S )
% 3.03/1.68       => ( ( B2 @ S )
% 3.03/1.68         => ( ( exec @ S @ C @ T2 )
% 3.03/1.68           => ( termi @ ( while @ B2 @ C ) @ T2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_147_exec1E_I5_J,axiom,
% 3.03/1.68      ! [B2: state > $o,C: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 3.03/1.68       => ( ( ( Cs = Cs2 )
% 3.03/1.68           => ( ( S2 = S )
% 3.03/1.68             => ( B2 @ S ) ) )
% 3.03/1.68         => ~ ( ( Cs
% 3.03/1.68                = ( cons_com @ C @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) ) )
% 3.03/1.68             => ( ( S2 = S )
% 3.03/1.68               => ~ ( B2 @ S ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_148_termi_OSemi,axiom,
% 3.03/1.68      ! [C1: com,S0: state,C22: com] :
% 3.03/1.68        ( ( termi @ C1 @ S0 )
% 3.03/1.68       => ( ! [S1: state] :
% 3.03/1.68              ( ( exec @ S0 @ C1 @ S1 )
% 3.03/1.68             => ( termi @ C22 @ S1 ) )
% 3.03/1.68         => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_149_termi_OWhileTrue,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C: com] :
% 3.03/1.68        ( ( B2 @ S )
% 3.03/1.68       => ( ( termi @ C @ S )
% 3.03/1.68         => ( ! [T3: state] :
% 3.03/1.68                ( ( exec @ S @ C @ T3 )
% 3.03/1.68               => ( termi @ ( while @ B2 @ C ) @ T3 ) )
% 3.03/1.68           => ( termi @ ( while @ B2 @ C ) @ S ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_150_com_Oinject_I2_J,axiom,
% 3.03/1.68      ! [X21: com,X22: com,Y21: com,Y22: com] :
% 3.03/1.68        ( ( ( semi @ X21 @ X22 )
% 3.03/1.68          = ( semi @ Y21 @ Y22 ) )
% 3.03/1.68        = ( ( X21 = Y21 )
% 3.03/1.68          & ( X22 = Y22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_151_com_Oinject_I1_J,axiom,
% 3.03/1.68      ! [X1: state > set_state,Y1: state > set_state] :
% 3.03/1.68        ( ( ( do @ X1 )
% 3.03/1.68          = ( do @ Y1 ) )
% 3.03/1.68        = ( X1 = Y1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_152_com_Oinject_I3_J,axiom,
% 3.03/1.68      ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 3.03/1.68        ( ( ( cond @ X31 @ X322 @ X33 )
% 3.03/1.68          = ( cond @ Y31 @ Y32 @ Y33 ) )
% 3.03/1.68        = ( ( X31 = Y31 )
% 3.03/1.68          & ( X322 = Y32 )
% 3.03/1.68          & ( X33 = Y33 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_153_com_Oinject_I4_J,axiom,
% 3.03/1.68      ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 3.03/1.68        ( ( ( while @ X41 @ X42 )
% 3.03/1.68          = ( while @ Y41 @ Y42 ) )
% 3.03/1.68        = ( ( X41 = Y41 )
% 3.03/1.68          & ( X42 = Y42 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_154_exec_OWhileFalse,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C: com] :
% 3.03/1.68        ( ~ ( B2 @ S )
% 3.03/1.68       => ( exec @ S @ ( while @ B2 @ C ) @ S ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_155_exec_OWhileTrue,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C: com,T2: state,U: state] :
% 3.03/1.68        ( ( B2 @ S )
% 3.03/1.68       => ( ( exec @ S @ C @ T2 )
% 3.03/1.68         => ( ( exec @ T2 @ ( while @ B2 @ C ) @ U )
% 3.03/1.68           => ( exec @ S @ ( while @ B2 @ C ) @ U ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_156_com_Odistinct_I19_J,axiom,
% 3.03/1.68      ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 3.03/1.68        ( ( cond @ X31 @ X322 @ X33 )
% 3.03/1.68       != ( while @ X41 @ X42 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_157_termi_OWhileFalse,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C: com] :
% 3.03/1.68        ( ~ ( B2 @ S )
% 3.03/1.68       => ( termi @ ( while @ B2 @ C ) @ S ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_158_com_Odistinct_I5_J,axiom,
% 3.03/1.68      ! [X1: state > set_state,X41: state > $o,X42: com] :
% 3.03/1.68        ( ( do @ X1 )
% 3.03/1.68       != ( while @ X41 @ X42 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_159_exec_OIfFalse,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C22: com,T2: state,C1: com] :
% 3.03/1.68        ( ~ ( B2 @ S )
% 3.03/1.68       => ( ( exec @ S @ C22 @ T2 )
% 3.03/1.68         => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_160_exec_OIfTrue,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C1: com,T2: state,C22: com] :
% 3.03/1.68        ( ( B2 @ S )
% 3.03/1.68       => ( ( exec @ S @ C1 @ T2 )
% 3.03/1.68         => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_161_com_Odistinct_I13_J,axiom,
% 3.03/1.68      ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 3.03/1.68        ( ( semi @ X21 @ X22 )
% 3.03/1.68       != ( while @ X41 @ X42 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_162_exec_ODo,axiom,
% 3.03/1.68      ! [T2: state,F2: state > set_state,S: state] :
% 3.03/1.68        ( ( member_state @ T2 @ ( F2 @ S ) )
% 3.03/1.68       => ( exec @ S @ ( do @ F2 ) @ T2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_163_exec_OSemi,axiom,
% 3.03/1.68      ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 3.03/1.68        ( ( exec @ S0 @ C1 @ S12 )
% 3.03/1.68       => ( ( exec @ S12 @ C22 @ S22 )
% 3.03/1.68         => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_164_termi_OIfFalse,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C22: com,C1: com] :
% 3.03/1.68        ( ~ ( B2 @ S )
% 3.03/1.68       => ( ( termi @ C22 @ S )
% 3.03/1.68         => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_165_termi_OIfTrue,axiom,
% 3.03/1.68      ! [B2: state > $o,S: state,C1: com,C22: com] :
% 3.03/1.68        ( ( B2 @ S )
% 3.03/1.68       => ( ( termi @ C1 @ S )
% 3.03/1.68         => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_166_com_Odistinct_I3_J,axiom,
% 3.03/1.68      ! [X1: state > set_state,X31: state > $o,X322: com,X33: com] :
% 3.03/1.68        ( ( do @ X1 )
% 3.03/1.68       != ( cond @ X31 @ X322 @ X33 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_167_com_Odistinct_I11_J,axiom,
% 3.03/1.68      ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 3.03/1.68        ( ( semi @ X21 @ X22 )
% 3.03/1.68       != ( cond @ X31 @ X322 @ X33 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_168_com_Odistinct_I1_J,axiom,
% 3.03/1.68      ! [X1: state > set_state,X21: com,X22: com] :
% 3.03/1.68        ( ( do @ X1 )
% 3.03/1.68       != ( semi @ X21 @ X22 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_169_product__lists_Osimps_I1_J,axiom,
% 3.03/1.68      ( ( product_lists_com @ nil_list_com )
% 3.03/1.68      = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_170_subseqs_Osimps_I1_J,axiom,
% 3.03/1.68      ( ( subseqs_com @ nil_com )
% 3.03/1.68      = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_171_app__execs,axiom,
% 3.03/1.68      ! [Cs2: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_172_insert__Nil,axiom,
% 3.03/1.68      ! [X: com] :
% 3.03/1.68        ( ( insert_com @ X @ nil_com )
% 3.03/1.68        = ( cons_com @ X @ nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_173_listrel_Oinducts,axiom,
% 3.03/1.68      ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 3.03/1.68       => ( ( P @ nil_com @ nil_com )
% 3.03/1.68         => ( ! [X3: com,Y3: com,Xs: list_com,Ys: list_com] :
% 3.03/1.68                ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 3.03/1.68               => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) )
% 3.03/1.68                 => ( ( P @ Xs @ Ys )
% 3.03/1.68                   => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_174_listrel_Oinducts,axiom,
% 3.03/1.68      ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 3.03/1.68       => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 3.03/1.68         => ( ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 3.03/1.68                ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 3.03/1.68               => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) )
% 3.03/1.68                 => ( ( P @ Xs @ Ys )
% 3.03/1.68                   => ( P @ ( cons_P465369265_state @ X3 @ Xs ) @ ( cons_P465369265_state @ Y3 @ Ys ) ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_175_listrel_Oinducts,axiom,
% 3.03/1.68      ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 3.03/1.68        ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68       => ( ( P @ nil_list_com @ nil_state )
% 3.03/1.68         => ( ! [X3: list_com,Y3: state,Xs: list_list_com,Ys: list_state] :
% 3.03/1.68                ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 3.03/1.68               => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68                 => ( ( P @ Xs @ Ys )
% 3.03/1.68                   => ( P @ ( cons_list_com @ X3 @ Xs ) @ ( cons_state @ Y3 @ Ys ) ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_176_listrel_Oinducts,axiom,
% 3.03/1.68      ! [X1: list_P890094829_state,X2: list_P890094829_state,R: set_Pr2096893127_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ X1 @ X2 ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68       => ( ( P @ nil_Pr1347322605_state @ nil_Pr1347322605_state )
% 3.03/1.68         => ( ! [X3: produc410756839_state,Y3: produc410756839_state,Xs: list_P890094829_state,Ys: list_P890094829_state] :
% 3.03/1.68                ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 3.03/1.68               => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68                 => ( ( P @ Xs @ Ys )
% 3.03/1.68                   => ( P @ ( cons_P438230685_state @ X3 @ Xs ) @ ( cons_P438230685_state @ Y3 @ Ys ) ) ) ) )
% 3.03/1.68           => ( P @ X1 @ X2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_177_append_Oassoc,axiom,
% 3.03/1.68      ! [A2: list_com,B2: list_com,C: list_com] :
% 3.03/1.68        ( ( append_com @ ( append_com @ A2 @ B2 ) @ C )
% 3.03/1.68        = ( append_com @ A2 @ ( append_com @ B2 @ C ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_178_append__assoc,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( append_com @ ( append_com @ Xs2 @ Ys2 ) @ Zs2 )
% 3.03/1.68        = ( append_com @ Xs2 @ ( append_com @ Ys2 @ Zs2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_179_append__same__eq,axiom,
% 3.03/1.68      ! [Ys2: list_com,Xs2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Ys2 @ Xs2 )
% 3.03/1.68          = ( append_com @ Zs2 @ Xs2 ) )
% 3.03/1.68        = ( Ys2 = Zs2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_180_same__append__eq,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ Ys2 )
% 3.03/1.68          = ( append_com @ Xs2 @ Zs2 ) )
% 3.03/1.68        = ( Ys2 = Zs2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_181_append__Nil2,axiom,
% 3.03/1.68      ! [Xs2: list_com] :
% 3.03/1.68        ( ( append_com @ Xs2 @ nil_com )
% 3.03/1.68        = Xs2 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_182_append__self__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ Ys2 )
% 3.03/1.68          = Xs2 )
% 3.03/1.68        = ( Ys2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_183_self__append__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( Xs2
% 3.03/1.68          = ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68        = ( Ys2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_184_append__self__conv2,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ Ys2 )
% 3.03/1.68          = Ys2 )
% 3.03/1.68        = ( Xs2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_185_self__append__conv2,axiom,
% 3.03/1.68      ! [Ys2: list_com,Xs2: list_com] :
% 3.03/1.68        ( ( Ys2
% 3.03/1.68          = ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68        = ( Xs2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_186_Nil__is__append__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( nil_com
% 3.03/1.68          = ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68        = ( ( Xs2 = nil_com )
% 3.03/1.68          & ( Ys2 = nil_com ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_187_append__is__Nil__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ Ys2 )
% 3.03/1.68          = nil_com )
% 3.03/1.68        = ( ( Xs2 = nil_com )
% 3.03/1.68          & ( Ys2 = nil_com ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_188_append_Oright__neutral,axiom,
% 3.03/1.68      ! [A2: list_com] :
% 3.03/1.68        ( ( append_com @ A2 @ nil_com )
% 3.03/1.68        = A2 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_189_append1__eq__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com,Ys2: list_com,Y: com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) )
% 3.03/1.68          = ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) )
% 3.03/1.68        = ( ( Xs2 = Ys2 )
% 3.03/1.68          & ( X = Y ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_190_listrel__rtrancl__refl,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_191_listrel__rtrancl__refl,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,R: set_Pr2096893127_state] : ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_192_append__Cons,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( append_com @ ( cons_com @ X @ Xs2 ) @ Ys2 )
% 3.03/1.68        = ( cons_com @ X @ ( append_com @ Xs2 @ Ys2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_193_Cons__eq__appendI,axiom,
% 3.03/1.68      ! [X: com,Xs1: list_com,Ys2: list_com,Xs2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( ( cons_com @ X @ Xs1 )
% 3.03/1.68          = Ys2 )
% 3.03/1.68       => ( ( Xs2
% 3.03/1.68            = ( append_com @ Xs1 @ Zs2 ) )
% 3.03/1.68         => ( ( cons_com @ X @ Xs2 )
% 3.03/1.68            = ( append_com @ Ys2 @ Zs2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_194_append_Oleft__neutral,axiom,
% 3.03/1.68      ! [A2: list_com] :
% 3.03/1.68        ( ( append_com @ nil_com @ A2 )
% 3.03/1.68        = A2 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_195_append__Nil,axiom,
% 3.03/1.68      ! [Ys2: list_com] :
% 3.03/1.68        ( ( append_com @ nil_com @ Ys2 )
% 3.03/1.68        = Ys2 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_196_eq__Nil__appendI,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( Xs2 = Ys2 )
% 3.03/1.68       => ( Xs2
% 3.03/1.68          = ( append_com @ nil_com @ Ys2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_197_append__eq__appendI,axiom,
% 3.03/1.68      ! [Xs2: list_com,Xs1: list_com,Zs2: list_com,Ys2: list_com,Us: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ Xs1 )
% 3.03/1.68          = Zs2 )
% 3.03/1.68       => ( ( Ys2
% 3.03/1.68            = ( append_com @ Xs1 @ Us ) )
% 3.03/1.68         => ( ( append_com @ Xs2 @ Ys2 )
% 3.03/1.68            = ( append_com @ Zs2 @ Us ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_198_append__eq__append__conv2,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com,Ts: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ Ys2 )
% 3.03/1.68          = ( append_com @ Zs2 @ Ts ) )
% 3.03/1.68        = ( ? [Us2: list_com] :
% 3.03/1.68              ( ( ( Xs2
% 3.03/1.68                  = ( append_com @ Zs2 @ Us2 ) )
% 3.03/1.68                & ( ( append_com @ Us2 @ Ys2 )
% 3.03/1.68                  = Ts ) )
% 3.03/1.68              | ( ( ( append_com @ Xs2 @ Us2 )
% 3.03/1.68                  = Zs2 )
% 3.03/1.68                & ( Ys2
% 3.03/1.68                  = ( append_com @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_199_rev__induct,axiom,
% 3.03/1.68      ! [P: list_com > $o,Xs2: list_com] :
% 3.03/1.68        ( ( P @ nil_com )
% 3.03/1.68       => ( ! [X3: com,Xs: list_com] :
% 3.03/1.68              ( ( P @ Xs )
% 3.03/1.68             => ( P @ ( append_com @ Xs @ ( cons_com @ X3 @ nil_com ) ) ) )
% 3.03/1.68         => ( P @ Xs2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_200_rev__exhaust,axiom,
% 3.03/1.68      ! [Xs2: list_com] :
% 3.03/1.68        ( ( Xs2 != nil_com )
% 3.03/1.68       => ~ ! [Ys: list_com,Y3: com] :
% 3.03/1.68              ( Xs2
% 3.03/1.68             != ( append_com @ Ys @ ( cons_com @ Y3 @ nil_com ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_201_Cons__eq__append__conv,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( ( cons_com @ X @ Xs2 )
% 3.03/1.68          = ( append_com @ Ys2 @ Zs2 ) )
% 3.03/1.68        = ( ( ( Ys2 = nil_com )
% 3.03/1.68            & ( ( cons_com @ X @ Xs2 )
% 3.03/1.68              = Zs2 ) )
% 3.03/1.68          | ? [Ys4: list_com] :
% 3.03/1.68              ( ( ( cons_com @ X @ Ys4 )
% 3.03/1.68                = Ys2 )
% 3.03/1.68              & ( Xs2
% 3.03/1.68                = ( append_com @ Ys4 @ Zs2 ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_202_append__eq__Cons__conv,axiom,
% 3.03/1.68      ! [Ys2: list_com,Zs2: list_com,X: com,Xs2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Ys2 @ Zs2 )
% 3.03/1.68          = ( cons_com @ X @ Xs2 ) )
% 3.03/1.68        = ( ( ( Ys2 = nil_com )
% 3.03/1.68            & ( Zs2
% 3.03/1.68              = ( cons_com @ X @ Xs2 ) ) )
% 3.03/1.68          | ? [Ys4: list_com] :
% 3.03/1.68              ( ( Ys2
% 3.03/1.68                = ( cons_com @ X @ Ys4 ) )
% 3.03/1.68              & ( ( append_com @ Ys4 @ Zs2 )
% 3.03/1.68                = Xs2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_203_rev__nonempty__induct,axiom,
% 3.03/1.68      ! [Xs2: list_com,P: list_com > $o] :
% 3.03/1.68        ( ( Xs2 != nil_com )
% 3.03/1.68       => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 3.03/1.68         => ( ! [X3: com,Xs: list_com] :
% 3.03/1.68                ( ( Xs != nil_com )
% 3.03/1.68               => ( ( P @ Xs )
% 3.03/1.68                 => ( P @ ( append_com @ Xs @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 3.03/1.68           => ( P @ Xs2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_204_listrel__Nil2,axiom,
% 3.03/1.68      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( listrel_com_com @ R ) )
% 3.03/1.68       => ( Xs2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_205_listrel__Nil1,axiom,
% 3.03/1.68      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs2 ) @ ( listrel_com_com @ R ) )
% 3.03/1.68       => ( Xs2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_206_listrel_ONil,axiom,
% 3.03/1.68      ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_207_listrel__rtrancl__trans,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state,Zs2: list_P1040014977_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 3.03/1.68       => ( ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 3.03/1.68         => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_208_listrel__rtrancl__trans,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state,Zs2: list_P890094829_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 3.03/1.68       => ( ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 3.03/1.68         => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_209_listrel_OCons,axiom,
% 3.03/1.68      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 3.03/1.68       => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel_com_com @ R ) )
% 3.03/1.68         => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_210_listrel_OCons,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 3.03/1.68       => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) )
% 3.03/1.68         => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_211_listrel_OCons,axiom,
% 3.03/1.68      ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs2: list_list_com,Ys2: list_state] :
% 3.03/1.68        ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 3.03/1.68       => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68         => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs2 ) @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_212_listrel_OCons,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 3.03/1.68       => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68         => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_213_listrel__Cons1,axiom,
% 3.03/1.68      ! [Y: com,Ys2: list_com,Xs2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys2 ) @ Xs2 ) @ ( listrel_com_com @ R ) )
% 3.03/1.68       => ~ ! [Y3: com,Ys: list_com] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_com @ Y3 @ Ys ) )
% 3.03/1.68             => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y3 ) @ R )
% 3.03/1.68               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_214_listrel__Cons1,axiom,
% 3.03/1.68      ! [Y: produc2041926651_state,Ys2: list_P1040014977_state,Xs2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys2 ) @ Xs2 ) @ ( listre194873521_state @ R ) )
% 3.03/1.68       => ~ ! [Y3: produc2041926651_state,Ys: list_P1040014977_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_P465369265_state @ Y3 @ Ys ) )
% 3.03/1.68             => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y3 ) @ R )
% 3.03/1.68               => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_215_listrel__Cons1,axiom,
% 3.03/1.68      ! [Y: list_com,Ys2: list_list_com,Xs2: list_state,R: set_Pr849496667_state] :
% 3.03/1.68        ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys2 ) @ Xs2 ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68       => ~ ! [Y3: state,Ys: list_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_state @ Y3 @ Ys ) )
% 3.03/1.68             => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y3 ) @ R )
% 3.03/1.68               => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys2 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_216_listrel__Cons1,axiom,
% 3.03/1.68      ! [Y: produc410756839_state,Ys2: list_P890094829_state,Xs2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ Y @ Ys2 ) @ Xs2 ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68       => ~ ! [Y3: produc410756839_state,Ys: list_P890094829_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_P438230685_state @ Y3 @ Ys ) )
% 3.03/1.68             => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Y3 ) @ R )
% 3.03/1.68               => ~ ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_217_listrel__Cons2,axiom,
% 3.03/1.68      ! [Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) )
% 3.03/1.68       => ~ ! [X3: com,Xs: list_com] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_com @ X3 @ Xs ) )
% 3.03/1.68             => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 3.03/1.68               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_218_listrel__Cons2,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) )
% 3.03/1.68       => ~ ! [X3: produc2041926651_state,Xs: list_P1040014977_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_P465369265_state @ X3 @ Xs ) )
% 3.03/1.68             => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 3.03/1.68               => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_219_listrel__Cons2,axiom,
% 3.03/1.68      ! [Xs2: list_list_com,Y: state,Ys2: list_state,R: set_Pr849496667_state] :
% 3.03/1.68        ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68       => ~ ! [X3: list_com,Xs: list_list_com] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_list_com @ X3 @ Xs ) )
% 3.03/1.68             => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 3.03/1.68               => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys2 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_220_listrel__Cons2,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68       => ~ ! [X3: produc410756839_state,Xs: list_P890094829_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_P438230685_state @ X3 @ Xs ) )
% 3.03/1.68             => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R )
% 3.03/1.68               => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_221_app__exec,axiom,
% 3.03/1.68      ! [Cs2: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 3.03/1.68       => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_222_listrel_Ocases,axiom,
% 3.03/1.68      ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 3.03/1.68       => ( ( ( A1 = nil_com )
% 3.03/1.68           => ( A22 != nil_com ) )
% 3.03/1.68         => ~ ! [X3: com,Y3: com,Xs: list_com] :
% 3.03/1.68                ( ( A1
% 3.03/1.68                  = ( cons_com @ X3 @ Xs ) )
% 3.03/1.68               => ! [Ys: list_com] :
% 3.03/1.68                    ( ( A22
% 3.03/1.68                      = ( cons_com @ Y3 @ Ys ) )
% 3.03/1.68                   => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 3.03/1.68                     => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_223_listrel_Ocases,axiom,
% 3.03/1.68      ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 3.03/1.68       => ( ( ( A1 = nil_Pr1844458753_state )
% 3.03/1.68           => ( A22 != nil_Pr1844458753_state ) )
% 3.03/1.68         => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs: list_P1040014977_state] :
% 3.03/1.68                ( ( A1
% 3.03/1.68                  = ( cons_P465369265_state @ X3 @ Xs ) )
% 3.03/1.68               => ! [Ys: list_P1040014977_state] :
% 3.03/1.68                    ( ( A22
% 3.03/1.68                      = ( cons_P465369265_state @ Y3 @ Ys ) )
% 3.03/1.68                   => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 3.03/1.68                     => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_224_listrel_Ocases,axiom,
% 3.03/1.68      ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 3.03/1.68        ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68       => ( ( ( A1 = nil_list_com )
% 3.03/1.68           => ( A22 != nil_state ) )
% 3.03/1.68         => ~ ! [X3: list_com,Y3: state,Xs: list_list_com] :
% 3.03/1.68                ( ( A1
% 3.03/1.68                  = ( cons_list_com @ X3 @ Xs ) )
% 3.03/1.68               => ! [Ys: list_state] :
% 3.03/1.68                    ( ( A22
% 3.03/1.68                      = ( cons_state @ Y3 @ Ys ) )
% 3.03/1.68                   => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 3.03/1.68                     => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_225_listrel_Ocases,axiom,
% 3.03/1.68      ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68       => ( ( ( A1 = nil_Pr1347322605_state )
% 3.03/1.68           => ( A22 != nil_Pr1347322605_state ) )
% 3.03/1.68         => ~ ! [X3: produc410756839_state,Y3: produc410756839_state,Xs: list_P890094829_state] :
% 3.03/1.68                ( ( A1
% 3.03/1.68                  = ( cons_P438230685_state @ X3 @ Xs ) )
% 3.03/1.68               => ! [Ys: list_P890094829_state] :
% 3.03/1.68                    ( ( A22
% 3.03/1.68                      = ( cons_P438230685_state @ Y3 @ Ys ) )
% 3.03/1.68                   => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 3.03/1.68                     => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_226_listrel_Osimps,axiom,
% 3.03/1.68      ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 3.03/1.68        = ( ( ( A1 = nil_com )
% 3.03/1.68            & ( A22 = nil_com ) )
% 3.03/1.68          | ? [X4: com,Y4: com,Xs3: list_com,Ys3: list_com] :
% 3.03/1.68              ( ( A1
% 3.03/1.68                = ( cons_com @ X4 @ Xs3 ) )
% 3.03/1.68              & ( A22
% 3.03/1.68                = ( cons_com @ Y4 @ Ys3 ) )
% 3.03/1.68              & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y4 ) @ R )
% 3.03/1.68              & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_227_listrel_Osimps,axiom,
% 3.03/1.68      ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 3.03/1.68        = ( ( ( A1 = nil_Pr1844458753_state )
% 3.03/1.68            & ( A22 = nil_Pr1844458753_state ) )
% 3.03/1.68          | ? [X4: produc2041926651_state,Y4: produc2041926651_state,Xs3: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 3.03/1.68              ( ( A1
% 3.03/1.68                = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 3.03/1.68              & ( A22
% 3.03/1.68                = ( cons_P465369265_state @ Y4 @ Ys3 ) )
% 3.03/1.68              & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y4 ) @ R )
% 3.03/1.68              & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_228_listrel_Osimps,axiom,
% 3.03/1.68      ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 3.03/1.68        ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 3.03/1.68        = ( ( ( A1 = nil_list_com )
% 3.03/1.68            & ( A22 = nil_state ) )
% 3.03/1.68          | ? [X4: list_com,Y4: state,Xs3: list_list_com,Ys3: list_state] :
% 3.03/1.68              ( ( A1
% 3.03/1.68                = ( cons_list_com @ X4 @ Xs3 ) )
% 3.03/1.68              & ( A22
% 3.03/1.68                = ( cons_state @ Y4 @ Ys3 ) )
% 3.03/1.68              & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y4 ) @ R )
% 3.03/1.68              & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_229_listrel_Osimps,axiom,
% 3.03/1.68      ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 3.03/1.68        = ( ( ( A1 = nil_Pr1347322605_state )
% 3.03/1.68            & ( A22 = nil_Pr1347322605_state ) )
% 3.03/1.68          | ? [X4: produc410756839_state,Y4: produc410756839_state,Xs3: list_P890094829_state,Ys3: list_P890094829_state] :
% 3.03/1.68              ( ( A1
% 3.03/1.68                = ( cons_P438230685_state @ X4 @ Xs3 ) )
% 3.03/1.68              & ( A22
% 3.03/1.68                = ( cons_P438230685_state @ Y4 @ Ys3 ) )
% 3.03/1.68              & ( member512523024_state @ ( produc2065881943_state @ X4 @ Y4 ) @ R )
% 3.03/1.68              & ( member423306384_state @ ( produc1354769367_state @ Xs3 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_230_bind__simps_I2_J,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com,F2: com > list_com] :
% 3.03/1.68        ( ( bind_com_com @ ( cons_com @ X @ Xs2 ) @ F2 )
% 3.03/1.68        = ( append_com @ ( F2 @ X ) @ ( bind_com_com @ Xs2 @ F2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_231_snoc__listrel1__snoc__iff,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com,Ys2: list_com,Y: com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 3.03/1.68        = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 3.03/1.68            & ( X = Y ) )
% 3.03/1.68          | ( ( Xs2 = Ys2 )
% 3.03/1.68            & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_232_snoc__listrel1__snoc__iff,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,X: produc2041926651_state,Ys2: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys2 @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68        = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68            & ( X = Y ) )
% 3.03/1.68          | ( ( Xs2 = Ys2 )
% 3.03/1.68            & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_233_snoc__listrel1__snoc__iff,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,X: produc410756839_state,Ys2: list_P890094829_state,Y: produc410756839_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ ( cons_P438230685_state @ X @ nil_Pr1347322605_state ) ) @ ( append221843330_state @ Ys2 @ ( cons_P438230685_state @ Y @ nil_Pr1347322605_state ) ) ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68        = ( ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68            & ( X = Y ) )
% 3.03/1.68          | ( ( Xs2 = Ys2 )
% 3.03/1.68            & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_234_maps__simps_I1_J,axiom,
% 3.03/1.68      ! [F2: com > list_com,X: com,Xs2: list_com] :
% 3.03/1.68        ( ( maps_com_com @ F2 @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68        = ( append_com @ ( F2 @ X ) @ ( maps_com_com @ F2 @ Xs2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_235_concat__eq__append__conv,axiom,
% 3.03/1.68      ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( ( concat_com @ Xss2 )
% 3.03/1.68          = ( append_com @ Ys2 @ Zs2 ) )
% 3.03/1.68        = ( ( ( Xss2 = nil_list_com )
% 3.03/1.68           => ( ( Ys2 = nil_com )
% 3.03/1.68              & ( Zs2 = nil_com ) ) )
% 3.03/1.68          & ( ( Xss2 != nil_list_com )
% 3.03/1.68           => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 3.03/1.68                ( ( Xss2
% 3.03/1.68                  = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 3.03/1.68                & ( Ys2
% 3.03/1.68                  = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 3.03/1.68                & ( Zs2
% 3.03/1.68                  = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_236_bind__simps_I1_J,axiom,
% 3.03/1.68      ! [F2: com > list_com] :
% 3.03/1.68        ( ( bind_com_com @ nil_com @ F2 )
% 3.03/1.68        = nil_com ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_237_concat__append,axiom,
% 3.03/1.68      ! [Xs2: list_list_com,Ys2: list_list_com] :
% 3.03/1.68        ( ( concat_com @ ( append_list_com @ Xs2 @ Ys2 ) )
% 3.03/1.68        = ( append_com @ ( concat_com @ Xs2 ) @ ( concat_com @ Ys2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_238_Cons__listrel1__Cons,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 3.03/1.68        = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 3.03/1.68            & ( Xs2 = Ys2 ) )
% 3.03/1.68          | ( ( X = Y )
% 3.03/1.68            & ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_239_Cons__listrel1__Cons,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68        = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 3.03/1.68            & ( Xs2 = Ys2 ) )
% 3.03/1.68          | ( ( X = Y )
% 3.03/1.68            & ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_240_Cons__listrel1__Cons,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68        = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 3.03/1.68            & ( Xs2 = Ys2 ) )
% 3.03/1.68          | ( ( X = Y )
% 3.03/1.68            & ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_241_listrel1I2,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ X @ Ys2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_242_rtrancl__listrel1__ConsI1,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ X @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_243_not__Nil__listrel1,axiom,
% 3.03/1.68      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs2 ) @ ( listrel1_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_244_not__listrel1__Nil,axiom,
% 3.03/1.68      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_245_append__listrel1I,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Us: list_com,Vs: list_com] :
% 3.03/1.68        ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 3.03/1.68            & ( Us = Vs ) )
% 3.03/1.68          | ( ( Xs2 = Ys2 )
% 3.03/1.68            & ( member32358020st_com @ ( produc1307105171st_com @ Us @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Us ) @ ( append_com @ Ys2 @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_246_concat_Osimps_I1_J,axiom,
% 3.03/1.68      ( ( concat_com @ nil_list_com )
% 3.03/1.68      = nil_com ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_247_concat_Osimps_I2_J,axiom,
% 3.03/1.68      ! [X: list_com,Xs2: list_list_com] :
% 3.03/1.68        ( ( concat_com @ ( cons_list_com @ X @ Xs2 ) )
% 3.03/1.68        = ( append_com @ X @ ( concat_com @ Xs2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_248_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 3.03/1.68        = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_249_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( listre1244407729_state @ ( transi463013610_state @ R ) )
% 3.03/1.68        = ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_250_maps__simps_I2_J,axiom,
% 3.03/1.68      ! [F2: com > list_com] :
% 3.03/1.68        ( ( maps_com_com @ F2 @ nil_com )
% 3.03/1.68        = nil_com ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_251_Cons__listrel1E2,axiom,
% 3.03/1.68      ! [Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 3.03/1.68       => ( ! [X3: com] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_com @ X3 @ Ys2 ) )
% 3.03/1.68             => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 3.03/1.68         => ~ ! [Zs: list_com] :
% 3.03/1.68                ( ( Xs2
% 3.03/1.68                  = ( cons_com @ Y @ Zs ) )
% 3.03/1.68               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_252_Cons__listrel1E2,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68       => ( ! [X3: produc2041926651_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_P465369265_state @ X3 @ Ys2 ) )
% 3.03/1.68             => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 3.03/1.68         => ~ ! [Zs: list_P1040014977_state] :
% 3.03/1.68                ( ( Xs2
% 3.03/1.68                  = ( cons_P465369265_state @ Y @ Zs ) )
% 3.03/1.68               => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_253_Cons__listrel1E2,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68       => ( ! [X3: produc410756839_state] :
% 3.03/1.68              ( ( Xs2
% 3.03/1.68                = ( cons_P438230685_state @ X3 @ Ys2 ) )
% 3.03/1.68             => ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R ) )
% 3.03/1.68         => ~ ! [Zs: list_P890094829_state] :
% 3.03/1.68                ( ( Xs2
% 3.03/1.68                  = ( cons_P438230685_state @ Y @ Zs ) )
% 3.03/1.68               => ~ ( member423306384_state @ ( produc1354769367_state @ Zs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_254_Cons__listrel1E1,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ Ys2 ) @ ( listrel1_com @ R ) )
% 3.03/1.68       => ( ! [Y3: com] :
% 3.03/1.68              ( ( Ys2
% 3.03/1.68                = ( cons_com @ Y3 @ Xs2 ) )
% 3.03/1.68             => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y3 ) @ R ) )
% 3.03/1.68         => ~ ! [Zs: list_com] :
% 3.03/1.68                ( ( Ys2
% 3.03/1.68                  = ( cons_com @ X @ Zs ) )
% 3.03/1.68               => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Zs ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_255_Cons__listrel1E1,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68       => ( ! [Y3: produc2041926651_state] :
% 3.03/1.68              ( ( Ys2
% 3.03/1.68                = ( cons_P465369265_state @ Y3 @ Xs2 ) )
% 3.03/1.68             => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R ) )
% 3.03/1.68         => ~ ! [Zs: list_P1040014977_state] :
% 3.03/1.68                ( ( Ys2
% 3.03/1.68                  = ( cons_P465369265_state @ X @ Zs ) )
% 3.03/1.68               => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Zs ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_256_Cons__listrel1E1,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68       => ( ! [Y3: produc410756839_state] :
% 3.03/1.68              ( ( Ys2
% 3.03/1.68                = ( cons_P438230685_state @ Y3 @ Xs2 ) )
% 3.03/1.68             => ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y3 ) @ R ) )
% 3.03/1.68         => ~ ! [Zs: list_P890094829_state] :
% 3.03/1.68                ( ( Ys2
% 3.03/1.68                  = ( cons_P438230685_state @ X @ Zs ) )
% 3.03/1.68               => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Zs ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_257_listrel1I1,axiom,
% 3.03/1.68      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com] :
% 3.03/1.68        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Xs2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_258_listrel1I1,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 3.03/1.68       => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Xs2 ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_259_listrel1I1,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 3.03/1.68       => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Xs2 ) ) @ ( listre1725776070_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_260_listrel__reflcl__if__listrel1,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68       => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_261_listrel__reflcl__if__listrel1,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68       => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_262_concat__eq__appendD,axiom,
% 3.03/1.68      ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( ( concat_com @ Xss2 )
% 3.03/1.68          = ( append_com @ Ys2 @ Zs2 ) )
% 3.03/1.68       => ( ( Xss2 != nil_list_com )
% 3.03/1.68         => ? [Xss12: list_list_com,Xs: list_com,Xs5: list_com,Xss23: list_list_com] :
% 3.03/1.68              ( ( Xss2
% 3.03/1.68                = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs @ Xs5 ) @ Xss23 ) ) )
% 3.03/1.68              & ( Ys2
% 3.03/1.68                = ( append_com @ ( concat_com @ Xss12 ) @ Xs ) )
% 3.03/1.68              & ( Zs2
% 3.03/1.68                = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_263_listrel1I,axiom,
% 3.03/1.68      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Us: list_com,Vs: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 3.03/1.68       => ( ( Xs2
% 3.03/1.68            = ( append_com @ Us @ ( cons_com @ X @ Vs ) ) )
% 3.03/1.68         => ( ( Ys2
% 3.03/1.68              = ( append_com @ Us @ ( cons_com @ Y @ Vs ) ) )
% 3.03/1.68           => ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_264_listrel1I,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Us: list_P1040014977_state,Vs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 3.03/1.68       => ( ( Xs2
% 3.03/1.68            = ( append982487830_state @ Us @ ( cons_P465369265_state @ X @ Vs ) ) )
% 3.03/1.68         => ( ( Ys2
% 3.03/1.68              = ( append982487830_state @ Us @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 3.03/1.68           => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_265_listrel1I,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Us: list_P890094829_state,Vs: list_P890094829_state,Ys2: list_P890094829_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 3.03/1.68       => ( ( Xs2
% 3.03/1.68            = ( append221843330_state @ Us @ ( cons_P438230685_state @ X @ Vs ) ) )
% 3.03/1.68         => ( ( Ys2
% 3.03/1.68              = ( append221843330_state @ Us @ ( cons_P438230685_state @ Y @ Vs ) ) )
% 3.03/1.68           => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_266_listrel1E,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 3.03/1.68       => ~ ! [X3: com,Y3: com] :
% 3.03/1.68              ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 3.03/1.68             => ! [Us3: list_com,Vs2: list_com] :
% 3.03/1.68                  ( ( Xs2
% 3.03/1.68                    = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 3.03/1.68                 => ( Ys2
% 3.03/1.68                   != ( append_com @ Us3 @ ( cons_com @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_267_listrel1E,axiom,
% 3.03/1.68      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 3.03/1.68       => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 3.03/1.68              ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 3.03/1.68             => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 3.03/1.68                  ( ( Xs2
% 3.03/1.68                    = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 3.03/1.68                 => ( Ys2
% 3.03/1.68                   != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_268_listrel1E,axiom,
% 3.03/1.68      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 3.03/1.68       => ~ ! [X3: produc410756839_state,Y3: produc410756839_state] :
% 3.03/1.68              ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 3.03/1.68             => ! [Us3: list_P890094829_state,Vs2: list_P890094829_state] :
% 3.03/1.68                  ( ( Xs2
% 3.03/1.68                    = ( append221843330_state @ Us3 @ ( cons_P438230685_state @ X3 @ Vs2 ) ) )
% 3.03/1.68                 => ( Ys2
% 3.03/1.68                   != ( append221843330_state @ Us3 @ ( cons_P438230685_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_269_rtrancl__listrel1__ConsI2,axiom,
% 3.03/1.68      ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 3.03/1.68       => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 3.03/1.68         => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_270_rtrancl__listrel1__ConsI2,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 3.03/1.68       => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 3.03/1.68         => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_271_rtrancl__listrel1__ConsI2,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 3.03/1.68       => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) )
% 3.03/1.68         => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_272_lexord__append__left__rightI,axiom,
% 3.03/1.68      ! [A2: com,B2: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 3.03/1.68        ( ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ B2 ) @ R )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A2 @ X ) ) @ ( append_com @ U @ ( cons_com @ B2 @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_273_lexord__append__left__rightI,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 3.03/1.68        ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 3.03/1.68       => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A2 @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B2 @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_274_lexord__append__left__rightI,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,U: list_P890094829_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 3.03/1.68        ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 3.03/1.68       => ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ U @ ( cons_P438230685_state @ A2 @ X ) ) @ ( append221843330_state @ U @ ( cons_P438230685_state @ B2 @ Y ) ) ) @ ( lexord1893203674_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_275_rotate1_Osimps_I2_J,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com] :
% 3.03/1.68        ( ( rotate1_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68        = ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_276_butlast__snoc,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com] :
% 3.03/1.68        ( ( butlast_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) )
% 3.03/1.68        = Xs2 ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_277_rotate1__is__Nil__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com] :
% 3.03/1.68        ( ( ( rotate1_com @ Xs2 )
% 3.03/1.68          = nil_com )
% 3.03/1.68        = ( Xs2 = nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_278_lexord__cons__cons,axiom,
% 3.03/1.68      ! [A2: com,X: list_com,B2: com,Y: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A2 @ X ) @ ( cons_com @ B2 @ Y ) ) @ ( lexord_com @ R ) )
% 3.03/1.68        = ( ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ B2 ) @ R )
% 3.03/1.68          | ( ( A2 = B2 )
% 3.03/1.68            & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_279_lexord__cons__cons,axiom,
% 3.03/1.68      ! [A2: produc2041926651_state,X: list_P1040014977_state,B2: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A2 @ X ) @ ( cons_P465369265_state @ B2 @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 3.03/1.68        = ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 3.03/1.68          | ( ( A2 = B2 )
% 3.03/1.68            & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_280_lexord__cons__cons,axiom,
% 3.03/1.68      ! [A2: produc410756839_state,X: list_P890094829_state,B2: produc410756839_state,Y: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ A2 @ X ) @ ( cons_P438230685_state @ B2 @ Y ) ) @ ( lexord1893203674_state @ R ) )
% 3.03/1.68        = ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 3.03/1.68          | ( ( A2 = B2 )
% 3.03/1.68            & ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_281_lexord__Nil__left,axiom,
% 3.03/1.68      ! [Y: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 3.03/1.68        = ( ? [A5: com,X4: list_com] :
% 3.03/1.68              ( Y
% 3.03/1.68              = ( cons_com @ A5 @ X4 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_282_butlast_Osimps_I1_J,axiom,
% 3.03/1.68      ( ( butlast_com @ nil_com )
% 3.03/1.68      = nil_com ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_283_rotate1_Osimps_I1_J,axiom,
% 3.03/1.68      ( ( rotate1_com @ nil_com )
% 3.03/1.68      = nil_com ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_284_lexord__linear,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 3.03/1.68        ( ! [A: produc2041926651_state,B: produc2041926651_state] :
% 3.03/1.68            ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 3.03/1.68            | ( A = B )
% 3.03/1.68            | ( member1069318160_state @ ( produc1909270103_state @ B @ A ) @ R ) )
% 3.03/1.68       => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 3.03/1.68          | ( X = Y )
% 3.03/1.68          | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_285_lexord__linear,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 3.03/1.68        ( ! [A: produc410756839_state,B: produc410756839_state] :
% 3.03/1.68            ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 3.03/1.68            | ( A = B )
% 3.03/1.68            | ( member512523024_state @ ( produc2065881943_state @ B @ A ) @ R ) )
% 3.03/1.68       => ( ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) )
% 3.03/1.68          | ( X = Y )
% 3.03/1.68          | ( member423306384_state @ ( produc1354769367_state @ Y @ X ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_286_lexord__irreflexive,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 3.03/1.68        ( ! [X3: produc2041926651_state] :
% 3.03/1.68            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( lexord1062073966_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_287_lexord__irreflexive,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 3.03/1.68        ( ! [X3: produc410756839_state] :
% 3.03/1.68            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( lexord1893203674_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_288_butlast_Osimps_I2_J,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com] :
% 3.03/1.68        ( ( ( Xs2 = nil_com )
% 3.03/1.68         => ( ( butlast_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68            = nil_com ) )
% 3.03/1.68        & ( ( Xs2 != nil_com )
% 3.03/1.68         => ( ( butlast_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68            = ( cons_com @ X @ ( butlast_com @ Xs2 ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_289_lexord__Nil__right,axiom,
% 3.03/1.68      ! [X: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_290_butlast__append,axiom,
% 3.03/1.68      ! [Ys2: list_com,Xs2: list_com] :
% 3.03/1.68        ( ( ( Ys2 = nil_com )
% 3.03/1.68         => ( ( butlast_com @ ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68            = ( butlast_com @ Xs2 ) ) )
% 3.03/1.68        & ( ( Ys2 != nil_com )
% 3.03/1.68         => ( ( butlast_com @ ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68            = ( append_com @ Xs2 @ ( butlast_com @ Ys2 ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_291_lexord__append__leftI,axiom,
% 3.03/1.68      ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_292_lexord__append__leftD,axiom,
% 3.03/1.68      ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 3.03/1.68       => ( ! [A: com] :
% 3.03/1.68              ~ ( member1333916004om_com @ ( product_Pair_com_com @ A @ A ) @ R )
% 3.03/1.68         => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_293_lexord__append__leftD,axiom,
% 3.03/1.68      ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 3.03/1.68       => ( ! [A: produc2041926651_state] :
% 3.03/1.68              ~ ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ R )
% 3.03/1.68         => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_294_lexord__append__leftD,axiom,
% 3.03/1.68      ! [X: list_P890094829_state,U: list_P890094829_state,V: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ X @ U ) @ ( append221843330_state @ X @ V ) ) @ ( lexord1893203674_state @ R ) )
% 3.03/1.68       => ( ! [A: produc410756839_state] :
% 3.03/1.68              ~ ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ R )
% 3.03/1.68         => ( member423306384_state @ ( produc1354769367_state @ U @ V ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_295_lexord__append__rightI,axiom,
% 3.03/1.68      ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ? [B5: com,Z3: list_com] :
% 3.03/1.68            ( Y
% 3.03/1.68            = ( cons_com @ B5 @ Z3 ) )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_296_lexord__same__pref__if__irrefl,axiom,
% 3.03/1.68      ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ( irrefl_com @ R )
% 3.03/1.68       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lexord_com @ R ) )
% 3.03/1.68          = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lexord_com @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_297_append__butlast__last__id,axiom,
% 3.03/1.68      ! [Xs2: list_com] :
% 3.03/1.68        ( ( Xs2 != nil_com )
% 3.03/1.68       => ( ( append_com @ ( butlast_com @ Xs2 ) @ ( cons_com @ ( last_com @ Xs2 ) @ nil_com ) )
% 3.03/1.68          = Xs2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_298_snoc__eq__iff__butlast,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com,Ys2: list_com] :
% 3.03/1.68        ( ( ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) )
% 3.03/1.68          = Ys2 )
% 3.03/1.68        = ( ( Ys2 != nil_com )
% 3.03/1.68          & ( ( butlast_com @ Ys2 )
% 3.03/1.68            = Xs2 )
% 3.03/1.68          & ( ( last_com @ Ys2 )
% 3.03/1.68            = X ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_299_last__appendR,axiom,
% 3.03/1.68      ! [Ys2: list_com,Xs2: list_com] :
% 3.03/1.68        ( ( Ys2 != nil_com )
% 3.03/1.68       => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68          = ( last_com @ Ys2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_300_last__appendL,axiom,
% 3.03/1.68      ! [Ys2: list_com,Xs2: list_com] :
% 3.03/1.68        ( ( Ys2 = nil_com )
% 3.03/1.68       => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68          = ( last_com @ Xs2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_301_last__snoc,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com] :
% 3.03/1.68        ( ( last_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) )
% 3.03/1.68        = X ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_302_last__ConsR,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com] :
% 3.03/1.68        ( ( Xs2 != nil_com )
% 3.03/1.68       => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68          = ( last_com @ Xs2 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_303_last__ConsL,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com] :
% 3.03/1.68        ( ( Xs2 = nil_com )
% 3.03/1.68       => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68          = X ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_304_last_Osimps,axiom,
% 3.03/1.68      ! [Xs2: list_com,X: com] :
% 3.03/1.68        ( ( ( Xs2 = nil_com )
% 3.03/1.68         => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68            = X ) )
% 3.03/1.68        & ( ( Xs2 != nil_com )
% 3.03/1.68         => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 3.03/1.68            = ( last_com @ Xs2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_305_longest__common__suffix,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.68      ? [Ss: list_com,Xs5: list_com,Ys5: list_com] :
% 3.03/1.68        ( ( Xs2
% 3.03/1.68          = ( append_com @ Xs5 @ Ss ) )
% 3.03/1.68        & ( Ys2
% 3.03/1.68          = ( append_com @ Ys5 @ Ss ) )
% 3.03/1.68        & ( ( Xs5 = nil_com )
% 3.03/1.68          | ( Ys5 = nil_com )
% 3.03/1.68          | ( ( last_com @ Xs5 )
% 3.03/1.68           != ( last_com @ Ys5 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_306_last__append,axiom,
% 3.03/1.68      ! [Ys2: list_com,Xs2: list_com] :
% 3.03/1.68        ( ( ( Ys2 = nil_com )
% 3.03/1.68         => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68            = ( last_com @ Xs2 ) ) )
% 3.03/1.68        & ( ( Ys2 != nil_com )
% 3.03/1.68         => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 3.03/1.68            = ( last_com @ Ys2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_307_irreflI,axiom,
% 3.03/1.68      ! [R2: set_Pr1165141447_state] :
% 3.03/1.68        ( ! [A: produc2041926651_state] :
% 3.03/1.68            ~ ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ R2 )
% 3.03/1.68       => ( irrefl654089520_state @ R2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_308_irreflI,axiom,
% 3.03/1.68      ! [R2: set_Pr2096893127_state] :
% 3.03/1.68        ( ! [A: produc410756839_state] :
% 3.03/1.68            ~ ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ R2 )
% 3.03/1.68       => ( irrefl1358048924_state @ R2 ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_309_irrefl__def,axiom,
% 3.03/1.68      ( irrefl654089520_state
% 3.03/1.68      = ( ^ [R3: set_Pr1165141447_state] :
% 3.03/1.68          ! [A5: produc2041926651_state] :
% 3.03/1.68            ~ ( member1069318160_state @ ( produc1909270103_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_310_irrefl__def,axiom,
% 3.03/1.68      ( irrefl1358048924_state
% 3.03/1.68      = ( ^ [R3: set_Pr2096893127_state] :
% 3.03/1.68          ! [A5: produc410756839_state] :
% 3.03/1.68            ~ ( member512523024_state @ ( produc2065881943_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_311_lenlex__append2,axiom,
% 3.03/1.68      ! [R2: set_Pr1822651163om_com,Us: list_com,Xs2: list_com,Ys2: list_com] :
% 3.03/1.68        ( ( irrefl_com @ R2 )
% 3.03/1.68       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us @ Xs2 ) @ ( append_com @ Us @ Ys2 ) ) @ ( lenlex_com @ R2 ) )
% 3.03/1.68          = ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_312_Nil__lenlex__iff1,axiom,
% 3.03/1.68      ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ns ) @ ( lenlex_com @ R ) )
% 3.03/1.68        = ( Ns != nil_com ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_313_Nil__notin__lex,axiom,
% 3.03/1.68      ! [Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ys2 ) @ ( lex_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_314_Nil2__notin__lex,axiom,
% 3.03/1.68      ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( lex_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_315_lex__append__leftI,axiom,
% 3.03/1.68      ! [Ys2: list_com,Zs2: list_com,R: set_Pr1822651163om_com,Xs2: list_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) )
% 3.03/1.68       => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_316_lenlex__irreflexive,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 3.03/1.68        ( ! [X3: produc2041926651_state] :
% 3.03/1.68            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( lenlex295247238_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_317_lenlex__irreflexive,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 3.03/1.68        ( ! [X3: produc410756839_state] :
% 3.03/1.68            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( lenlex1401983474_state @ R ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_318_Nil__lenlex__iff2,axiom,
% 3.03/1.68      ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ~ ( member32358020st_com @ ( produc1307105171st_com @ Ns @ nil_com ) @ ( lenlex_com @ R ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_319_lex__append__leftD,axiom,
% 3.03/1.68      ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ! [X3: com] :
% 3.03/1.68            ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 3.03/1.68       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) )
% 3.03/1.68         => ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_320_lex__append__leftD,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,Zs2: list_P1040014977_state] :
% 3.03/1.68        ( ! [X3: produc2041926651_state] :
% 3.03/1.68            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ Ys2 ) @ ( append982487830_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 3.03/1.68         => ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_321_lex__append__leftD,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,Zs2: list_P890094829_state] :
% 3.03/1.68        ( ! [X3: produc410756839_state] :
% 3.03/1.68            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ Ys2 ) @ ( append221843330_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 3.03/1.68         => ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_322_lex__append__left__iff,axiom,
% 3.03/1.68      ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 3.03/1.68        ( ! [X3: com] :
% 3.03/1.68            ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 3.03/1.68       => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) )
% 3.03/1.68          = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_323_lex__append__left__iff,axiom,
% 3.03/1.68      ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,Zs2: list_P1040014977_state] :
% 3.03/1.68        ( ! [X3: produc2041926651_state] :
% 3.03/1.68            ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ Ys2 ) @ ( append982487830_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 3.03/1.68          = ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_324_lex__append__left__iff,axiom,
% 3.03/1.68      ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,Zs2: list_P890094829_state] :
% 3.03/1.68        ( ! [X3: produc410756839_state] :
% 3.03/1.68            ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 3.03/1.68       => ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ Ys2 ) @ ( append221843330_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 3.03/1.68          = ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_325_Cons__in__lex,axiom,
% 3.03/1.68      ! [X: com,Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.68        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( lex_com @ R ) )
% 3.03/1.68        = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 3.03/1.68            & ( ( size_size_list_com @ Xs2 )
% 3.03/1.68              = ( size_size_list_com @ Ys2 ) ) )
% 3.03/1.68          | ( ( X = Y )
% 3.03/1.68            & ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lex_com @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_326_Cons__in__lex,axiom,
% 3.03/1.68      ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.68        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 3.03/1.68        = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 3.03/1.68            & ( ( size_s213202669_state @ Xs2 )
% 3.03/1.68              = ( size_s213202669_state @ Ys2 ) ) )
% 3.03/1.68          | ( ( X = Y )
% 3.03/1.68            & ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_327_Cons__in__lex,axiom,
% 3.03/1.68      ! [X: produc410756839_state,Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.68        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 3.03/1.68        = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 3.03/1.68            & ( ( size_s837829465_state @ Xs2 )
% 3.03/1.68              = ( size_s837829465_state @ Ys2 ) ) )
% 3.03/1.68          | ( ( X = Y )
% 3.03/1.68            & ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ) ).
% 3.03/1.68  
% 3.03/1.68  thf(fact_328_append__eq__append__conv,axiom,
% 3.03/1.68      ! [Xs2: list_com,Ys2: list_com,Us: list_com,Vs: list_com] :
% 3.03/1.69        ( ( ( ( size_size_list_com @ Xs2 )
% 3.03/1.69            = ( size_size_list_com @ Ys2 ) )
% 3.03/1.69          | ( ( size_size_list_com @ Us )
% 3.03/1.69            = ( size_size_list_com @ Vs ) ) )
% 3.03/1.69       => ( ( ( append_com @ Xs2 @ Us )
% 3.03/1.69            = ( append_com @ Ys2 @ Vs ) )
% 3.03/1.69          = ( ( Xs2 = Ys2 )
% 3.03/1.69            & ( Us = Vs ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_329_list__induct3,axiom,
% 3.03/1.69      ! [Xs2: list_com,Ys2: list_com,Zs2: list_com,P: list_com > list_com > list_com > $o] :
% 3.03/1.69        ( ( ( size_size_list_com @ Xs2 )
% 3.03/1.69          = ( size_size_list_com @ Ys2 ) )
% 3.03/1.69       => ( ( ( size_size_list_com @ Ys2 )
% 3.03/1.69            = ( size_size_list_com @ Zs2 ) )
% 3.03/1.69         => ( ( P @ nil_com @ nil_com @ nil_com )
% 3.03/1.69           => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com,Z: com,Zs: list_com] :
% 3.03/1.69                  ( ( ( size_size_list_com @ Xs )
% 3.03/1.69                    = ( size_size_list_com @ Ys ) )
% 3.03/1.69                 => ( ( ( size_size_list_com @ Ys )
% 3.03/1.69                      = ( size_size_list_com @ Zs ) )
% 3.03/1.69                   => ( ( P @ Xs @ Ys @ Zs )
% 3.03/1.69                     => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) @ ( cons_com @ Z @ Zs ) ) ) ) )
% 3.03/1.69             => ( P @ Xs2 @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_330_list__induct2,axiom,
% 3.03/1.69      ! [Xs2: list_com,Ys2: list_com,P: list_com > list_com > $o] :
% 3.03/1.69        ( ( ( size_size_list_com @ Xs2 )
% 3.03/1.69          = ( size_size_list_com @ Ys2 ) )
% 3.03/1.69       => ( ( P @ nil_com @ nil_com )
% 3.03/1.69         => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 3.03/1.69                ( ( ( size_size_list_com @ Xs )
% 3.03/1.69                  = ( size_size_list_com @ Ys ) )
% 3.03/1.69               => ( ( P @ Xs @ Ys )
% 3.03/1.69                 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) )
% 3.03/1.69           => ( P @ Xs2 @ Ys2 ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_331_same__length__different,axiom,
% 3.03/1.69      ! [Xs2: list_com,Ys2: list_com] :
% 3.03/1.69        ( ( Xs2 != Ys2 )
% 3.03/1.69       => ( ( ( size_size_list_com @ Xs2 )
% 3.03/1.69            = ( size_size_list_com @ Ys2 ) )
% 3.03/1.69         => ? [Pre: list_com,X3: com,Xs5: list_com,Y3: com,Ys5: list_com] :
% 3.03/1.69              ( ( X3 != Y3 )
% 3.03/1.69              & ( Xs2
% 3.03/1.69                = ( append_com @ Pre @ ( append_com @ ( cons_com @ X3 @ nil_com ) @ Xs5 ) ) )
% 3.03/1.69              & ( Ys2
% 3.03/1.69                = ( append_com @ Pre @ ( append_com @ ( cons_com @ Y3 @ nil_com ) @ Ys5 ) ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_332_lexord__sufE,axiom,
% 3.03/1.69      ! [Xs2: list_com,Zs2: list_com,Ys2: list_com,Qs: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.69        ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Zs2 ) @ ( append_com @ Ys2 @ Qs ) ) @ ( lexord_com @ R ) )
% 3.03/1.69       => ( ( Xs2 != Ys2 )
% 3.03/1.69         => ( ( ( size_size_list_com @ Xs2 )
% 3.03/1.69              = ( size_size_list_com @ Ys2 ) )
% 3.03/1.69           => ( ( ( size_size_list_com @ Zs2 )
% 3.03/1.69                = ( size_size_list_com @ Qs ) )
% 3.03/1.69             => ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lexord_com @ R ) ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_333_lex__append__rightI,axiom,
% 3.03/1.69      ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Vs: list_com,Us: list_com] :
% 3.03/1.69        ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lex_com @ R ) )
% 3.03/1.69       => ( ( ( size_size_list_com @ Vs )
% 3.03/1.69            = ( size_size_list_com @ Us ) )
% 3.03/1.69         => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Us ) @ ( append_com @ Ys2 @ Vs ) ) @ ( lex_com @ R ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_334_lenlex__append1,axiom,
% 3.03/1.69      ! [Us: list_com,Xs2: list_com,R2: set_Pr1822651163om_com,Vs: list_com,Ys2: list_com] :
% 3.03/1.69        ( ( member32358020st_com @ ( produc1307105171st_com @ Us @ Xs2 ) @ ( lenlex_com @ R2 ) )
% 3.03/1.69       => ( ( ( size_size_list_com @ Vs )
% 3.03/1.69            = ( size_size_list_com @ Ys2 ) )
% 3.03/1.69         => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us @ Vs ) @ ( append_com @ Xs2 @ Ys2 ) ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_335_Cons__lenlex__iff,axiom,
% 3.03/1.69      ! [M: com,Ms: list_com,N: com,Ns: list_com,R: set_Pr1822651163om_com] :
% 3.03/1.69        ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ M @ Ms ) @ ( cons_com @ N @ Ns ) ) @ ( lenlex_com @ R ) )
% 3.03/1.69        = ( ( ord_less_nat @ ( size_size_list_com @ Ms ) @ ( size_size_list_com @ Ns ) )
% 3.03/1.69          | ( ( ( size_size_list_com @ Ms )
% 3.03/1.69              = ( size_size_list_com @ Ns ) )
% 3.03/1.69            & ( member1333916004om_com @ ( product_Pair_com_com @ M @ N ) @ R ) )
% 3.03/1.69          | ( ( M = N )
% 3.03/1.69            & ( member32358020st_com @ ( produc1307105171st_com @ Ms @ Ns ) @ ( lenlex_com @ R ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_336_Cons__lenlex__iff,axiom,
% 3.03/1.69      ! [M: produc2041926651_state,Ms: list_P1040014977_state,N: produc2041926651_state,Ns: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.69        ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ M @ Ms ) @ ( cons_P465369265_state @ N @ Ns ) ) @ ( lenlex295247238_state @ R ) )
% 3.03/1.69        = ( ( ord_less_nat @ ( size_s213202669_state @ Ms ) @ ( size_s213202669_state @ Ns ) )
% 3.03/1.69          | ( ( ( size_s213202669_state @ Ms )
% 3.03/1.69              = ( size_s213202669_state @ Ns ) )
% 3.03/1.69            & ( member1069318160_state @ ( produc1909270103_state @ M @ N ) @ R ) )
% 3.03/1.69          | ( ( M = N )
% 3.03/1.69            & ( member1267359376_state @ ( produc1298457559_state @ Ms @ Ns ) @ ( lenlex295247238_state @ R ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_337_Cons__lenlex__iff,axiom,
% 3.03/1.69      ! [M: produc410756839_state,Ms: list_P890094829_state,N: produc410756839_state,Ns: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.69        ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ M @ Ms ) @ ( cons_P438230685_state @ N @ Ns ) ) @ ( lenlex1401983474_state @ R ) )
% 3.03/1.69        = ( ( ord_less_nat @ ( size_s837829465_state @ Ms ) @ ( size_s837829465_state @ Ns ) )
% 3.03/1.69          | ( ( ( size_s837829465_state @ Ms )
% 3.03/1.69              = ( size_s837829465_state @ Ns ) )
% 3.03/1.69            & ( member512523024_state @ ( produc2065881943_state @ M @ N ) @ R ) )
% 3.03/1.69          | ( ( M = N )
% 3.03/1.69            & ( member423306384_state @ ( produc1354769367_state @ Ms @ Ns ) @ ( lenlex1401983474_state @ R ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_338_list__ex1__simps_I1_J,axiom,
% 3.03/1.69      ! [P: com > $o] :
% 3.03/1.69        ~ ( list_ex1_com @ P @ nil_com ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_339_in__measures_I2_J,axiom,
% 3.03/1.69      ! [X: produc2041926651_state,Y: produc2041926651_state,F2: produc2041926651_state > nat,Fs: list_P1178430914te_nat] :
% 3.03/1.69        ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ ( cons_P1821701106te_nat @ F2 @ Fs ) ) )
% 3.03/1.69        = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 3.03/1.69          | ( ( ( F2 @ X )
% 3.03/1.69              = ( F2 @ Y ) )
% 3.03/1.69            & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ Fs ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_340_in__measures_I2_J,axiom,
% 3.03/1.69      ! [X: produc410756839_state,Y: produc410756839_state,F2: produc410756839_state > nat,Fs: list_P1627643054te_nat] :
% 3.03/1.69        ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ ( cons_P1631380062te_nat @ F2 @ Fs ) ) )
% 3.03/1.69        = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 3.03/1.69          | ( ( ( F2 @ X )
% 3.03/1.69              = ( F2 @ Y ) )
% 3.03/1.69            & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ Fs ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_341_listrel__iff__nth,axiom,
% 3.03/1.69      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.69        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) )
% 3.03/1.69        = ( ( ( size_s213202669_state @ Xs2 )
% 3.03/1.69            = ( size_s213202669_state @ Ys2 ) )
% 3.03/1.69          & ! [N2: nat] :
% 3.03/1.69              ( ( ord_less_nat @ N2 @ ( size_s213202669_state @ Xs2 ) )
% 3.03/1.69             => ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ N2 ) @ ( nth_Pr553241858_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_342_listrel__iff__nth,axiom,
% 3.03/1.69      ! [Xs2: list_list_com,Ys2: list_state,R: set_Pr849496667_state] :
% 3.03/1.69        ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 3.03/1.69        = ( ( ( size_s318434721st_com @ Xs2 )
% 3.03/1.69            = ( size_size_list_state @ Ys2 ) )
% 3.03/1.69          & ! [N2: nat] :
% 3.03/1.69              ( ( ord_less_nat @ N2 @ ( size_s318434721st_com @ Xs2 ) )
% 3.03/1.69             => ( member64234660_state @ ( produc1204172211_state @ ( nth_list_com @ Xs2 @ N2 ) @ ( nth_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_343_listrel__iff__nth,axiom,
% 3.03/1.69      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.69        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 3.03/1.69        = ( ( ( size_s837829465_state @ Xs2 )
% 3.03/1.69            = ( size_s837829465_state @ Ys2 ) )
% 3.03/1.69          & ! [N2: nat] :
% 3.03/1.69              ( ( ord_less_nat @ N2 @ ( size_s837829465_state @ Xs2 ) )
% 3.03/1.69             => ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ N2 ) @ ( nth_Pr526167918_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_344_in__measures_I1_J,axiom,
% 3.03/1.69      ! [X: produc2041926651_state,Y: produc2041926651_state] :
% 3.03/1.69        ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ nil_Pr1876916290te_nat ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_345_in__measures_I1_J,axiom,
% 3.03/1.69      ! [X: produc410756839_state,Y: produc410756839_state] :
% 3.03/1.69        ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ nil_Pr164089518te_nat ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_346_nth__append__length,axiom,
% 3.03/1.69      ! [Xs2: list_com,X: com,Ys2: list_com] :
% 3.03/1.69        ( ( nth_com @ ( append_com @ Xs2 @ ( cons_com @ X @ Ys2 ) ) @ ( size_size_list_com @ Xs2 ) )
% 3.03/1.69        = X ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_347_measures__less,axiom,
% 3.03/1.69      ! [F2: produc2041926651_state > nat,X: produc2041926651_state,Y: produc2041926651_state,Fs: list_P1178430914te_nat] :
% 3.03/1.69        ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 3.03/1.69       => ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ ( cons_P1821701106te_nat @ F2 @ Fs ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_348_measures__less,axiom,
% 3.03/1.69      ! [F2: produc410756839_state > nat,X: produc410756839_state,Y: produc410756839_state,Fs: list_P1627643054te_nat] :
% 3.03/1.69        ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 3.03/1.69       => ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ ( cons_P1631380062te_nat @ F2 @ Fs ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_349_listrel1__iff__update,axiom,
% 3.03/1.69      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.69        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 3.03/1.69        = ( ? [Y4: produc2041926651_state,N2: nat] :
% 3.03/1.69              ( ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ N2 ) @ Y4 ) @ R )
% 3.03/1.69              & ( ord_less_nat @ N2 @ ( size_s213202669_state @ Xs2 ) )
% 3.03/1.69              & ( Ys2
% 3.03/1.69                = ( list_u737668969_state @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_350_listrel1__iff__update,axiom,
% 3.03/1.69      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.69        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 3.03/1.69        = ( ? [Y4: produc410756839_state,N2: nat] :
% 3.03/1.69              ( ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ N2 ) @ Y4 ) @ R )
% 3.03/1.69              & ( ord_less_nat @ N2 @ ( size_s837829465_state @ Xs2 ) )
% 3.03/1.69              & ( Ys2
% 3.03/1.69                = ( list_u364351829_state @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_351_lex__take__index,axiom,
% 3.03/1.69      ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 3.03/1.69        ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( lex_Pr570247525_state @ R ) )
% 3.03/1.69       => ~ ! [I: nat] :
% 3.03/1.69              ( ( ord_less_nat @ I @ ( size_s213202669_state @ Xs2 ) )
% 3.03/1.69             => ( ( ord_less_nat @ I @ ( size_s213202669_state @ Ys2 ) )
% 3.03/1.69               => ( ( ( take_P558217449_state @ I @ Xs2 )
% 3.03/1.69                    = ( take_P558217449_state @ I @ Ys2 ) )
% 3.03/1.69                 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ I ) @ ( nth_Pr553241858_state @ Ys2 @ I ) ) @ R ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_352_lex__take__index,axiom,
% 3.03/1.69      ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 3.03/1.69        ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( lex_Pr1762629969_state @ R ) )
% 3.03/1.69       => ~ ! [I: nat] :
% 3.03/1.69              ( ( ord_less_nat @ I @ ( size_s837829465_state @ Xs2 ) )
% 3.03/1.69             => ( ( ord_less_nat @ I @ ( size_s837829465_state @ Ys2 ) )
% 3.03/1.69               => ( ( ( take_P1852316373_state @ I @ Xs2 )
% 3.03/1.69                    = ( take_P1852316373_state @ I @ Ys2 ) )
% 3.03/1.69                 => ~ ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ I ) @ ( nth_Pr526167918_state @ Ys2 @ I ) ) @ R ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(fact_353_list__update__nonempty,axiom,
% 3.03/1.69      ! [Xs2: list_com,K: nat,X: com] :
% 3.03/1.69        ( ( ( list_update_com @ Xs2 @ K @ X )
% 3.03/1.69          = nil_com )
% 3.03/1.69        = ( Xs2 = nil_com ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(conj_0,hypothesis,
% 3.03/1.69      member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 3.03/1.69  
% 3.03/1.69  thf(conj_1,hypothesis,
% 3.03/1.69      termi @ c @ s ).
% 3.03/1.69  
% 3.03/1.69  thf(conj_2,hypothesis,
% 3.03/1.69      ! [S5: state,S6: state] :
% 3.03/1.69        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ S5 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ S6 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 3.03/1.69       => ( ( termi @ c @ S5 )
% 3.03/1.69         => ( ( termi @ c2 @ S6 )
% 3.03/1.69            & ! [T4: state] :
% 3.03/1.69                ( ( exec @ S6 @ c2 @ T4 )
% 3.03/1.69               => ( pHoare806997636termis @ cs @ T4 ) ) ) ) ) ).
% 3.03/1.69  
% 3.03/1.69  thf(conj_3,conjecture,
% 3.03/1.69      termi @ c2 @ s2 ).
% 3.03/1.69  ------------------------
% 3.14/1.71  % (12017)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/183Mi)
% 3.14/1.71  % (12019)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_11910 for (2999ds/27Mi)
% 3.14/1.71  % (12018)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_11910 for (2999ds/4Mi)
% 3.14/1.72  % (12023)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/18Mi)
% 3.14/1.72  % (12018)Instruction limit reached!
% 3.14/1.72  % (12018)------------------------------
% 3.14/1.72  % (12018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72  % (12018)Termination reason: Unknown
% 3.14/1.72  % (12018)Termination phase: shuffling
% 3.14/1.72  
% 3.14/1.72  % (12018)Memory used [KB]: 1791
% 3.14/1.72  % (12018)Time elapsed: 0.003 s
% 3.14/1.72  % (12018)Instructions burned: 6 (million)
% 3.14/1.72  % (12018)------------------------------
% 3.14/1.72  % (12018)------------------------------
% 3.14/1.72  % (12020)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/2Mi)
% 3.14/1.72  % (12021)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_11910 for (2999ds/2Mi)
% 3.14/1.72  % (12022)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_11910 for (2999ds/275Mi)
% 3.14/1.72  % (12023)Instruction limit reached!
% 3.14/1.72  % (12023)------------------------------
% 3.14/1.72  % (12023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72  % (12023)Termination reason: Unknown
% 3.14/1.72  % (12023)Termination phase: shuffling
% 3.14/1.72  
% 3.14/1.72  % (12023)Memory used [KB]: 2174
% 3.14/1.72  % (12023)Time elapsed: 0.008 s
% 3.14/1.72  % (12023)Instructions burned: 20 (million)
% 3.14/1.72  % (12023)------------------------------
% 3.14/1.72  % (12023)------------------------------
% 3.14/1.72  % (12019)Instruction limit reached!
% 3.14/1.72  % (12019)------------------------------
% 3.14/1.72  % (12019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72  % (12019)Termination reason: Unknown
% 3.14/1.72  % (12019)Termination phase: shuffling
% 3.14/1.72  
% 3.14/1.72  % (12019)Memory used [KB]: 2302
% 3.14/1.72  % (12019)Time elapsed: 0.011 s
% 3.14/1.72  % (12019)Instructions burned: 29 (million)
% 3.14/1.72  % (12019)------------------------------
% 3.14/1.72  % (12019)------------------------------
% 3.14/1.72  % (12020)Instruction limit reached!
% 3.14/1.72  % (12020)------------------------------
% 3.14/1.72  % (12020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72  % (12021)Instruction limit reached!
% 3.14/1.72  % (12021)------------------------------
% 3.14/1.72  % (12021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72  % (12020)Termination reason: Unknown
% 3.14/1.72  % (12020)Termination phase: shuffling
% 3.14/1.72  
% 3.14/1.72  % (12020)Memory used [KB]: 1663
% 3.14/1.72  % (12020)Time elapsed: 0.004 s
% 3.14/1.72  % (12020)Instructions burned: 2 (million)
% 3.14/1.72  % (12020)------------------------------
% 3.14/1.72  % (12020)------------------------------
% 3.14/1.72  % (12021)Termination reason: Unknown
% 3.14/1.72  % (12021)Termination phase: shuffling
% 3.14/1.72  
% 3.14/1.72  % (12021)Memory used [KB]: 1663
% 3.14/1.72  % (12021)Time elapsed: 0.004 s
% 3.14/1.72  % (12021)Instructions burned: 2 (million)
% 3.14/1.72  % (12021)------------------------------
% 3.14/1.72  % (12021)------------------------------
% 3.14/1.73  % (12024)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/3Mi)
% 3.14/1.73  % (12024)Instruction limit reached!
% 3.14/1.73  % (12024)------------------------------
% 3.14/1.73  % (12024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73  % (12024)Termination reason: Unknown
% 3.14/1.73  % (12024)Termination phase: shuffling
% 3.14/1.73  
% 3.14/1.73  % (12024)Memory used [KB]: 1791
% 3.14/1.73  % (12024)Time elapsed: 0.003 s
% 3.14/1.73  % (12024)Instructions burned: 6 (million)
% 3.14/1.73  % (12024)------------------------------
% 3.14/1.73  % (12024)------------------------------
% 3.14/1.73  % (12026)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_11910 for (2999ds/15Mi)
% 3.14/1.73  % (12025)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_11910 for (2999ds/37Mi)
% 3.14/1.74  % (12026)Instruction limit reached!
% 3.14/1.74  % (12026)------------------------------
% 3.14/1.74  % (12026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.74  % (12026)Termination reason: Unknown
% 3.14/1.74  % (12026)Termination phase: shuffling
% 3.14/1.74  % (12029)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/7Mi)
% 3.14/1.74  
% 3.14/1.74  % (12026)Memory used [KB]: 1918
% 3.14/1.74  % (12026)Time elapsed: 0.006 s
% 3.14/1.74  % (12026)Instructions burned: 16 (million)
% 3.14/1.74  % (12026)------------------------------
% 3.14/1.74  % (12026)------------------------------
% 3.14/1.74  % (12029)Instruction limit reached!
% 3.14/1.74  % (12029)------------------------------
% 3.14/1.74  % (12029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.74  % (12029)Termination reason: Unknown
% 3.14/1.74  % (12029)Termination phase: shuffling
% 3.14/1.74  
% 3.14/1.74  % (12029)Memory used [KB]: 1791
% 3.14/1.74  % (12029)Time elapsed: 0.004 s
% 3.14/1.74  % (12029)Instructions burned: 9 (million)
% 3.14/1.74  % (12029)------------------------------
% 3.14/1.74  % (12029)------------------------------
% 3.14/1.74  % (12027)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_11910 for (2999ds/3Mi)
% 3.14/1.74  % (12028)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_11910 for (2999ds/1041Mi)
% 3.14/1.74  % (12027)Instruction limit reached!
% 3.14/1.74  % (12027)------------------------------
% 3.14/1.74  % (12027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.74  % (12027)Termination reason: Unknown
% 3.14/1.74  % (12027)Termination phase: shuffling
% 3.14/1.74  
% 3.14/1.74  % (12027)Memory used [KB]: 1791
% 3.14/1.74  % (12027)Time elapsed: 0.004 s
% 3.14/1.74  % (12027)Instructions burned: 3 (million)
% 3.14/1.74  % (12027)------------------------------
% 3.14/1.74  % (12027)------------------------------
% 3.14/1.74  % (12025)Instruction limit reached!
% 3.14/1.74  % (12025)------------------------------
% 3.14/1.74  % (12025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.74  % (12025)Termination reason: Unknown
% 3.14/1.74  % (12025)Termination phase: shuffling
% 3.14/1.74  
% 3.14/1.74  % (12025)Memory used [KB]: 2686
% 3.14/1.74  % (12025)Time elapsed: 0.013 s
% 3.14/1.74  % (12025)Instructions burned: 38 (million)
% 3.14/1.74  % (12025)------------------------------
% 3.14/1.74  % (12025)------------------------------
% 3.14/1.75  % (12030)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/16Mi)
% 3.14/1.75  % (12031)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_11910 for (2999ds/3Mi)
% 3.14/1.75  % (12031)Instruction limit reached!
% 3.14/1.75  % (12031)------------------------------
% 3.14/1.75  % (12031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.75  % (12030)Instruction limit reached!
% 3.14/1.75  % (12030)------------------------------
% 3.14/1.75  % (12030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.75  % (12030)Termination reason: Unknown
% 3.14/1.75  % (12030)Termination phase: shuffling
% 3.14/1.75  
% 3.14/1.75  % (12030)Memory used [KB]: 2046
% 3.14/1.75  % (12030)Time elapsed: 0.006 s
% 3.14/1.75  % (12030)Instructions burned: 16 (million)
% 3.14/1.75  % (12030)------------------------------
% 3.14/1.75  % (12030)------------------------------
% 3.14/1.75  % (12031)Termination reason: Unknown
% 3.14/1.75  % (12031)Termination phase: shuffling
% 3.14/1.75  
% 3.14/1.75  % (12031)Memory used [KB]: 1791
% 3.14/1.75  % (12031)Time elapsed: 0.003 s
% 3.14/1.75  % (12031)Instructions burned: 6 (million)
% 3.14/1.75  % (12031)------------------------------
% 3.14/1.75  % (12031)------------------------------
% 3.14/1.75  % (12033)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/7Mi)
% 3.14/1.76  % (12033)Instruction limit reached!
% 3.14/1.76  % (12033)------------------------------
% 3.14/1.76  % (12033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76  % (12033)Termination reason: Unknown
% 3.14/1.76  % (12033)Termination phase: shuffling
% 3.14/1.76  
% 3.14/1.76  % (12033)Memory used [KB]: 1791
% 3.14/1.76  % (12033)Time elapsed: 0.004 s
% 3.14/1.76  % (12033)Instructions burned: 9 (million)
% 3.14/1.76  % (12033)------------------------------
% 3.14/1.76  % (12033)------------------------------
% 3.14/1.76  % (12032)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_11910 for (2999ds/3Mi)
% 3.14/1.76  % (12035)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/4Mi)
% 3.14/1.76  % (12034)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/3Mi)
% 3.14/1.76  % (12034)Instruction limit reached!
% 3.14/1.76  % (12034)------------------------------
% 3.14/1.76  % (12034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76  % (12034)Termination reason: Unknown
% 3.14/1.76  % (12034)Termination phase: shuffling
% 3.14/1.76  
% 3.14/1.76  % (12034)Memory used [KB]: 1791
% 3.14/1.76  % (12034)Time elapsed: 0.002 s
% 3.14/1.76  % (12034)Instructions burned: 3 (million)
% 3.14/1.76  % (12034)------------------------------
% 3.14/1.76  % (12034)------------------------------
% 3.14/1.76  % (12032)Instruction limit reached!
% 3.14/1.76  % (12032)------------------------------
% 3.14/1.76  % (12032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76  % (12032)Termination reason: Unknown
% 3.14/1.76  % (12032)Termination phase: shuffling
% 3.14/1.76  
% 3.14/1.76  % (12032)Memory used [KB]: 1791
% 3.14/1.76  % (12032)Time elapsed: 0.004 s
% 3.14/1.76  % (12032)Instructions burned: 3 (million)
% 3.14/1.76  % (12032)------------------------------
% 3.14/1.76  % (12032)------------------------------
% 3.14/1.76  % (12035)Instruction limit reached!
% 3.14/1.76  % (12035)------------------------------
% 3.14/1.76  % (12035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76  % (12035)Termination reason: Unknown
% 3.14/1.76  % (12035)Termination phase: shuffling
% 3.14/1.76  
% 3.14/1.76  % (12035)Memory used [KB]: 1791
% 3.14/1.76  % (12035)Time elapsed: 0.003 s
% 3.14/1.76  % (12035)Instructions burned: 6 (million)
% 3.14/1.76  % (12035)------------------------------
% 3.14/1.76  % (12035)------------------------------
% 3.14/1.76  % (12017)Instruction limit reached!
% 3.14/1.76  % (12017)------------------------------
% 3.14/1.76  % (12017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76  % (12017)Termination reason: Unknown
% 3.14/1.76  % (12017)Termination phase: Property scanning
% 3.14/1.76  
% 3.14/1.76  % (12017)Memory used [KB]: 3582
% 3.14/1.76  % (12017)Time elapsed: 0.052 s
% 3.14/1.76  % (12017)Instructions burned: 184 (million)
% 3.14/1.76  % (12017)------------------------------
% 3.14/1.76  % (12017)------------------------------
% 3.14/1.77  % (12036)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/18Mi)
% 3.14/1.77  % (12037)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/710Mi)
% 3.14/1.77  % (12039)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_11910 for (2999ds/902Mi)
% 3.14/1.77  % (12040)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_11910 for (2999ds/21Mi)
% 3.14/1.77  % (12036)Instruction limit reached!
% 3.14/1.77  % (12036)------------------------------
% 3.14/1.77  % (12036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.77  % (12036)Termination reason: Unknown
% 3.14/1.77  % (12036)Termination phase: shuffling
% 3.14/1.77  
% 3.14/1.77  % (12036)Memory used [KB]: 2174
% 3.14/1.77  % (12036)Time elapsed: 0.008 s
% 3.14/1.77  % (12036)Instructions burned: 19 (million)
% 3.14/1.77  % (12036)------------------------------
% 3.14/1.77  % (12036)------------------------------
% 3.14/1.78  % (12038)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/6Mi)
% 3.14/1.78  % (12022)First to succeed.
% 3.14/1.78  % (12038)Instruction limit reached!
% 3.14/1.78  % (12038)------------------------------
% 3.14/1.78  % (12038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.78  % (12038)Termination reason: Unknown
% 3.14/1.78  % (12038)Termination phase: shuffling
% 3.14/1.78  
% 3.14/1.78  % (12038)Memory used [KB]: 1791
% 3.14/1.78  % (12038)Time elapsed: 0.005 s
% 3.14/1.78  % (12038)Instructions burned: 8 (million)
% 3.14/1.78  % (12038)------------------------------
% 3.14/1.78  % (12038)------------------------------
% 3.14/1.78  % (12022)Refutation found. Thanks to Tanya!
% 3.14/1.78  % SZS status Theorem for DTF2THF_11910
% 3.14/1.78  % SZS output start Proof for DTF2THF_11910
% 3.14/1.78  thf(type_def_5, type, list_list_com: $tType).
% 3.14/1.78  thf(type_def_7, type, list_com: $tType).
% 3.14/1.78  thf(type_def_8, type, list_P1040014977_state: $tType).
% 3.14/1.78  thf(type_def_9, type, list_P890094829_state: $tType).
% 3.14/1.78  thf(type_def_10, type, com: $tType).
% 3.14/1.78  thf(type_def_11, type, set_Pr1822651163om_com: $tType).
% 3.14/1.78  thf(type_def_12, type, set_Pr602326075st_com: $tType).
% 3.14/1.78  thf(type_def_13, type, set_Pr1165141447_state: $tType).
% 3.14/1.78  thf(type_def_14, type, set_Pr1142642759_state: $tType).
% 3.14/1.78  thf(type_def_15, type, set_Pr2096893127_state: $tType).
% 3.14/1.78  thf(type_def_16, type, set_Pr1325664839_state: $tType).
% 3.14/1.78  thf(type_def_17, type, produc2041926651_state: $tType).
% 3.14/1.78  thf(type_def_18, type, nat: $tType).
% 3.14/1.78  thf(type_def_19, type, list_P1178430914te_nat: $tType).
% 3.14/1.78  thf(type_def_20, type, produc410756839_state: $tType).
% 3.14/1.78  thf(type_def_21, type, list_P1627643054te_nat: $tType).
% 3.14/1.78  thf(type_def_22, type, state: $tType).
% 3.14/1.78  thf(type_def_23, type, list_state: $tType).
% 3.14/1.78  thf(type_def_24, type, set_Pr849496667_state: $tType).
% 3.14/1.78  thf(type_def_25, type, set_Pr391631483_state: $tType).
% 3.14/1.78  thf(type_def_26, type, set_state: $tType).
% 3.14/1.78  thf(type_def_27, type, produc2058209240st_com: $tType).
% 3.14/1.78  thf(type_def_28, type, produc1393453339_state: $tType).
% 3.14/1.78  thf(type_def_29, type, produc258871771st_com: $tType).
% 3.14/1.78  thf(type_def_30, type, produc1225889383_state: $tType).
% 3.14/1.78  thf(type_def_31, type, produc1586269031_state: $tType).
% 3.14/1.78  thf(type_def_32, type, product_prod_com_com: $tType).
% 3.14/1.78  thf(type_def_33, type, produc1440412305st_com: $tType).
% 3.14/1.78  thf(type_def_34, type, produc392316135_state: $tType).
% 3.14/1.78  thf(type_def_35, type, produc1762014951st_com: $tType).
% 3.14/1.78  thf(type_def_36, type, produc1519776487_state: $tType).
% 3.14/1.78  thf(type_def_37, type, produc270545127_state: $tType).
% 3.14/1.78  thf(type_def_38, type, produc186437863_state: $tType).
% 3.14/1.78  thf(type_def_39, type, produc2046512871_state: $tType).
% 3.14/1.78  thf(type_def_40, type, set_Pr135335153st_com: $tType).
% 3.14/1.78  thf(type_def_41, type, set_Pr1419004359_state: $tType).
% 3.14/1.78  thf(type_def_42, type, set_Pr2083163591st_com: $tType).
% 3.14/1.78  thf(type_def_43, type, set_Pr1847866567_state: $tType).
% 3.14/1.78  thf(type_def_44, type, set_Pr1696918727_state: $tType).
% 3.14/1.78  thf(type_def_45, type, set_Pr541394119_state: $tType).
% 3.14/1.78  thf(func_def_0, type, set_Pr1696918727_state: $tType).
% 3.14/1.78  thf(func_def_1, type, produc270545127_state: $tType).
% 3.14/1.78  thf(func_def_2, type, set_Pr541394119_state: $tType).
% 3.14/1.78  thf(func_def_3, type, produc2046512871_state: $tType).
% 3.14/1.78  thf(func_def_4, type, set_Pr1847866567_state: $tType).
% 3.14/1.78  thf(func_def_5, type, produc1519776487_state: $tType).
% 3.14/1.78  thf(func_def_6, type, set_Pr1325664839_state: $tType).
% 3.14/1.78  thf(func_def_7, type, produc1586269031_state: $tType).
% 3.14/1.78  thf(func_def_8, type, set_Pr2096893127_state: $tType).
% 3.14/1.78  thf(func_def_9, type, produc186437863_state: $tType).
% 3.14/1.78  thf(func_def_10, type, set_Pr1419004359_state: $tType).
% 3.14/1.78  thf(func_def_11, type, set_Pr135335153st_com: $tType).
% 3.14/1.78  thf(func_def_12, type, produc392316135_state: $tType).
% 3.14/1.78  thf(func_def_13, type, produc1440412305st_com: $tType).
% 3.14/1.78  thf(func_def_14, type, set_Pr1142642759_state: $tType).
% 3.14/1.78  thf(func_def_15, type, set_Pr2083163591st_com: $tType).
% 3.14/1.78  thf(func_def_16, type, list_P1627643054te_nat: $tType).
% 3.14/1.78  thf(func_def_17, type, produc1225889383_state: $tType).
% 3.14/1.78  thf(func_def_18, type, produc1762014951st_com: $tType).
% 3.14/1.78  thf(func_def_19, type, list_P890094829_state: $tType).
% 3.14/1.78  thf(func_def_20, type, set_Pr1165141447_state: $tType).
% 3.14/1.78  thf(func_def_21, type, produc410756839_state: $tType).
% 3.14/1.78  thf(func_def_22, type, set_Pr391631483_state: $tType).
% 3.14/1.78  thf(func_def_23, type, list_P1178430914te_nat: $tType).
% 3.14/1.78  thf(func_def_24, type, produc1393453339_state: $tType).
% 3.14/1.78  thf(func_def_25, type, produc2058209240st_com: $tType).
% 3.14/1.78  thf(func_def_26, type, set_Pr602326075st_com: $tType).
% 3.14/1.78  thf(func_def_27, type, list_P1040014977_state: $tType).
% 3.14/1.78  thf(func_def_28, type, set_Pr849496667_state: $tType).
% 3.14/1.78  thf(func_def_29, type, produc258871771st_com: $tType).
% 3.14/1.78  thf(func_def_30, type, produc2041926651_state: $tType).
% 3.14/1.78  thf(func_def_31, type, set_Pr1822651163om_com: $tType).
% 3.14/1.78  thf(func_def_32, type, product_prod_com_com: $tType).
% 3.14/1.78  thf(func_def_33, type, list_list_com: $tType).
% 3.14/1.78  thf(func_def_34, type, list_state: $tType).
% 3.14/1.78  thf(func_def_35, type, set_state: $tType).
% 3.14/1.78  thf(func_def_36, type, list_com: $tType).
% 3.14/1.78  thf(func_def_37, type, state: $tType).
% 3.14/1.78  thf(func_def_38, type, com: $tType).
% 3.14/1.78  thf(func_def_39, type, nat: $tType).
% 3.14/1.78  thf(func_def_40, type, append_list_com: list_list_com > list_list_com > list_list_com).
% 3.14/1.78  thf(func_def_41, type, append_com: list_com > list_com > list_com).
% 3.14/1.78  thf(func_def_42, type, append982487830_state: list_P1040014977_state > list_P1040014977_state > list_P1040014977_state).
% 3.14/1.78  thf(func_def_43, type, append221843330_state: list_P890094829_state > list_P890094829_state > list_P890094829_state).
% 3.14/1.78  thf(func_def_44, type, bind_com_com: list_com > (com > list_com) > list_com).
% 3.14/1.78  thf(func_def_45, type, butlast_com: list_com > list_com).
% 3.14/1.78  thf(func_def_46, type, concat_com: list_list_com > list_com).
% 3.14/1.78  thf(func_def_47, type, insert_com: com > list_com > list_com).
% 3.14/1.78  thf(func_def_48, type, last_com: list_com > com).
% 3.14/1.78  thf(func_def_49, type, lenlex_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 3.14/1.78  thf(func_def_50, type, lenlex295247238_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 3.14/1.78  thf(func_def_51, type, lenlex1401983474_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 3.14/1.78  thf(func_def_52, type, lex_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 3.14/1.78  thf(func_def_53, type, lex_Pr570247525_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 3.14/1.78  thf(func_def_54, type, lex_Pr1762629969_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 3.14/1.78  thf(func_def_55, type, lexord_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 3.14/1.78  thf(func_def_56, type, lexord1062073966_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 3.14/1.78  thf(func_def_57, type, lexord1893203674_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 3.14/1.78  thf(func_def_58, type, cons_P1821701106te_nat: (produc2041926651_state > nat) > list_P1178430914te_nat > list_P1178430914te_nat).
% 3.14/1.78  thf(func_def_59, type, cons_P1631380062te_nat: (produc410756839_state > nat) > list_P1627643054te_nat > list_P1627643054te_nat).
% 3.14/1.78  thf(func_def_60, type, cons_list_com: list_com > list_list_com > list_list_com).
% 3.14/1.78  thf(func_def_61, type, cons_com: com > list_com > list_com).
% 3.14/1.78  thf(func_def_62, type, cons_state: state > list_state > list_state).
% 3.14/1.78  thf(func_def_63, type, cons_P465369265_state: produc2041926651_state > list_P1040014977_state > list_P1040014977_state).
% 3.14/1.78  thf(func_def_64, type, cons_P438230685_state: produc410756839_state > list_P890094829_state > list_P890094829_state).
% 3.14/1.78  thf(func_def_65, type, nil_Pr1876916290te_nat: list_P1178430914te_nat).
% 3.14/1.78  thf(func_def_66, type, nil_Pr164089518te_nat: list_P1627643054te_nat).
% 3.14/1.78  thf(func_def_67, type, nil_list_com: list_list_com).
% 3.14/1.78  thf(func_def_68, type, nil_com: list_com).
% 3.14/1.78  thf(func_def_69, type, nil_state: list_state).
% 3.14/1.78  thf(func_def_70, type, nil_Pr1844458753_state: list_P1040014977_state).
% 3.14/1.78  thf(func_def_71, type, nil_Pr1347322605_state: list_P890094829_state).
% 3.14/1.78  thf(func_def_72, type, list_ex1_com: (com > $o) > list_com > $o).
% 3.14/1.78  thf(func_def_73, type, list_update_com: list_com > nat > com > list_com).
% 3.14/1.78  thf(func_def_74, type, list_u737668969_state: list_P1040014977_state > nat > produc2041926651_state > list_P1040014977_state).
% 3.14/1.78  thf(func_def_75, type, list_u364351829_state: list_P890094829_state > nat > produc410756839_state > list_P890094829_state).
% 3.14/1.78  thf(func_def_76, type, listrel1_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 3.14/1.78  thf(func_def_77, type, listre1738592858_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 3.14/1.78  thf(func_def_78, type, listre1725776070_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 3.14/1.78  thf(func_def_79, type, listre1268245261_state: set_Pr849496667_state > set_Pr391631483_state).
% 3.14/1.78  thf(func_def_80, type, listrel_com_com: set_Pr1822651163om_com > set_Pr602326075st_com).
% 3.14/1.78  thf(func_def_81, type, listre194873521_state: set_Pr1165141447_state > set_Pr1142642759_state).
% 3.14/1.78  thf(func_def_82, type, listre1244407729_state: set_Pr2096893127_state > set_Pr1325664839_state).
% 3.14/1.78  thf(func_def_83, type, maps_com_com: (com > list_com) > list_com > list_com).
% 3.14/1.78  thf(func_def_84, type, measur1071343867_state: list_P1178430914te_nat > set_Pr1165141447_state).
% 3.14/1.78  thf(func_def_85, type, measur768621543_state: list_P1627643054te_nat > set_Pr2096893127_state).
% 3.14/1.78  thf(func_def_86, type, nth_list_com: list_list_com > nat > list_com).
% 3.14/1.78  thf(func_def_87, type, nth_com: list_com > nat > com).
% 3.14/1.78  thf(func_def_88, type, nth_state: list_state > nat > state).
% 3.14/1.78  thf(func_def_89, type, nth_Pr553241858_state: list_P1040014977_state > nat > produc2041926651_state).
% 3.14/1.78  thf(func_def_90, type, nth_Pr526167918_state: list_P890094829_state > nat > produc410756839_state).
% 3.14/1.78  thf(func_def_91, type, product_lists_com: list_list_com > list_list_com).
% 3.14/1.78  thf(func_def_92, type, rotate1_com: list_com > list_com).
% 3.14/1.78  thf(func_def_93, type, subseqs_com: list_com > list_list_com).
% 3.14/1.78  thf(func_def_94, type, take_P558217449_state: nat > list_P1040014977_state > list_P1040014977_state).
% 3.14/1.78  thf(func_def_95, type, take_P1852316373_state: nat > list_P890094829_state > list_P890094829_state).
% 3.14/1.78  thf(func_def_96, type, size_s318434721st_com: list_list_com > nat).
% 3.14/1.78  thf(func_def_97, type, size_size_list_com: list_com > nat).
% 3.14/1.78  thf(func_def_98, type, size_size_list_state: list_state > nat).
% 3.14/1.78  thf(func_def_99, type, size_s213202669_state: list_P1040014977_state > nat).
% 3.14/1.78  thf(func_def_100, type, size_s837829465_state: list_P890094829_state > nat).
% 3.14/1.78  thf(func_def_101, type, ord_less_nat: nat > nat > $o).
% 3.14/1.78  thf(func_def_102, type, pHoare259243666_exec1: set_Pr1165141447_state).
% 3.14/1.78  thf(func_def_103, type, pHoare259243732_execs: state > list_com > state > $o).
% 3.14/1.78  thf(func_def_104, type, pHoare806997636termis: list_com > state > $o).
% 3.14/1.78  thf(func_def_105, type, cond: (state > $o) > com > com > com).
% 3.14/1.78  thf(func_def_106, type, do: (state > set_state) > com).
% 3.14/1.78  thf(func_def_107, type, semi: com > com > com).
% 3.14/1.78  thf(func_def_108, type, while: (state > $o) > com > com).
% 3.14/1.78  thf(func_def_109, type, exec: state > com > state > $o).
% 3.14/1.78  thf(func_def_110, type, termi: com > state > $o).
% 3.14/1.78  thf(func_def_111, type, produc1914379986st_com: (com > com > $o) > list_com > produc2058209240st_com).
% 3.14/1.78  thf(func_def_112, type, produc1742567891_state: list_list_com > list_state > produc1393453339_state).
% 3.14/1.78  thf(func_def_113, type, produc1307105171st_com: list_com > list_com > produc258871771st_com).
% 3.14/1.78  thf(func_def_114, type, produc1204172211_state: list_com > state > produc2041926651_state).
% 3.14/1.78  thf(func_def_115, type, produc1298457559_state: list_P1040014977_state > list_P1040014977_state > produc1225889383_state).
% 3.14/1.78  thf(func_def_116, type, produc1354769367_state: list_P890094829_state > list_P890094829_state > produc1586269031_state).
% 3.14/1.78  thf(func_def_117, type, product_Pair_com_com: com > com > product_prod_com_com).
% 3.14/1.78  thf(func_def_118, type, produc67337417st_com: produc2058209240st_com > produc2058209240st_com > produc1440412305st_com).
% 3.14/1.78  thf(func_def_119, type, produc67381847_state: produc1393453339_state > produc1393453339_state > produc392316135_state).
% 3.14/1.78  thf(func_def_120, type, produc313736791st_com: produc258871771st_com > produc258871771st_com > produc1762014951st_com).
% 3.14/1.78  thf(func_def_121, type, produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state).
% 3.14/1.78  thf(func_def_122, type, produc984060759_state: produc1225889383_state > produc1225889383_state > produc1519776487_state).
% 3.14/1.78  thf(func_def_123, type, produc1576663895_state: produc1586269031_state > produc1586269031_state > produc270545127_state).
% 3.14/1.78  thf(func_def_124, type, produc2065881943_state: produc410756839_state > produc410756839_state > produc186437863_state).
% 3.14/1.78  thf(func_def_125, type, produc2049704791_state: produc186437863_state > produc186437863_state > produc2046512871_state).
% 3.14/1.78  thf(func_def_126, type, irrefl_com: set_Pr1822651163om_com > $o).
% 3.14/1.78  thf(func_def_127, type, irrefl654089520_state: set_Pr1165141447_state > $o).
% 3.14/1.78  thf(func_def_128, type, irrefl1358048924_state: set_Pr2096893127_state > $o).
% 3.14/1.78  thf(func_def_129, type, collect_state: (state > $o) > set_state).
% 3.14/1.78  thf(func_def_130, type, collec300063826_state: (produc410756839_state > $o) > set_Pr1165141447_state).
% 3.14/1.78  thf(func_def_131, type, collec489924946_state: (produc186437863_state > $o) > set_Pr2096893127_state).
% 3.14/1.78  thf(func_def_132, type, transi436345274st_com: set_Pr602326075st_com > set_Pr602326075st_com).
% 3.14/1.78  thf(func_def_133, type, transi339813252_state: set_Pr1142642759_state > set_Pr1142642759_state).
% 3.14/1.78  thf(func_def_134, type, transi1965148016_state: set_Pr1325664839_state > set_Pr1325664839_state).
% 3.14/1.78  thf(func_def_135, type, transi863150634cl_com: set_Pr1822651163om_com > set_Pr1822651163om_com).
% 3.14/1.78  thf(func_def_136, type, transi1592315797st_com: set_Pr135335153st_com > set_Pr135335153st_com).
% 3.14/1.78  thf(func_def_137, type, transi89280670_state: set_Pr1419004359_state > set_Pr1419004359_state).
% 3.14/1.78  thf(func_def_138, type, transi1782245470st_com: set_Pr2083163591st_com > set_Pr2083163591st_com).
% 3.14/1.78  thf(func_def_139, type, transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state).
% 3.14/1.78  thf(func_def_140, type, transi1428749162_state: set_Pr1847866567_state > set_Pr1847866567_state).
% 3.14/1.78  thf(func_def_141, type, transi445721450_state: set_Pr1696918727_state > set_Pr1696918727_state).
% 3.14/1.78  thf(func_def_142, type, transi463013610_state: set_Pr2096893127_state > set_Pr2096893127_state).
% 3.14/1.78  thf(func_def_143, type, transi152726506_state: set_Pr541394119_state > set_Pr541394119_state).
% 3.14/1.78  thf(func_def_144, type, member_state: state > set_state > $o).
% 3.14/1.78  thf(func_def_145, type, member1442949316_state: produc1393453339_state > set_Pr391631483_state > $o).
% 3.14/1.78  thf(func_def_146, type, member32358020st_com: produc258871771st_com > set_Pr602326075st_com > $o).
% 3.14/1.78  thf(func_def_147, type, member64234660_state: produc2041926651_state > set_Pr849496667_state > $o).
% 3.14/1.78  thf(func_def_148, type, member1267359376_state: produc1225889383_state > set_Pr1142642759_state > $o).
% 3.14/1.78  thf(func_def_149, type, member423306384_state: produc1586269031_state > set_Pr1325664839_state > $o).
% 3.14/1.78  thf(func_def_150, type, member1333916004om_com: product_prod_com_com > set_Pr1822651163om_com > $o).
% 3.14/1.78  thf(func_def_151, type, member89779770st_com: produc1440412305st_com > set_Pr135335153st_com > $o).
% 3.14/1.78  thf(func_def_152, type, member1414265872_state: produc392316135_state > set_Pr1419004359_state > $o).
% 3.14/1.78  thf(func_def_153, type, member919914512st_com: produc1762014951st_com > set_Pr2083163591st_com > $o).
% 3.14/1.78  thf(func_def_154, type, member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o).
% 3.14/1.78  thf(func_def_155, type, member2092727056_state: produc1519776487_state > set_Pr1847866567_state > $o).
% 3.14/1.78  thf(func_def_156, type, member1642814224_state: produc270545127_state > set_Pr1696918727_state > $o).
% 3.14/1.78  thf(func_def_157, type, member512523024_state: produc186437863_state > set_Pr2096893127_state > $o).
% 3.14/1.78  thf(func_def_158, type, member284400400_state: produc2046512871_state > set_Pr541394119_state > $o).
% 3.14/1.78  thf(func_def_159, type, c: com).
% 3.14/1.78  thf(func_def_160, type, c2: com).
% 3.14/1.78  thf(func_def_161, type, cs: list_com).
% 3.14/1.78  thf(func_def_162, type, s: state).
% 3.14/1.78  thf(func_def_163, type, s2: state).
% 3.14/1.78  thf(func_def_182, type, sP0: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > $o).
% 3.14/1.78  thf(func_def_183, type, sP1: state > (state > $o) > state > com > list_com > list_com > $o).
% 3.14/1.78  thf(func_def_184, type, sP2: com > list_com > list_com > (state > $o) > state > state > $o).
% 3.14/1.78  thf(func_def_185, type, sK3: produc410756839_state > state).
% 3.14/1.78  thf(func_def_186, type, sK4: produc410756839_state > list_com).
% 3.14/1.78  thf(func_def_187, type, sK5: produc410756839_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_188, type, sK6: (produc410756839_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_189, type, sK7: (produc410756839_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_190, type, sK8: (produc186437863_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_191, type, sK9: (produc186437863_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_192, type, sK10: (produc186437863_state > $o) > produc410756839_state).
% 3.14/1.78  thf(func_def_193, type, sK11: (produc410756839_state > $o) > list_com).
% 3.14/1.78  thf(func_def_194, type, sK12: (produc410756839_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_195, type, sK13: (produc410756839_state > $o) > state).
% 3.14/1.78  thf(func_def_196, type, sK14: (list_com > state > $o) > set_Pr1165141447_state > state > list_com > state).
% 3.14/1.78  thf(func_def_197, type, sK15: (list_com > state > $o) > set_Pr1165141447_state > state > list_com > list_com).
% 3.14/1.78  thf(func_def_198, type, sK16: (list_com > state > $o) > set_Pr1165141447_state > state > list_com > list_com).
% 3.14/1.78  thf(func_def_199, type, sK17: (list_com > state > $o) > set_Pr1165141447_state > state > list_com > state).
% 3.14/1.78  thf(func_def_200, type, sK18: produc410756839_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_201, type, sK19: produc410756839_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_202, type, sK20: ((com > com) > list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_203, type, sK21: ((com > com) > list_com > list_com > $o) > com > com).
% 3.14/1.78  thf(func_def_204, type, sK22: ((com > com) > list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_205, type, sK23: ((com > com) > list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_206, type, sK24: ((com > com) > list_com > list_com > $o) > com > com).
% 3.14/1.78  thf(func_def_207, type, sK25: ((com > com) > list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_208, type, sK26: produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_209, type, sK27: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_210, type, sK28: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_211, type, sK29: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_212, type, sK30: state > set_Pr1165141447_state > (list_com > state > $o) > list_com > state).
% 3.14/1.78  thf(func_def_213, type, sK31: state > set_Pr1165141447_state > (list_com > state > $o) > list_com > state).
% 3.14/1.78  thf(func_def_214, type, sK32: state > set_Pr1165141447_state > (list_com > state > $o) > list_com > list_com).
% 3.14/1.78  thf(func_def_215, type, sK33: state > set_Pr1165141447_state > (list_com > state > $o) > list_com > list_com).
% 3.14/1.78  thf(func_def_216, type, sK34: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_217, type, sK35: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_218, type, sK36: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_219, type, sK37: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_220, type, sK38: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_221, type, sK39: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_222, type, sK40: (produc186437863_state > $o) > produc410756839_state).
% 3.14/1.78  thf(func_def_223, type, sK41: (produc186437863_state > $o) > produc410756839_state).
% 3.14/1.78  thf(func_def_224, type, sK42: produc2041926651_state > list_com).
% 3.14/1.78  thf(func_def_225, type, sK43: produc2041926651_state > state).
% 3.14/1.78  thf(func_def_226, type, sK44: list_com > list_com > list_com > list_com > list_com).
% 3.14/1.78  thf(func_def_227, type, sK45: state > state > list_com > list_com > set_Pr1165141447_state > state).
% 3.14/1.78  thf(func_def_228, type, sK46: state > state > list_com > list_com > set_Pr1165141447_state > list_com).
% 3.14/1.78  thf(func_def_229, type, sK47: produc410756839_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_230, type, sK48: produc410756839_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_231, type, sK49: (produc186437863_state > $o) > produc410756839_state).
% 3.14/1.78  thf(func_def_232, type, sK50: (produc186437863_state > $o) > state).
% 3.14/1.78  thf(func_def_233, type, sK51: (produc186437863_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_234, type, sK52: (produc186437863_state > $o) > list_com).
% 3.14/1.78  thf(func_def_235, type, sK53: ((com > com > $o) > list_com > $o) > com > com > $o).
% 3.14/1.78  thf(func_def_236, type, sK54: ((com > com > $o) > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_237, type, sK55: ((com > com > $o) > list_com > $o) > com).
% 3.14/1.78  thf(func_def_238, type, sK56: ((com > com > $o) > list_com > $o) > com).
% 3.14/1.78  thf(func_def_239, type, sK57: ((com > com > $o) > list_com > $o) > com).
% 3.14/1.78  thf(func_def_240, type, sK58: ((com > com > $o) > list_com > $o) > com > com > $o).
% 3.14/1.78  thf(func_def_241, type, sK59: ((com > com > $o) > list_com > $o) > com > com > $o).
% 3.14/1.78  thf(func_def_242, type, sK60: list_com > list_com).
% 3.14/1.78  thf(func_def_243, type, sK61: list_com > com).
% 3.14/1.78  thf(func_def_244, type, sK62: (produc2041926651_state > $o) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_245, type, sK63: (produc2041926651_state > $o) > produc2041926651_state > set_Pr1165141447_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_246, type, sK64: (list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_247, type, sK65: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_248, type, sK66: list_com > com).
% 3.14/1.78  thf(func_def_249, type, sK67: list_com > list_com).
% 3.14/1.78  thf(func_def_250, type, sK68: list_com > com).
% 3.14/1.78  thf(func_def_251, type, sK69: list_com > com).
% 3.14/1.78  thf(func_def_252, type, sK70: produc186437863_state > produc410756839_state).
% 3.14/1.78  thf(func_def_253, type, sK71: produc186437863_state > produc410756839_state).
% 3.14/1.78  thf(func_def_254, type, sK72: produc186437863_state > produc410756839_state).
% 3.14/1.78  thf(func_def_255, type, sK73: produc186437863_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_256, type, sK74: produc186437863_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_257, type, sK75: list_com > com > list_com > list_com > list_com).
% 3.14/1.78  thf(func_def_258, type, sK76: list_com > list_com).
% 3.14/1.78  thf(func_def_259, type, sK77: list_com > com).
% 3.14/1.78  thf(func_def_260, type, sK78: (produc2041926651_state > produc2041926651_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_261, type, sK79: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_262, type, sK80: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_263, type, sK81: (produc2041926651_state > produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_264, type, sK82: state > (state > $o) > com > state).
% 3.14/1.78  thf(func_def_265, type, sK83: state > list_com > com > state).
% 3.14/1.78  thf(func_def_266, type, sK84: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_267, type, sK85: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_268, type, sK86: (list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_269, type, sK87: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_270, type, sK88: (produc186437863_state > $o) > produc410756839_state).
% 3.14/1.78  thf(func_def_271, type, sK89: (produc186437863_state > $o) > produc410756839_state).
% 3.14/1.78  thf(func_def_272, type, sK90: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_273, type, sK91: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_274, type, sK92: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_275, type, sK93: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_276, type, sK94: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_277, type, sK95: (list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_278, type, sK96: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_279, type, sK97: (produc2041926651_state > $o) > state).
% 3.14/1.78  thf(func_def_280, type, sK98: (produc2041926651_state > $o) > list_com).
% 3.14/1.78  thf(func_def_281, type, sK99: set_Pr1165141447_state > produc2041926651_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_282, type, sK100: (produc2041926651_state > $o) > list_com).
% 3.14/1.78  thf(func_def_283, type, sK101: (produc2041926651_state > $o) > state).
% 3.14/1.78  thf(func_def_284, type, sK102: (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_285, type, sK103: (produc2041926651_state > $o) > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_286, type, sK104: (produc410756839_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_287, type, sK105: (produc410756839_state > $o) > produc2041926651_state).
% 3.14/1.78  thf(func_def_288, type, sK106: (list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_289, type, sK107: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_290, type, sK108: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_291, type, sK109: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_292, type, sK110: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_293, type, sK111: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_294, type, sK112: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_295, type, sK113: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_296, type, sK114: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_297, type, sK115: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_298, type, sK116: (list_com > list_com > $o) > com).
% 3.14/1.78  thf(func_def_299, type, sK117: (list_com > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_300, type, sK118: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_301, type, sK119: (list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_302, type, sK120: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_303, type, sK121: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_304, type, sK122: produc186437863_state > produc410756839_state).
% 3.14/1.78  thf(func_def_305, type, sK123: produc186437863_state > produc410756839_state).
% 3.14/1.78  thf(func_def_306, type, sK124: list_com > com).
% 3.14/1.78  thf(func_def_307, type, sK125: list_com > list_com).
% 3.14/1.78  thf(func_def_308, type, sK126: produc2041926651_state > set_Pr1165141447_state > produc2041926651_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_309, type, sK127: (list_com > $o) > com).
% 3.14/1.78  thf(func_def_310, type, sK128: (list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_311, type, sK129: produc2041926651_state > list_com).
% 3.14/1.78  thf(func_def_312, type, sK130: produc2041926651_state > state).
% 3.14/1.78  thf(func_def_313, type, sK131: produc186437863_state > state).
% 3.14/1.78  thf(func_def_314, type, sK132: produc186437863_state > list_com).
% 3.14/1.78  thf(func_def_315, type, sK133: produc186437863_state > produc410756839_state).
% 3.14/1.78  thf(func_def_316, type, sK134: produc186437863_state > produc2041926651_state).
% 3.14/1.78  thf(func_def_317, type, sK135: ((com > com > $o) > list_com > $o) > com).
% 3.14/1.78  thf(func_def_318, type, sK136: ((com > com > $o) > list_com > $o) > com > com > $o).
% 3.14/1.78  thf(func_def_319, type, sK137: ((com > com > $o) > list_com > $o) > list_com).
% 3.14/1.78  thf(func_def_320, type, sK138: ((com > com > $o) > list_com > $o) > com > com > $o).
% 3.14/1.78  thf(func_def_321, type, sK139: list_com > list_com > com > list_com > list_com).
% 3.14/1.78  thf(func_def_323, type, ph141: !>[X0: $tType]:(X0)).
% 3.14/1.78  thf(f1569,plain,(
% 3.14/1.78    $false),
% 3.14/1.78    inference(subsumption_resolution,[status(thm)],[f1568,f1362])).
% 3.14/1.78  thf(f1362,plain,(
% 3.14/1.78    ((termi @ c @ s) = $true)),
% 3.14/1.78    inference(cnf_transformation,[status(thm)],[f884])).
% 3.14/1.78  thf(f884,plain,(
% 3.14/1.78    ((termi @ c @ s) = $true)),
% 3.14/1.78    inference(fool_elimination,[status(thm)],[f883])).
% 3.14/1.78  thf(f883,plain,(
% 3.14/1.78    (termi @ c @ s)),
% 3.14/1.78    inference(rectify,[status(thm)],[f356])).
% 3.14/1.78  thf(f356,axiom,(
% 3.14/1.78    (termi @ c @ s)),
% 3.14/1.78    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_1)).
% 3.14/1.78  thf(f1568,plain,(
% 3.14/1.78    ((termi @ c @ s) != $true)),
% 3.14/1.78    inference(subsumption_resolution,[status(thm)],[f1567,f1411])).
% 3.14/1.78  thf(f1411,plain,(
% 3.14/1.78    ((termi @ c2 @ s2) != $true)),
% 3.14/1.78    inference(cnf_transformation,[status(thm)],[f919])).
% 3.14/1.78  thf(f919,plain,(
% 3.14/1.78    ((termi @ c2 @ s2) != $true)),
% 3.14/1.78    inference(flattening,[status(thm)],[f558])).
% 3.14/1.78  thf(f558,plain,(
% 3.14/1.78    ~((termi @ c2 @ s2) = $true)),
% 3.14/1.78    inference(fool_elimination,[status(thm)],[f557])).
% 3.14/1.78  thf(f557,plain,(
% 3.14/1.78    ~(termi @ c2 @ s2)),
% 3.14/1.78    inference(rectify,[status(thm)],[f359])).
% 3.14/1.78  thf(f359,negated_conjecture,(
% 3.14/1.78    ~(termi @ c2 @ s2)),
% 3.14/1.78    inference(negated_conjecture,[status(cth)],[f358])).
% 3.14/1.78  thf(f358,conjecture,(
% 3.14/1.78    (termi @ c2 @ s2)),
% 3.14/1.78    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_3)).
% 3.14/1.78  thf(f1567,plain,(
% 3.14/1.78    ((termi @ c2 @ s2) = $true) | ((termi @ c @ s) != $true)),
% 3.14/1.78    inference(trivial_inequality_removal,[status(thm)],[f1556])).
% 3.14/1.78  thf(f1556,plain,(
% 3.14/1.78    ((termi @ c @ s) != $true) | ($true != $true) | ((termi @ c2 @ s2) = $true)),
% 3.14/1.78    inference(superposition,[status(thm)],[f1386,f1416])).
% 3.14/1.78  thf(f1416,plain,(
% 3.14/1.78    ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ s2)) @ (transi1302705790_state @ pHoare259243666_exec1)) = $true)),
% 3.14/1.78    inference(cnf_transformation,[status(thm)],[f854])).
% 3.14/1.78  thf(f854,plain,(
% 3.14/1.78    ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ s2)) @ (transi1302705790_state @ pHoare259243666_exec1)) = $true)),
% 3.14/1.78    inference(fool_elimination,[status(thm)],[f853])).
% 3.14/1.78  thf(f853,plain,(
% 3.14/1.78    (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ s2)) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 3.14/1.78    inference(rectify,[status(thm)],[f355])).
% 3.14/1.78  thf(f355,axiom,(
% 3.14/1.78    (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ s2)) @ (transi1302705790_state @ pHoare259243666_exec1))),
% 3.14/1.78    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_0)).
% 3.14/1.78  thf(f1386,plain,(
% 3.14/1.78    ( ! [X0 : state,X1 : state] : (($true != (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ X1) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ X0)) @ (transi1302705790_state @ pHoare259243666_exec1))) | ((termi @ c @ X1) != $true) | ((termi @ c2 @ X0) = $true)) )),
% 3.14/1.78    inference(cnf_transformation,[status(thm)],[f985])).
% 3.14/1.78  thf(f985,plain,(
% 3.14/1.78    ! [X0 : state,X1 : state] : ((! [X2 : state] : (($true != (exec @ X0 @ c2 @ X2)) | ((pHoare806997636termis @ cs @ X2) = $true)) & ((termi @ c2 @ X0) = $true)) | ($true != (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ X1) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ X0)) @ (transi1302705790_state @ pHoare259243666_exec1))) | ((termi @ c @ X1) != $true))),
% 3.14/1.78    inference(flattening,[status(thm)],[f984])).
% 3.14/1.78  thf(f984,plain,(
% 3.14/1.78    ! [X0 : state,X1 : state] : (((! [X2 : state] : (($true != (exec @ X0 @ c2 @ X2)) | ((pHoare806997636termis @ cs @ X2) = $true)) & ((termi @ c2 @ X0) = $true)) | ((termi @ c @ X1) != $true)) | ($true != (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ X1) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ X0)) @ (transi1302705790_state @ pHoare259243666_exec1))))),
% 3.14/1.78    inference(ennf_transformation,[status(thm)],[f746])).
% 3.14/1.78  thf(f746,plain,(
% 3.14/1.78    ! [X0 : state,X1 : state] : (($true = (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ X1) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ X0)) @ (transi1302705790_state @ pHoare259243666_exec1))) => (((termi @ c @ X1) = $true) => (! [X2 : state] : (($true = (exec @ X0 @ c2 @ X2)) => ((pHoare806997636termis @ cs @ X2) = $true)) & ((termi @ c2 @ X0) = $true))))),
% 3.14/1.78    inference(fool_elimination,[status(thm)],[f745])).
% 3.14/1.78  thf(f745,plain,(
% 3.14/1.78    ! [X0 : state,X1 : state] : ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ X1) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ X0)) @ (transi1302705790_state @ pHoare259243666_exec1)) => ((termi @ c @ X1) => (! [X2 : state] : ((exec @ X0 @ c2 @ X2) => (pHoare806997636termis @ cs @ X2)) & (termi @ c2 @ X0))))),
% 3.14/1.78    inference(rectify,[status(thm)],[f357])).
% 3.14/1.78  thf(f357,axiom,(
% 3.14/1.78    ! [X135 : state,X134 : state] : ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ X134) @ (produc1204172211_state @ (cons_com @ c2 @ cs) @ X135)) @ (transi1302705790_state @ pHoare259243666_exec1)) => ((termi @ c @ X134) => (! [X136 : state] : ((exec @ X135 @ c2 @ X136) => (pHoare806997636termis @ cs @ X136)) & (termi @ c2 @ X135))))),
% 3.14/1.78    file('/export/starexec/sandbox/tmp/tmp.n8D0SPRkhP/DTF2THF_11910.p',conj_2)).
% 3.14/1.78  % SZS output end Proof for DTF2THF_11910
% 3.14/1.78  % (12022)------------------------------
% 3.14/1.78  % (12022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.78  % (12022)Termination reason: Refutation
% 3.14/1.78  
% 3.14/1.78  % (12022)Memory used [KB]: 8187
% 3.14/1.78  % (12022)Time elapsed: 0.059 s
% 3.14/1.78  % (12022)Instructions burned: 153 (million)
% 3.14/1.78  % (12022)------------------------------
% 3.14/1.78  % (12022)------------------------------
% 3.14/1.78  % (12016)Success in time 0.095 s
%------------------------------------------------------------------------------