DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP182^1 : 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 : n005.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 08:56:13 AM UTC 2026

% Result   : Theorem 3.16s 1.69s
% Output   : Refutation 3.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   22 (  16 unt;   0 typ;   0 def)
%            Number of atoms       :   58 (  18 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  226 (  11   ~;   3   |;   0   &; 209   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :   47 (  46 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  284 ( 281 usr;  15 con; 0-5 aty)
%            Number of variables   :   29 (   0   ^;  29   !;   0   ?;  29   :)

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

thf(type_def_6,type,
    pi: $tType ).

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

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

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

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

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

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

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

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

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

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

thf(type_def_18,type,
    list_P227219501e_name: $tType ).

thf(type_def_19,type,
    list_l1406151091e_name: $tType ).

thf(type_def_20,type,
    produc367475239e_name: $tType ).

thf(type_def_21,type,
    produc1141751126_pi_pi: $tType ).

thf(type_def_22,type,
    list_P431515740_pi_pi: $tType ).

thf(type_def_23,type,
    produc2008547984reeRes: $tType ).

thf(type_def_24,type,
    produc865358760ubject: $tType ).

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

thf(type_def_26,type,
    produc2052722628s_name: $tType ).

thf(type_def_27,type,
    produc992857746Res_pi: $tType ).

thf(type_def_28,type,
    produc1357834675reeRes: $tType ).

thf(type_def_29,type,
    produc214645451ubject: $tType ).

thf(type_def_30,type,
    produc1998742700t_name: $tType ).

thf(type_def_31,type,
    produc140253050ect_pi: $tType ).

thf(type_def_32,type,
    produc355105483reeRes: $tType ).

thf(type_def_33,type,
    produc1359399907ubject: $tType ).

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

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

thf(type_def_36,type,
    produc1777919905pi_Rep: $tType ).

thf(type_def_37,type,
    produc257012921pi_Rep: $tType ).

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

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

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

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

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

thf(type_def_43,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(type_def_44,type,
    set_Pr443758855e_name: $tType ).

thf(type_def_45,type,
    set_Pr1654044726_pi_pi: $tType ).

thf(type_def_46,type,
    produc1872410278e_name: $tType ).

thf(type_def_47,type,
    produc1212344719pi_Rep: $tType ).

thf(type_def_48,type,
    produc890461031e_name: $tType ).

thf(type_def_49,type,
    set_Pr1131282415pi_Rep: $tType ).

thf(type_def_50,type,
    set_Pr1780909331reeRes: $tType ).

thf(type_def_51,type,
    set_Pr806375235ubject: $tType ).

thf(func_def_0,type,
    produc1872410278e_name: $tType ).

thf(func_def_1,type,
    produc890461031e_name: $tType ).

thf(func_def_2,type,
    list_P431515740_pi_pi: $tType ).

thf(func_def_3,type,
    set_Pr1654044726_pi_pi: $tType ).

thf(func_def_4,type,
    set_Pr806375235ubject: $tType ).

thf(func_def_5,type,
    set_Pr1780909331reeRes: $tType ).

thf(func_def_6,type,
    produc1141751126_pi_pi: $tType ).

thf(func_def_7,type,
    list_l1406151091e_name: $tType ).

thf(func_def_8,type,
    produc1359399907ubject: $tType ).

thf(func_def_9,type,
    produc355105483reeRes: $tType ).

thf(func_def_10,type,
    produc214645451ubject: $tType ).

thf(func_def_11,type,
    produc1357834675reeRes: $tType ).

thf(func_def_12,type,
    set_Pr1131282415pi_Rep: $tType ).

thf(func_def_13,type,
    produc257012921pi_Rep: $tType ).

thf(func_def_14,type,
    produc1777919905pi_Rep: $tType ).

thf(func_def_15,type,
    list_P227219501e_name: $tType ).

thf(func_def_16,type,
    set_Pr443758855e_name: $tType ).

thf(func_def_17,type,
    produc1998742700t_name: $tType ).

thf(func_def_18,type,
    produc2052722628s_name: $tType ).

thf(func_def_19,type,
    produc865358760ubject: $tType ).

thf(func_def_20,type,
    produc2008547984reeRes: $tType ).

thf(func_def_21,type,
    produc140253050ect_pi: $tType ).

thf(func_def_22,type,
    produc992857746Res_pi: $tType ).

thf(func_def_23,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(func_def_24,type,
    produc1212344719pi_Rep: $tType ).

thf(func_def_25,type,
    produc367475239e_name: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_40,type,
    late_subject: $tType ).

thf(func_def_41,type,
    late_freeRes: $tType ).

thf(func_def_42,type,
    set_pi: $tType ).

thf(func_def_43,type,
    pi_Rep: $tType ).

thf(func_def_44,type,
    name: $tType ).

thf(func_def_45,type,
    pi: $tType ).

thf(func_def_46,type,
    input: name > name > pi > pi ).

thf(func_def_47,type,
    res: name > pi > pi ).

thf(func_def_48,type,
    sum: pi > pi > pi ).

thf(func_def_49,type,
    if_name: $o > name > name > name ).

thf(func_def_50,type,
    if_pi: $o > pi > pi > pi ).

thf(func_def_51,type,
    if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).

thf(func_def_52,type,
    if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).

thf(func_def_53,type,
    if_Late_subject: $o > late_subject > late_subject > late_subject ).

thf(func_def_54,type,
    late_OutputR: name > name > late_freeRes ).

thf(func_def_55,type,
    late_BoundR: late_subject > name > pi > late_residual ).

thf(func_def_56,type,
    late_FreeR: late_freeRes > pi > late_residual ).

thf(func_def_57,type,
    late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).

thf(func_def_58,type,
    late_BoundOutputS: name > late_subject ).

thf(func_def_59,type,
    late_InputS: name > late_subject ).

thf(func_def_60,type,
    late_transitions: pi > late_residual > $o ).

thf(func_def_61,type,
    cons_name: name > list_name > list_name ).

thf(func_def_62,type,
    cons_pi: pi > list_pi > list_pi ).

thf(func_def_63,type,
    cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep ).

thf(func_def_64,type,
    cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes ).

thf(func_def_65,type,
    cons_Late_subject: late_subject > list_Late_subject > list_Late_subject ).

thf(func_def_66,type,
    cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name ).

thf(func_def_67,type,
    cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).

thf(func_def_68,type,
    cons_P749510156_pi_pi: produc1141751126_pi_pi > list_P431515740_pi_pi > list_P431515740_pi_pi ).

thf(func_def_69,type,
    nil_li29751603e_name: list_l1406151091e_name ).

thf(func_def_70,type,
    nil_Pr743626285e_name: list_P227219501e_name ).

thf(func_def_71,type,
    fresh_name_name: name > name > $o ).

thf(func_def_72,type,
    fresh_name_pi: name > pi > $o ).

thf(func_def_73,type,
    fresh_name_pi_Rep: name > pi_Rep > $o ).

thf(func_def_74,type,
    fresh_1641682979reeRes: name > late_freeRes > $o ).

thf(func_def_75,type,
    fresh_81631222sidual: name > late_residual > $o ).

thf(func_def_76,type,
    fresh_717452603ubject: name > late_subject > $o ).

thf(func_def_77,type,
    fresh_name_list_name: name > list_name > $o ).

thf(func_def_78,type,
    fresh_name_list_pi: name > list_pi > $o ).

thf(func_def_79,type,
    fresh_1981651763reeRes: name > list_Late_freeRes > $o ).

thf(func_def_80,type,
    fresh_838462539ubject: name > list_Late_subject > $o ).

thf(func_def_81,type,
    fresh_922791155e_name: name > list_P227219501e_name > $o ).

thf(func_def_82,type,
    fresh_1958133282_pi_pi: name > list_P431515740_pi_pi > $o ).

thf(func_def_83,type,
    fresh_441084397e_name: name > produc367475239e_name > $o ).

thf(func_def_84,type,
    fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).

thf(func_def_85,type,
    fresh_820177506ubject: name > produc865358760ubject > $o ).

thf(func_def_86,type,
    fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).

thf(func_def_87,type,
    fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).

thf(func_def_88,type,
    fresh_2007541374s_name: name > produc2052722628s_name > $o ).

thf(func_def_89,type,
    fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).

thf(func_def_90,type,
    fresh_493808761reeRes: name > produc1357834675reeRes > $o ).

thf(func_def_91,type,
    fresh_1498103185ubject: name > produc214645451ubject > $o ).

thf(func_def_92,type,
    fresh_1953561446t_name: name > produc1998742700t_name > $o ).

thf(func_def_93,type,
    fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).

thf(func_def_94,type,
    fresh_1638563217reeRes: name > produc355105483reeRes > $o ).

thf(func_def_95,type,
    fresh_495373993ubject: name > produc1359399907ubject > $o ).

thf(func_def_96,type,
    perm_n382765978reeRes: list_P227219501e_name > ( name > late_freeRes ) > name > late_freeRes ).

thf(func_def_97,type,
    perm_n1387060402ubject: list_P227219501e_name > ( name > late_subject ) > name > late_subject ).

thf(func_def_98,type,
    perm_n1333244520reeRes: list_P227219501e_name > ( pi > late_freeRes ) > pi > late_freeRes ).

thf(func_def_99,type,
    perm_n190055296ubject: list_P227219501e_name > ( pi > late_subject ) > pi > late_subject ).

thf(func_def_100,type,
    perm_n1841560599reeRes: list_P227219501e_name > ( pi_Rep > late_freeRes ) > pi_Rep > late_freeRes ).

thf(func_def_101,type,
    perm_n698371375ubject: list_P227219501e_name > ( pi_Rep > late_subject ) > pi_Rep > late_subject ).

thf(func_def_102,type,
    perm_n1446290985reeRes: list_P227219501e_name > ( late_freeRes > late_freeRes ) > late_freeRes > late_freeRes ).

thf(func_def_103,type,
    perm_n303101761ubject: list_P227219501e_name > ( late_freeRes > late_subject ) > late_freeRes > late_subject ).

thf(func_def_104,type,
    perm_n443561793reeRes: list_P227219501e_name > ( late_subject > late_freeRes ) > late_subject > late_freeRes ).

thf(func_def_105,type,
    perm_n1447856217ubject: list_P227219501e_name > ( late_subject > late_subject ) > late_subject > late_subject ).

thf(func_def_106,type,
    perm_name_o: list_P227219501e_name > $o > $o ).

thf(func_def_107,type,
    perm_name_name: list_P227219501e_name > name > name ).

thf(func_def_108,type,
    perm_name_pi: list_P227219501e_name > pi > pi ).

thf(func_def_109,type,
    perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep ).

thf(func_def_110,type,
    perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes ).

thf(func_def_111,type,
    perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep ).

thf(func_def_112,type,
    perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual ).

thf(func_def_113,type,
    perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep ).

thf(func_def_114,type,
    perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject ).

thf(func_def_115,type,
    perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep ).

thf(func_def_116,type,
    perm_name_list_name: list_P227219501e_name > list_name > list_name ).

thf(func_def_117,type,
    perm_name_list_pi: list_P227219501e_name > list_pi > list_pi ).

thf(func_def_118,type,
    perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep ).

thf(func_def_119,type,
    perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes ).

thf(func_def_120,type,
    perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject ).

thf(func_def_121,type,
    perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).

thf(func_def_122,type,
    perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi ).

thf(func_def_123,type,
    perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).

thf(func_def_124,type,
    perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).

thf(func_def_125,type,
    perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).

thf(func_def_126,type,
    perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).

thf(func_def_127,type,
    perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).

thf(func_def_128,type,
    perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).

thf(func_def_129,type,
    perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).

thf(func_def_130,type,
    perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).

thf(func_def_131,type,
    perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).

thf(func_def_132,type,
    perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).

thf(func_def_133,type,
    perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).

thf(func_def_134,type,
    perm_name_set_name: list_P227219501e_name > set_name > set_name ).

thf(func_def_135,type,
    perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).

thf(func_def_136,type,
    perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).

thf(func_def_137,type,
    perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).

thf(func_def_138,type,
    perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).

thf(func_def_139,type,
    perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).

thf(func_def_140,type,
    swap_name: produc367475239e_name > name > name ).

thf(func_def_141,type,
    ord_le793202855e_name: set_Pr443758855e_name > set_Pr443758855e_name > $o ).

thf(func_def_142,type,
    ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).

thf(func_def_143,type,
    ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(func_def_144,type,
    produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).

thf(func_def_145,type,
    produc1570949143e_name: name > name > produc367475239e_name ).

thf(func_def_146,type,
    produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).

thf(func_def_147,type,
    produc607574050ubject: name > late_subject > produc865358760ubject ).

thf(func_def_148,type,
    produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).

thf(func_def_149,type,
    product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).

thf(func_def_150,type,
    produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).

thf(func_def_151,type,
    produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).

thf(func_def_152,type,
    produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).

thf(func_def_153,type,
    produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).

thf(func_def_154,type,
    produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).

thf(func_def_155,type,
    produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).

thf(func_def_156,type,
    produc1647375838t_name: late_subject > name > produc1998742700t_name ).

thf(func_def_157,type,
    produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).

thf(func_def_158,type,
    produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).

thf(func_def_159,type,
    produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).

thf(func_def_160,type,
    produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).

thf(func_def_161,type,
    produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).

thf(func_def_162,type,
    eqvt_name: set_Pr443758855e_name > $o ).

thf(func_def_163,type,
    eqvt_pi: set_Pr1834926343_pi_pi > $o ).

thf(func_def_164,type,
    eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).

thf(func_def_165,type,
    eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).

thf(func_def_166,type,
    eqvt_Late_subject: set_Pr806375235ubject > $o ).

thf(func_def_167,type,
    id_name: set_Pr443758855e_name ).

thf(func_def_168,type,
    id_pi: set_Pr1834926343_pi_pi ).

thf(func_def_169,type,
    collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).

thf(func_def_170,type,
    strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).

thf(func_def_171,type,
    strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).

thf(func_def_172,type,
    member_name: name > set_name > $o ).

thf(func_def_173,type,
    member_pi: pi > set_pi > $o ).

thf(func_def_174,type,
    member_pi_Rep: pi_Rep > set_pi_Rep > $o ).

thf(func_def_175,type,
    member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).

thf(func_def_176,type,
    member_Late_subject: late_subject > set_Late_subject > $o ).

thf(func_def_177,type,
    member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).

thf(func_def_178,type,
    member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).

thf(func_def_179,type,
    member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(func_def_180,type,
    member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).

thf(func_def_181,type,
    member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).

thf(func_def_182,type,
    member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).

thf(func_def_183,type,
    p: pi ).

thf(func_def_184,type,
    pq: pi ).

thf(func_def_185,type,
    p2: pi ).

thf(func_def_186,type,
    q: pi ).

thf(func_def_187,type,
    rel: set_Pr1834926343_pi_pi ).

thf(func_def_188,type,
    a: late_subject ).

thf(func_def_189,type,
    aa: name ).

thf(func_def_190,type,
    x: name ).

thf(func_def_191,type,
    y: name ).

thf(func_def_209,type,
    sP0: pi > ( late_subject > pi > $o ) > name > name > late_subject > $o ).

thf(func_def_210,type,
    sP1: late_subject > name > pi > name > pi > $o ).

thf(func_def_211,type,
    sP2: name > pi > late_residual > $o ).

thf(func_def_212,type,
    sP3: name > pi > late_residual > $o ).

thf(func_def_213,type,
    sK4: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_214,type,
    sK5: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_215,type,
    sK6: pi > ( late_subject > pi > $o ) > name > name > late_subject > name ).

thf(func_def_216,type,
    sK7: pi > ( late_subject > pi > $o ) > name > name > late_subject > pi ).

thf(func_def_217,type,
    sK8: pi > ( late_subject > pi > $o ) > name > late_subject > name > pi ).

thf(func_def_218,type,
    sK9: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_219,type,
    sK10: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_220,type,
    sK11: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_221,type,
    sK12: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_222,type,
    sK13: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_223,type,
    sK14: ( produc367475239e_name > $o ) > name ).

thf(func_def_224,type,
    sK15: ( produc367475239e_name > $o ) > name ).

thf(func_def_225,type,
    sK16: list_P227219501e_name > produc367475239e_name ).

thf(func_def_226,type,
    sK17: list_P227219501e_name > produc367475239e_name ).

thf(func_def_227,type,
    sK18: list_P227219501e_name > list_P227219501e_name ).

thf(func_def_228,type,
    sK19: list_P227219501e_name > produc367475239e_name ).

thf(func_def_229,type,
    sK20: pi > late_freeRes > ( pi > $o ) > name > pi ).

thf(func_def_230,type,
    sK21: product_prod_pi_pi > pi ).

thf(func_def_231,type,
    sK22: product_prod_pi_pi > pi ).

thf(func_def_232,type,
    sK23: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_233,type,
    sK24: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_234,type,
    sK25: product_prod_pi_pi > pi ).

thf(func_def_235,type,
    sK26: produc367475239e_name > name ).

thf(func_def_236,type,
    sK27: produc367475239e_name > name ).

thf(func_def_237,type,
    sK28: list_P227219501e_name > produc367475239e_name ).

thf(func_def_238,type,
    sK29: list_P227219501e_name > list_P227219501e_name ).

thf(func_def_239,type,
    sK30: late_subject > name ).

thf(func_def_240,type,
    sK31: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_241,type,
    sK32: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_242,type,
    sK33: product_prod_pi_pi > pi ).

thf(func_def_243,type,
    sK34: product_prod_pi_pi > pi ).

thf(func_def_244,type,
    sK35: late_subject > name > pi > name > pi > pi ).

thf(func_def_245,type,
    sK36: late_subject > name > pi > name > pi > name ).

thf(func_def_246,type,
    sK37: late_subject > name > pi > name > pi > late_subject ).

thf(func_def_247,type,
    sK38: late_subject > name > pi > name > pi > pi ).

thf(func_def_248,type,
    sK39: late_subject > name > pi > name > pi > name ).

thf(func_def_249,type,
    sK40: name > pi > late_subject > pi > name > name ).

thf(func_def_250,type,
    sK41: name > pi > late_subject > pi > name > name ).

thf(func_def_251,type,
    sK42: name > pi > late_subject > pi > name > pi ).

thf(func_def_252,type,
    sK43: name > pi > late_subject > pi > name > pi ).

thf(func_def_253,type,
    sK44: name > pi > pi > late_subject > set_Pr1834926343_pi_pi > pi ).

thf(func_def_254,type,
    sK45: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_255,type,
    sK46: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_256,type,
    sK47: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_257,type,
    sK48: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_258,type,
    sK49: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_259,type,
    sK50: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_260,type,
    sK51: produc367475239e_name > name ).

thf(func_def_261,type,
    sK52: produc367475239e_name > name ).

thf(func_def_262,type,
    sK53: ( produc367475239e_name > $o ) > name ).

thf(func_def_263,type,
    sK54: ( produc367475239e_name > $o ) > name ).

thf(func_def_264,type,
    sK55: name > late_freeRes > pi > pi > name ).

thf(func_def_265,type,
    sK56: name > late_freeRes > pi > pi > late_freeRes ).

thf(func_def_266,type,
    sK57: name > late_freeRes > pi > pi > pi ).

thf(func_def_267,type,
    sK58: name > late_freeRes > pi > pi > pi ).

thf(func_def_268,type,
    sK59: pi > name ).

thf(func_def_269,type,
    sK60: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_270,type,
    sK61: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_271,type,
    sK62: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_272,type,
    sK63: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_273,type,
    sK64: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_274,type,
    sK65: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_275,type,
    sK66: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_276,type,
    sK67: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_277,type,
    sK68: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_278,type,
    sK69: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_279,type,
    sK70: pi > pi > set_Pr1834926343_pi_pi > late_subject ).

thf(func_def_280,type,
    sK71: pi > pi > set_Pr1834926343_pi_pi > name ).

thf(func_def_281,type,
    sK72: pi > pi > set_Pr1834926343_pi_pi > pi ).

thf(func_def_282,type,
    sK73: pi > pi > set_Pr1834926343_pi_pi > pi ).

thf(func_def_283,type,
    sK74: pi > pi > set_Pr1834926343_pi_pi > late_freeRes ).

thf(func_def_284,type,
    sK75: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_285,type,
    sK76: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_286,type,
    sK77: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_287,type,
    sK78: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_288,type,
    sK79: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_289,type,
    sK80: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_290,type,
    sK81: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_291,type,
    sK82: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_292,type,
    sK83: name > name ).

thf(func_def_293,type,
    sK84: ( late_residual > $o ) > name ).

thf(func_def_294,type,
    sK85: ( late_residual > $o ) > late_subject ).

thf(func_def_295,type,
    sK86: ( late_residual > $o ) > pi ).

thf(func_def_296,type,
    sK87: ( late_residual > $o ) > late_freeRes ).

thf(func_def_297,type,
    sK88: ( late_residual > $o ) > pi ).

thf(func_def_298,type,
    sK89: set_Pr1834926343_pi_pi > late_freeRes > pi > pi > pi ).

thf(func_def_299,type,
    sK90: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_300,type,
    sK91: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_301,type,
    sK92: ( ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_302,type,
    sK93: ( ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_303,type,
    sK94: ( ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_304,type,
    sK95: ( ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name ).

thf(func_def_305,type,
    sK96: ( ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name ).

thf(func_def_306,type,
    sK97: ( ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_307,type,
    sK98: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > product_prod_pi_pi ).

thf(func_def_308,type,
    sK99: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_309,type,
    sK100: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_310,type,
    sK101: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_311,type,
    sK102: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_312,type,
    sK103: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_313,type,
    sK104: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_314,type,
    sK105: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_315,type,
    sK106: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi ).

thf(func_def_316,type,
    sK107: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi ).

thf(func_def_317,type,
    sK108: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_318,type,
    sK109: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_319,type,
    sK110: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_320,type,
    sK111: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_321,type,
    sK112: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_322,type,
    sK113: list_P227219501e_name > produc367475239e_name ).

thf(func_def_323,type,
    sK114: list_P227219501e_name > list_P227219501e_name ).

thf(func_def_324,type,
    sK115: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_325,type,
    sK116: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_326,type,
    sK117: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_327,type,
    sK118: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_328,type,
    sK119: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_329,type,
    sK120: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).

thf(func_def_330,type,
    sK121: name > pi > late_residual > pi ).

thf(func_def_331,type,
    sK122: name > pi > late_residual > name ).

thf(func_def_332,type,
    sK123: name > pi > late_residual > name ).

thf(func_def_333,type,
    sK124: name > pi > late_residual > pi ).

thf(func_def_334,type,
    sK125: name > pi > late_residual > name ).

thf(func_def_335,type,
    sK126: name > pi > late_residual > pi ).

thf(func_def_336,type,
    sK127: name > pi > late_residual > name ).

thf(func_def_337,type,
    sK128: name > pi > late_residual > pi ).

thf(func_def_338,type,
    sK129: name > pi > late_residual > late_subject ).

thf(func_def_339,type,
    sK130: pi > late_residual > name > late_freeRes ).

thf(func_def_340,type,
    sK131: pi > late_residual > name > pi ).

thf(func_def_341,type,
    sK132: pi > late_residual > name > pi ).

thf(func_def_342,type,
    sK133: pi > late_residual > name > name ).

thf(func_def_344,type,
    ph135: 
      !>[X0: $tType] : X0 ).

thf(f1490,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f1488,f1426]) ).

thf(f1426,plain,
    ( ( ord_le630093991_pi_pi @ id_pi @ rel )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f557]) ).

thf(f557,plain,
    ( ( ord_le630093991_pi_pi @ id_pi @ rel )
    = $true ),
    inference(fool_elimination,[status(thm)],[f556]) ).

thf(f556,plain,
    ord_le630093991_pi_pi @ id_pi @ rel,
    inference(rectify,[status(thm)],[f1]) ).

thf(f1,axiom,
    ord_le630093991_pi_pi @ id_pi @ rel,
    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',fact_0_Id) ).

thf(f1488,plain,
    ( ( ord_le630093991_pi_pi @ id_pi @ rel )
   != $true ),
    inference(trivial_inequality_removal,[status(thm)],[f1486]) ).

thf(f1486,plain,
    ( ( ( ord_le630093991_pi_pi @ id_pi @ rel )
     != $true )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f1483,f1319]) ).

thf(f1319,plain,
    ! [X2: name,X3: late_subject,X0: pi,X1: set_Pr1834926343_pi_pi] :
      ( ( ( strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1 )
        = $true )
      | ( ( ord_le630093991_pi_pi @ id_pi @ X1 )
       != $true ) ),
    inference(cnf_transformation,[status(thm)],[f1010]) ).

thf(f1010,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: name,X3: late_subject] :
      ( ( ( ord_le630093991_pi_pi @ id_pi @ X1 )
       != $true )
      | ( ( strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1 )
        = $true ) ),
    inference(ennf_transformation,[status(thm)],[f471]) ).

thf(f471,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: name,X3: late_subject] :
      ( ( ( ord_le630093991_pi_pi @ id_pi @ X1 )
        = $true )
     => ( ( strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1 )
        = $true ) ),
    inference(fool_elimination,[status(thm)],[f470]) ).

thf(f470,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: name,X3: late_subject] :
      ( ( ord_le630093991_pi_pi @ id_pi @ X1 )
     => ( strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1 ) ),
    inference(rectify,[status(thm)],[f195]) ).

thf(f195,axiom,
    ! [X27: pi,X56: set_Pr1834926343_pi_pi,X2: name,X0: late_subject] :
      ( ( ord_le630093991_pi_pi @ id_pi @ X56 )
     => ( strong2129052853vative @ X27 @ X27 @ X0 @ X2 @ X56 ) ),
    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',fact_194_derivativeReflexive) ).

thf(f1483,plain,
    ( $true
   != ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ x @ y ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ x @ y ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ) ),
    inference(forward_demodulation,[status(thm)],[f1228,f1236]) ).

thf(f1236,plain,
    ! [X2: name,X0: pi,X1: name] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X2 @ X1 ) @ nil_Pr743626285e_name ) @ X0 )
      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X1 @ X2 ) @ nil_Pr743626285e_name ) @ X0 ) ),
    inference(cnf_transformation,[status(thm)],[f828]) ).

thf(f828,plain,
    ! [X0: pi,X1: name,X2: name] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X2 @ X1 ) @ nil_Pr743626285e_name ) @ X0 )
      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X1 @ X2 ) @ nil_Pr743626285e_name ) @ X0 ) ),
    inference(rectify,[status(thm)],[f20]) ).

thf(f20,axiom,
    ! [X2: pi,X1: name,X0: name] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X0 @ X1 ) @ nil_Pr743626285e_name ) @ X2 )
      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X1 @ X0 ) @ nil_Pr743626285e_name ) @ X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',fact_19_name__swap) ).

thf(f1228,plain,
    ( ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f814]) ).

thf(f814,plain,
    ( ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel )
   != $true ),
    inference(flattening,[status(thm)],[f443]) ).

thf(f443,plain,
    ( ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel )
   != $true ),
    inference(fool_elimination,[status(thm)],[f442]) ).

thf(f442,plain,
    ~ ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ),
    inference(rectify,[status(thm)],[f366]) ).

thf(f366,negated_conjecture,
    ~ ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ),
    inference(negated_conjecture,[status(cth)],[f365]) ).

thf(f365,conjecture,
    strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel,
    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP182^1 : 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 : n005.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 08:28:59 EST 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46  ---- Original DTF file ---
% 0.19/0.46  thf(spec,logic,$$dhol).
% 0.19/0.46  %------------------------------------------------------------------------------
% 0.19/0.46  % File     : ITP182^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46  % Domain   : Interactive Theorem Proving
% 0.19/0.46  % Problem  : Sledgehammer Strong_Late_Sim_SC problem prob_279__3411076_1
% 0.19/0.46  % Version  : Especial.
% 0.19/0.46  % English  :
% 0.19/0.46  
% 0.19/0.46  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46  % Source   : [Des21]
% 0.19/0.46  % Names    : Strong_Late_Sim_SC/prob_279__3411076_1 [Des21]
% 0.19/0.46  
% 0.19/0.46  % Status   : Theorem
% 0.19/0.46  % Rating   : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.19/0.46  % Syntax   : Number of formulae    :  557 ( 219 unt; 192 typ;   0 def)
% 0.19/0.46  %            Number of atoms       :  849 ( 387 equ;   0 cnn)
% 0.19/0.46  %            Maximal formula atoms :   16 (   2 avg)
% 0.19/0.46  %            Number of connectives : 3597 ( 111   ~;   1   |;  50   &;3097   @)
% 0.19/0.46  %                                         (   0 <=>; 338  =>;   0  <=;   0 <~>)
% 0.19/0.46  %            Maximal formula depth :   23 (   7 avg)
% 0.19/0.46  %            Number of types       :   47 (  46 usr)
% 0.19/0.46  %            Number of type conns  :  371 ( 371   >;   0   *;   0   +;   0  <<)
% 0.19/0.46  %            Number of symbols     :  149 ( 146 usr;  15 con; 0-5 aty)
% 0.19/0.46  %            Number of variables   : 1211 (  15   ^;1182   !;  14   ?;1211   :)
% 0.19/0.46  % SPC      : TH0_THM_EQU_NAR
% 0.19/0.46  
% 0.19/0.46  % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:40.333
% 0.19/0.46  %------------------------------------------------------------------------------
% 0.19/0.46  % Could-be-implicit typings (46)
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 0.19/0.46      produc1872410278e_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 0.19/0.46      produc890461031e_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.19/0.46      list_P431515740_pi_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.19/0.46      set_Pr1654044726_pi_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J,type,
% 0.19/0.46      set_Pr806375235ubject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J,type,
% 0.19/0.46      set_Pr1780909331reeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46      produc1141751126_pi_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 0.19/0.46      list_l1406151091e_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46      produc1359399907ubject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      produc355105483reeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46      produc214645451ubject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      produc1357834675reeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J_J,type,
% 0.19/0.46      set_Pr1131282415pi_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46      produc257012921pi_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46      produc1777919905pi_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46      list_P227219501e_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46      set_Pr443758855e_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 0.19/0.46      produc1998742700t_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.19/0.46      produc2052722628s_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46      produc865358760ubject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      produc2008547984reeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 0.19/0.46      produc140253050ect_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.19/0.46      produc992857746Res_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46      set_Pr1834926343_pi_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46      produc1212344719pi_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.19/0.46      produc367475239e_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46      product_prod_pi_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46      list_Late_subject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      list_Late_freeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46      set_Late_subject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      set_Late_freeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Agent__Opi____Rep_J,type,
% 0.19/0.46      list_pi_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Late____Semantics__Oresidual____Rep,type,
% 0.19/0.46      late_residual_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Late____Semantics__Osubject____Rep,type,
% 0.19/0.46      late_subject_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Late____Semantics__OfreeRes____Rep,type,
% 0.19/0.46      late_freeRes_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Agent__Opi____Rep_J,type,
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% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Agent__Oname_J,type,
% 0.19/0.46      list_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 0.19/0.46      set_name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__List__Olist_It__Agent__Opi_J,type,
% 0.19/0.46      list_pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Late____Semantics__Oresidual,type,
% 0.19/0.46      late_residual: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.19/0.46      late_subject: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      late_freeRes: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Set__Oset_It__Agent__Opi_J,type,
% 0.19/0.46      set_pi: $tType ).
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% 0.19/0.46  thf(ty_n_t__Agent__Opi____Rep,type,
% 0.19/0.46      pi_Rep: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Agent__Oname,type,
% 0.19/0.46      name: $tType ).
% 0.19/0.46  
% 0.19/0.46  thf(ty_n_t__Agent__Opi,type,
% 0.19/0.46      pi: $tType ).
% 0.19/0.46  
% 0.19/0.46  % Explicit typings (146)
% 0.19/0.46  thf(sy_c_Agent_Opi_OInput,type,
% 0.19/0.46      input: name > name > pi > pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Agent_Opi_ORes,type,
% 0.19/0.46      res: name > pi > pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Agent_Opi_OSum,type,
% 0.19/0.46      sum: pi > pi > pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_If_001t__Agent__Oname,type,
% 0.19/0.46      if_name: $o > name > name > name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_If_001t__Agent__Opi,type,
% 0.19/0.46      if_pi: $o > pi > pi > pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_If_001t__Agent__Opi____Rep,type,
% 0.19/0.46      if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_If_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_If_001t__Late____Semantics__Osubject,type,
% 0.19/0.46      if_Late_subject: $o > late_subject > late_subject > late_subject ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.19/0.46      late_OutputR: name > name > late_freeRes ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.19/0.46      late_BoundR: late_subject > name > pi > late_residual ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.19/0.46      late_FreeR: late_freeRes > pi > late_residual ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 0.19/0.46      late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.19/0.46      late_BoundOutputS: name > late_subject ).
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% 0.19/0.46      perm_name_set_name: list_P227219501e_name > set_name > set_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
% 0.19/0.46      perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 0.19/0.46      perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46      perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46      perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
% 0.19/0.46      swap_name: produc367475239e_name > name > name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46      ord_le793202855e_name: set_Pr443758855e_name > set_Pr443758855e_name > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.19/0.46      ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46      ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46      produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.19/0.46      produc1570949143e_name: name > name > produc367475239e_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.19/0.46      produc607574050ubject: name > late_subject > produc865358760ubject ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46      produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.19/0.46      product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Agent__Opi____Rep_001t__Agent__Opi____Rep,type,
% 0.19/0.46      produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.19/0.46      produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.19/0.46      produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi____Rep,type,
% 0.19/0.46      produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 0.19/0.46      produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.19/0.46      produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 0.19/0.46      produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
% 0.19/0.46      produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.19/0.46      produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46      produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
% 0.19/0.46      eqvt_name: set_Pr443758855e_name > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.19/0.46      eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
% 0.19/0.46      eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
% 0.19/0.46      eqvt_Late_subject: set_Pr806375235ubject > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Relation_OId_001t__Agent__Oname,type,
% 0.19/0.46      id_name: set_Pr443758855e_name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Relation_OId_001t__Agent__Opi,type,
% 0.19/0.46      id_pi: set_Pr1834926343_pi_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46      collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.19/0.46      strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.19/0.46      strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Agent__Oname,type,
% 0.19/0.46      member_name: name > set_name > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Agent__Opi,type,
% 0.19/0.46      member_pi: pi > set_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Agent__Opi____Rep,type,
% 0.19/0.46      member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46      member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Late____Semantics__Osubject,type,
% 0.19/0.46      member_Late_subject: late_subject > set_Late_subject > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.19/0.46      member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46      member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46      member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46      member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46      member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46      member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_P,type,
% 0.19/0.46      p: pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_PQ____,type,
% 0.19/0.46      pq: pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_P_H____,type,
% 0.19/0.46      p2: pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_Q,type,
% 0.19/0.46      q: pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_Rel,type,
% 0.19/0.46      rel: set_Pr1834926343_pi_pi ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_a____,type,
% 0.19/0.46      a: late_subject ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_aa____,type,
% 0.19/0.46      aa: name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_x,type,
% 0.19/0.46      x: name ).
% 0.19/0.46  
% 0.19/0.46  thf(sy_v_y____,type,
% 0.19/0.46      y: name ).
% 0.19/0.46  
% 0.19/0.46  % Relevant facts (353)
% 0.19/0.46  thf(fact_0_Id,axiom,
% 0.19/0.46      ord_le630093991_pi_pi @ id_pi @ rel ).
% 0.19/0.46  
% 0.19/0.46  % Id
% 0.19/0.46  thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 0.19/0.46      aa != x ).
% 0.19/0.46  
% 0.19/0.46  % cOpen.hyps(2)
% 0.19/0.46  thf(fact_2_cOpen_Ohyps_I3_J,axiom,
% 0.19/0.46      ( a
% 0.19/0.46      = ( late_BoundOutputS @ aa ) ) ).
% 0.19/0.46  
% 0.19/0.46  % cOpen.hyps(3)
% 0.19/0.46  thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.19/0.47      y != x ).
% 0.19/0.47  
% 0.19/0.47  % \<open>y \<noteq> x\<close>
% 0.19/0.47  thf(fact_4_Eqvt,axiom,
% 0.19/0.47      eqvt_pi @ rel ).
% 0.19/0.47  
% 0.19/0.47  % Eqvt
% 0.19/0.47  thf(fact_5_perm__swap_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(1)
% 0.19/0.47  thf(fact_6_perm__swap_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(1)
% 0.19/0.47  thf(fact_7_perm__swap_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(1)
% 0.19/0.47  thf(fact_8_perm__swap_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(1)
% 0.19/0.47  thf(fact_9_perm__swap_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(1)
% 0.19/0.47  thf(fact_10_name__id,axiom,
% 0.19/0.47      ! [A: name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_id
% 0.19/0.47  thf(fact_11_name__id,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_id
% 0.19/0.47  thf(fact_12_name__id,axiom,
% 0.19/0.47      ! [A: name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_id
% 0.19/0.47  thf(fact_13_name__id,axiom,
% 0.19/0.47      ! [A: name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_id
% 0.19/0.47  thf(fact_14_name__id,axiom,
% 0.19/0.47      ! [A: name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_id
% 0.19/0.47  thf(fact_15_name__swap,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap
% 0.19/0.47  thf(fact_16_name__swap,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap
% 0.19/0.47  thf(fact_17_name__swap,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap
% 0.19/0.47  thf(fact_18_name__swap,axiom,
% 0.19/0.47      ! [A: name,B: name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap
% 0.19/0.47  thf(fact_19_name__swap,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47        = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap
% 0.19/0.47  thf(fact_20_name__swap__bij,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap_bij
% 0.19/0.47  thf(fact_21_name__swap__bij,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap_bij
% 0.19/0.47  thf(fact_22_name__swap__bij,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap_bij
% 0.19/0.47  thf(fact_23_name__swap__bij,axiom,
% 0.19/0.47      ! [A: name,B: name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap_bij
% 0.19/0.47  thf(fact_24_name__swap__bij,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_swap_bij
% 0.19/0.47  thf(fact_25_pt__name1,axiom,
% 0.19/0.47      ! [X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_name1
% 0.19/0.47  thf(fact_26_pt__name1,axiom,
% 0.19/0.47      ! [X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_name1
% 0.19/0.47  thf(fact_27_pt__name1,axiom,
% 0.19/0.47      ! [X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_name1
% 0.19/0.47  thf(fact_28_pt__name1,axiom,
% 0.19/0.47      ! [X: name] :
% 0.19/0.47        ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_name1
% 0.19/0.47  thf(fact_29_pt__name1,axiom,
% 0.19/0.47      ! [X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_name1
% 0.19/0.47  thf(fact_30_perm__swap_I2_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(2)
% 0.19/0.47  thf(fact_31_perm__swap_I2_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(2)
% 0.19/0.47  thf(fact_32_perm__swap_I2_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(2)
% 0.19/0.47  thf(fact_33_perm__swap_I2_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(2)
% 0.19/0.47  thf(fact_34_perm__swap_I2_J,axiom,
% 0.19/0.47      ! [A: name,B: name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_swap(2)
% 0.19/0.47  thf(fact_35_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.19/0.47      ! [X1: name,Y1: name] :
% 0.19/0.47        ( ( ( late_BoundOutputS @ X1 )
% 0.19/0.47          = ( late_BoundOutputS @ Y1 ) )
% 0.19/0.47        = ( X1 = Y1 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics.subject.inject(2)
% 0.19/0.47  thf(fact_36_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.19/0.47      ! [X2: name,Y2: name] :
% 0.19/0.47        ( ( ( late_BoundOutputS @ X2 )
% 0.19/0.47          = ( late_BoundOutputS @ Y2 ) )
% 0.19/0.47        = ( X2 = Y2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics1.subject.inject(2)
% 0.19/0.47  thf(fact_37__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 0.19/0.47      fresh_name_pi @ y @ p2 ).
% 0.19/0.47  
% 0.19/0.47  % \<open>y \<sharp> P'\<close>
% 0.19/0.47  thf(fact_38_list_Oinject,axiom,
% 0.19/0.47      ! [X21: produc367475239e_name,X22: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 0.19/0.47        ( ( ( cons_P1213805021e_name @ X21 @ X22 )
% 0.19/0.47          = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 0.19/0.47        = ( ( X21 = Y21 )
% 0.19/0.47          & ( X22 = Y22 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list.inject
% 0.19/0.47  thf(fact_39_prod_Oinject,axiom,
% 0.19/0.47      ! [X1: name,X2: name,Y1: name,Y2: name] :
% 0.19/0.47        ( ( ( produc1570949143e_name @ X1 @ X2 )
% 0.19/0.47          = ( produc1570949143e_name @ Y1 @ Y2 ) )
% 0.19/0.47        = ( ( X1 = Y1 )
% 0.19/0.47          & ( X2 = Y2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod.inject
% 0.19/0.47  thf(fact_40_prod_Oinject,axiom,
% 0.19/0.47      ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 0.19/0.47        ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 0.19/0.47          = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 0.19/0.47        = ( ( X1 = Y1 )
% 0.19/0.47          & ( X2 = Y2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod.inject
% 0.19/0.47  thf(fact_41_prod_Oinject,axiom,
% 0.19/0.47      ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.19/0.47        ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.19/0.47          = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.19/0.47        = ( ( X1 = Y1 )
% 0.19/0.47          & ( X2 = Y2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod.inject
% 0.19/0.47  thf(fact_42_old_Oprod_Oinject,axiom,
% 0.19/0.47      ! [A: name,B: name,A2: name,B2: name] :
% 0.19/0.47        ( ( ( produc1570949143e_name @ A @ B )
% 0.19/0.47          = ( produc1570949143e_name @ A2 @ B2 ) )
% 0.19/0.47        = ( ( A = A2 )
% 0.19/0.47          & ( B = B2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.inject
% 0.19/0.47  thf(fact_43_old_Oprod_Oinject,axiom,
% 0.19/0.47      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.19/0.47        ( ( ( produc235456326_pi_pi @ A @ B )
% 0.19/0.47          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.19/0.47        = ( ( A = A2 )
% 0.19/0.47          & ( B = B2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.inject
% 0.19/0.47  thf(fact_44_old_Oprod_Oinject,axiom,
% 0.19/0.47      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.19/0.47        ( ( ( product_Pair_pi_pi @ A @ B )
% 0.19/0.47          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.19/0.47        = ( ( A = A2 )
% 0.19/0.47          & ( B = B2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.inject
% 0.19/0.47  thf(fact_45_residual__perm__empty,axiom,
% 0.19/0.47      ! [Residual_Rep: late_residual_Rep] :
% 0.19/0.47        ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 0.19/0.47        = Residual_Rep ) ).
% 0.19/0.47  
% 0.19/0.47  % residual_perm_empty
% 0.19/0.47  thf(fact_46_subject__perm__empty,axiom,
% 0.19/0.47      ! [Subject_Rep: late_subject_Rep] :
% 0.19/0.47        ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 0.19/0.47        = Subject_Rep ) ).
% 0.19/0.47  
% 0.19/0.47  % subject_perm_empty
% 0.19/0.47  thf(fact_47_freeRes__perm__empty,axiom,
% 0.19/0.47      ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.19/0.47        ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 0.19/0.47        = FreeRes_Rep ) ).
% 0.19/0.47  
% 0.19/0.47  % freeRes_perm_empty
% 0.19/0.47  thf(fact_48_pi__perm__empty,axiom,
% 0.19/0.47      ! [Pi_Rep: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 0.19/0.47        = Pi_Rep ) ).
% 0.19/0.47  
% 0.19/0.47  % pi_perm_empty
% 0.19/0.47  thf(fact_49_subject_Operm_I2_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X1: name] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.47        = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subject.perm(2)
% 0.19/0.47  thf(fact_50_perm__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: pi_Rep,B: name] :
% 0.19/0.47        ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.47       => ( ( fresh_name_pi_Rep @ B @ X )
% 0.19/0.47         => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_fresh_fresh
% 0.19/0.47  thf(fact_51_perm__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,B: name] :
% 0.19/0.47        ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47       => ( ( fresh_717452603ubject @ B @ X )
% 0.19/0.47         => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_fresh_fresh
% 0.19/0.47  thf(fact_52_perm__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,B: name] :
% 0.19/0.47        ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47       => ( ( fresh_1641682979reeRes @ B @ X )
% 0.19/0.47         => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_fresh_fresh
% 0.19/0.47  thf(fact_53_perm__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 0.19/0.47        ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.19/0.47       => ( ( fresh_1376661020_pi_pi @ B @ X )
% 0.19/0.47         => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_fresh_fresh
% 0.19/0.47  thf(fact_54_perm__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: name,B: name] :
% 0.19/0.47        ( ( fresh_name_name @ A @ X )
% 0.19/0.47       => ( ( fresh_name_name @ B @ X )
% 0.19/0.47         => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_fresh_fresh
% 0.19/0.47  thf(fact_55_perm__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: pi,B: name] :
% 0.19/0.47        ( ( fresh_name_pi @ A @ X )
% 0.19/0.47       => ( ( fresh_name_pi @ B @ X )
% 0.19/0.47         => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_fresh_fresh
% 0.19/0.47  thf(fact_56_name__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: pi_Rep,B: name] :
% 0.19/0.47        ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.47       => ( ( fresh_name_pi_Rep @ B @ X )
% 0.19/0.47         => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh_fresh
% 0.19/0.47  thf(fact_57_name__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,B: name] :
% 0.19/0.47        ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47       => ( ( fresh_717452603ubject @ B @ X )
% 0.19/0.47         => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh_fresh
% 0.19/0.47  thf(fact_58_name__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,B: name] :
% 0.19/0.47        ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47       => ( ( fresh_1641682979reeRes @ B @ X )
% 0.19/0.47         => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh_fresh
% 0.19/0.47  thf(fact_59_name__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 0.19/0.47        ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.19/0.47       => ( ( fresh_1376661020_pi_pi @ B @ X )
% 0.19/0.47         => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh_fresh
% 0.19/0.47  thf(fact_60_name__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: name,B: name] :
% 0.19/0.47        ( ( fresh_name_name @ A @ X )
% 0.19/0.47       => ( ( fresh_name_name @ B @ X )
% 0.19/0.47         => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh_fresh
% 0.19/0.47  thf(fact_61_name__fresh__fresh,axiom,
% 0.19/0.47      ! [A: name,X: pi,B: name] :
% 0.19/0.47        ( ( fresh_name_pi @ A @ X )
% 0.19/0.47       => ( ( fresh_name_pi @ B @ X )
% 0.19/0.47         => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.47            = X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh_fresh
% 0.19/0.47  thf(fact_62_Bound_Ohyps_I4_J,axiom,
% 0.19/0.47      fresh_717452603ubject @ y @ a ).
% 0.19/0.47  
% 0.19/0.47  % Bound.hyps(4)
% 0.19/0.47  thf(fact_63_subseteq__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X3: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( ord_le630093991_pi_pi @ X3 @ Y ) )
% 0.19/0.47        = ( ord_le630093991_pi_pi @ ( perm_n675238095_pi_pi @ Pi @ X3 ) @ ( perm_n675238095_pi_pi @ Pi @ Y ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subseteq_eqvt
% 0.19/0.47  thf(fact_64_fresh__perm__app,axiom,
% 0.19/0.47      ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.47        ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.47       => ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.47         => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_perm_app
% 0.19/0.47  thf(fact_65_fresh__perm__app,axiom,
% 0.19/0.47      ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 0.19/0.47        ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.47       => ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47         => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_perm_app
% 0.19/0.47  thf(fact_66_fresh__perm__app,axiom,
% 0.19/0.47      ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.47        ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.47       => ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47         => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_perm_app
% 0.19/0.47  thf(fact_67_fresh__perm__app,axiom,
% 0.19/0.47      ! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
% 0.19/0.47        ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.47       => ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.19/0.47         => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_perm_app
% 0.19/0.47  thf(fact_68_fresh__perm__app,axiom,
% 0.19/0.47      ! [A: name,Pi: list_P227219501e_name,X: name] :
% 0.19/0.47        ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.47       => ( ( fresh_name_name @ A @ X )
% 0.19/0.47         => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_perm_app
% 0.19/0.47  thf(fact_69_fresh__perm__app,axiom,
% 0.19/0.47      ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 0.19/0.47        ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.47       => ( ( fresh_name_pi @ A @ X )
% 0.19/0.47         => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_perm_app
% 0.19/0.47  thf(fact_70_name__exists__fresh,axiom,
% 0.19/0.47      ! [X: late_subject] :
% 0.19/0.47        ~ ! [C: name] :
% 0.19/0.47            ~ ( fresh_717452603ubject @ C @ X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_exists_fresh
% 0.19/0.47  thf(fact_71_name__exists__fresh,axiom,
% 0.19/0.47      ! [X: late_freeRes] :
% 0.19/0.47        ~ ! [C: name] :
% 0.19/0.47            ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_exists_fresh
% 0.19/0.47  thf(fact_72_name__exists__fresh,axiom,
% 0.19/0.47      ! [X: produc1141751126_pi_pi] :
% 0.19/0.47        ~ ! [C: name] :
% 0.19/0.47            ~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_exists_fresh
% 0.19/0.47  thf(fact_73_name__exists__fresh,axiom,
% 0.19/0.47      ! [X: name] :
% 0.19/0.47        ~ ! [C: name] :
% 0.19/0.47            ~ ( fresh_name_name @ C @ X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_exists_fresh
% 0.19/0.47  thf(fact_74_name__exists__fresh,axiom,
% 0.19/0.47      ! [X: pi] :
% 0.19/0.47        ~ ! [C: name] :
% 0.19/0.47            ~ ( fresh_name_pi @ C @ X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_exists_fresh
% 0.19/0.47  thf(fact_75_fresh__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 0.19/0.47        = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_eqvt
% 0.19/0.47  thf(fact_76_fresh__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 0.19/0.47        = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_eqvt
% 0.19/0.47  thf(fact_77_fresh__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 0.19/0.47        = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_eqvt
% 0.19/0.47  thf(fact_78_fresh__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
% 0.19/0.47        = ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_eqvt
% 0.19/0.47  thf(fact_79_fresh__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 0.19/0.47        = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_eqvt
% 0.19/0.47  thf(fact_80_fresh__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 0.19/0.47        = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_eqvt
% 0.19/0.47  thf(fact_81_fresh__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.19/0.47        ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 0.19/0.47        = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_bij
% 0.19/0.47  thf(fact_82_fresh__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.19/0.47        ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 0.19/0.47        = ( fresh_717452603ubject @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_bij
% 0.19/0.47  thf(fact_83_fresh__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.19/0.47        ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 0.19/0.47        = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_bij
% 0.19/0.47  thf(fact_84_fresh__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 0.19/0.47        ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
% 0.19/0.47        = ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_bij
% 0.19/0.47  thf(fact_85_fresh__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.19/0.47        ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 0.19/0.47        = ( fresh_name_name @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_bij
% 0.19/0.47  thf(fact_86_fresh__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.19/0.47        ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 0.19/0.47        = ( fresh_name_pi @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_bij
% 0.19/0.47  thf(fact_87_name__calc_I2_J,axiom,
% 0.19/0.47      ! [X: name] :
% 0.19/0.47        ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % name_calc(2)
% 0.19/0.47  thf(fact_88_successively_Ocases,axiom,
% 0.19/0.47      ! [X: produc1872410278e_name] :
% 0.19/0.47        ( ! [P: produc367475239e_name > produc367475239e_name > $o] :
% 0.19/0.47            ( X
% 0.19/0.47           != ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
% 0.19/0.47       => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] :
% 0.19/0.47              ( X
% 0.19/0.47             != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) ) )
% 0.19/0.47         => ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.19/0.47                ( X
% 0.19/0.47               != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % successively.cases
% 0.19/0.47  thf(fact_89_sorted__wrt_Ocases,axiom,
% 0.19/0.47      ! [X: produc1872410278e_name] :
% 0.19/0.47        ( ! [P: produc367475239e_name > produc367475239e_name > $o] :
% 0.19/0.47            ( X
% 0.19/0.47           != ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
% 0.19/0.47       => ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.47              ( X
% 0.19/0.47             != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sorted_wrt.cases
% 0.19/0.47  thf(fact_90_shuffles_Ocases,axiom,
% 0.19/0.47      ! [X: produc890461031e_name] :
% 0.19/0.47        ( ! [Ys: list_P227219501e_name] :
% 0.19/0.47            ( X
% 0.19/0.47           != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 0.19/0.47       => ( ! [Xs: list_P227219501e_name] :
% 0.19/0.47              ( X
% 0.19/0.47             != ( produc208131031e_name @ Xs @ nil_Pr743626285e_name ) )
% 0.19/0.47         => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.47                ( X
% 0.19/0.47               != ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % shuffles.cases
% 0.19/0.47  thf(fact_91_splice_Ocases,axiom,
% 0.19/0.47      ! [X: produc890461031e_name] :
% 0.19/0.47        ( ! [Ys: list_P227219501e_name] :
% 0.19/0.47            ( X
% 0.19/0.47           != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 0.19/0.47       => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
% 0.19/0.47              ( X
% 0.19/0.47             != ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % splice.cases
% 0.19/0.47  thf(fact_92_swap__simps_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 0.19/0.47        = B ) ).
% 0.19/0.47  
% 0.19/0.47  % swap_simps(1)
% 0.19/0.47  thf(fact_93_swap__simps_I2_J,axiom,
% 0.19/0.47      ! [A: name,B: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 0.19/0.47        = A ) ).
% 0.19/0.47  
% 0.19/0.47  % swap_simps(2)
% 0.19/0.47  thf(fact_94_swap__simps_I3_J,axiom,
% 0.19/0.47      ! [A: name,C2: name,B: name] :
% 0.19/0.47        ( ( A != C2 )
% 0.19/0.47       => ( ( B != C2 )
% 0.19/0.47         => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C2 )
% 0.19/0.47            = C2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % swap_simps(3)
% 0.19/0.47  thf(fact_95_fresh__aux,axiom,
% 0.19/0.47      ! [C2: name,A: name,X: pi_Rep,B: name] :
% 0.19/0.47        ( ( C2 != A )
% 0.19/0.47       => ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.47         => ( ( fresh_name_pi_Rep @ C2 @ X )
% 0.19/0.47           => ( fresh_name_pi_Rep @ C2 @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_aux
% 0.19/0.47  thf(fact_96_fresh__aux,axiom,
% 0.19/0.47      ! [C2: name,A: name,X: late_subject,B: name] :
% 0.19/0.47        ( ( C2 != A )
% 0.19/0.47       => ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47         => ( ( fresh_717452603ubject @ C2 @ X )
% 0.19/0.47           => ( fresh_717452603ubject @ C2 @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_aux
% 0.19/0.47  thf(fact_97_fresh__aux,axiom,
% 0.19/0.47      ! [C2: name,A: name,X: late_freeRes,B: name] :
% 0.19/0.47        ( ( C2 != A )
% 0.19/0.47       => ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47         => ( ( fresh_1641682979reeRes @ C2 @ X )
% 0.19/0.47           => ( fresh_1641682979reeRes @ C2 @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_aux
% 0.19/0.47  thf(fact_98_fresh__aux,axiom,
% 0.19/0.47      ! [C2: name,A: name,X: produc1141751126_pi_pi,B: name] :
% 0.19/0.47        ( ( C2 != A )
% 0.19/0.47       => ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.19/0.47         => ( ( fresh_1376661020_pi_pi @ C2 @ X )
% 0.19/0.47           => ( fresh_1376661020_pi_pi @ C2 @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_aux
% 0.19/0.47  thf(fact_99_fresh__aux,axiom,
% 0.19/0.47      ! [C2: name,A: name,X: name,B: name] :
% 0.19/0.47        ( ( C2 != A )
% 0.19/0.47       => ( ( fresh_name_name @ A @ X )
% 0.19/0.47         => ( ( fresh_name_name @ C2 @ X )
% 0.19/0.47           => ( fresh_name_name @ C2 @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_aux
% 0.19/0.47  thf(fact_100_fresh__aux,axiom,
% 0.19/0.47      ! [C2: name,A: name,X: pi,B: name] :
% 0.19/0.47        ( ( C2 != A )
% 0.19/0.47       => ( ( fresh_name_pi @ A @ X )
% 0.19/0.47         => ( ( fresh_name_pi @ C2 @ X )
% 0.19/0.47           => ( fresh_name_pi @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_aux
% 0.19/0.47  thf(fact_101_old_Oprod_Oinducts,axiom,
% 0.19/0.47      ! [P2: produc367475239e_name > $o,Prod: produc367475239e_name] :
% 0.19/0.47        ( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
% 0.19/0.47       => ( P2 @ Prod ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.inducts
% 0.19/0.47  thf(fact_102_old_Oprod_Oinducts,axiom,
% 0.19/0.47      ! [P2: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 0.19/0.47        ( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.19/0.47       => ( P2 @ Prod ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.inducts
% 0.19/0.47  thf(fact_103_old_Oprod_Oinducts,axiom,
% 0.19/0.47      ! [P2: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.19/0.47        ( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.19/0.47       => ( P2 @ Prod ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.inducts
% 0.19/0.47  thf(fact_104_old_Oprod_Oexhaust,axiom,
% 0.19/0.47      ! [Y4: produc367475239e_name] :
% 0.19/0.47        ~ ! [A3: name,B3: name] :
% 0.19/0.47            ( Y4
% 0.19/0.47           != ( produc1570949143e_name @ A3 @ B3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.exhaust
% 0.19/0.47  thf(fact_105_old_Oprod_Oexhaust,axiom,
% 0.19/0.47      ! [Y4: produc1141751126_pi_pi] :
% 0.19/0.47        ~ ! [A3: name,B3: product_prod_pi_pi] :
% 0.19/0.47            ( Y4
% 0.19/0.47           != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.exhaust
% 0.19/0.47  thf(fact_106_old_Oprod_Oexhaust,axiom,
% 0.19/0.47      ! [Y4: product_prod_pi_pi] :
% 0.19/0.47        ~ ! [A3: pi,B3: pi] :
% 0.19/0.47            ( Y4
% 0.19/0.47           != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % old.prod.exhaust
% 0.19/0.47  thf(fact_107_mem__Collect__eq,axiom,
% 0.19/0.47      ! [A: product_prod_pi_pi,P2: product_prod_pi_pi > $o] :
% 0.19/0.47        ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P2 ) )
% 0.19/0.47        = ( P2 @ A ) ) ).
% 0.19/0.47  
% 0.19/0.47  % mem_Collect_eq
% 0.19/0.47  thf(fact_108_Collect__mem__eq,axiom,
% 0.19/0.47      ! [A4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( collec1051790738_pi_pi
% 0.19/0.47          @ ^ [X5: product_prod_pi_pi] : ( member558706512_pi_pi @ X5 @ A4 ) )
% 0.19/0.47        = A4 ) ).
% 0.19/0.47  
% 0.19/0.47  % Collect_mem_eq
% 0.19/0.47  thf(fact_109_prod__induct3,axiom,
% 0.19/0.47      ! [P2: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 0.19/0.47        ( ! [A3: name,B3: pi,C: pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
% 0.19/0.47       => ( P2 @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod_induct3
% 0.19/0.47  thf(fact_110_prod__cases3,axiom,
% 0.19/0.47      ! [Y4: produc1141751126_pi_pi] :
% 0.19/0.47        ~ ! [A3: name,B3: pi,C: pi] :
% 0.19/0.47            ( Y4
% 0.19/0.47           != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod_cases3
% 0.19/0.47  thf(fact_111_Pair__inject,axiom,
% 0.19/0.47      ! [A: name,B: name,A2: name,B2: name] :
% 0.19/0.47        ( ( ( produc1570949143e_name @ A @ B )
% 0.19/0.47          = ( produc1570949143e_name @ A2 @ B2 ) )
% 0.19/0.47       => ~ ( ( A = A2 )
% 0.19/0.47           => ( B != B2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Pair_inject
% 0.19/0.47  thf(fact_112_Pair__inject,axiom,
% 0.19/0.47      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.19/0.47        ( ( ( produc235456326_pi_pi @ A @ B )
% 0.19/0.47          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.19/0.47       => ~ ( ( A = A2 )
% 0.19/0.47           => ( B != B2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Pair_inject
% 0.19/0.47  thf(fact_113_Pair__inject,axiom,
% 0.19/0.47      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.19/0.47        ( ( ( product_Pair_pi_pi @ A @ B )
% 0.19/0.47          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.19/0.47       => ~ ( ( A = A2 )
% 0.19/0.47           => ( B != B2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Pair_inject
% 0.19/0.47  thf(fact_114_prod__cases,axiom,
% 0.19/0.47      ! [P2: produc367475239e_name > $o,P3: produc367475239e_name] :
% 0.19/0.47        ( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
% 0.19/0.47       => ( P2 @ P3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod_cases
% 0.19/0.47  thf(fact_115_prod__cases,axiom,
% 0.19/0.47      ! [P2: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
% 0.19/0.47        ( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.19/0.47       => ( P2 @ P3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod_cases
% 0.19/0.47  thf(fact_116_prod__cases,axiom,
% 0.19/0.47      ! [P2: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 0.19/0.47        ( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.19/0.47       => ( P2 @ P3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % prod_cases
% 0.19/0.47  thf(fact_117_surj__pair,axiom,
% 0.19/0.47      ! [P3: produc367475239e_name] :
% 0.19/0.47      ? [X4: name,Y3: name] :
% 0.19/0.47        ( P3
% 0.19/0.47        = ( produc1570949143e_name @ X4 @ Y3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % surj_pair
% 0.19/0.47  thf(fact_118_surj__pair,axiom,
% 0.19/0.47      ! [P3: produc1141751126_pi_pi] :
% 0.19/0.47      ? [X4: name,Y3: product_prod_pi_pi] :
% 0.19/0.47        ( P3
% 0.19/0.47        = ( produc235456326_pi_pi @ X4 @ Y3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % surj_pair
% 0.19/0.47  thf(fact_119_surj__pair,axiom,
% 0.19/0.47      ! [P3: product_prod_pi_pi] :
% 0.19/0.47      ? [X4: pi,Y3: pi] :
% 0.19/0.47        ( P3
% 0.19/0.47        = ( product_Pair_pi_pi @ X4 @ Y3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % surj_pair
% 0.19/0.47  thf(fact_120_not__Cons__self2,axiom,
% 0.19/0.47      ! [X: produc367475239e_name,Xs2: list_P227219501e_name] :
% 0.19/0.47        ( ( cons_P1213805021e_name @ X @ Xs2 )
% 0.19/0.47       != Xs2 ) ).
% 0.19/0.47  
% 0.19/0.47  % not_Cons_self2
% 0.19/0.47  thf(fact_121_cp__name__name1,axiom,
% 0.19/0.47      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 0.19/0.47        = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cp_name_name1
% 0.19/0.47  thf(fact_122_cp__name__name1,axiom,
% 0.19/0.47      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 0.19/0.47        = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cp_name_name1
% 0.19/0.47  thf(fact_123_cp__name__name1,axiom,
% 0.19/0.47      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 0.19/0.47        = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cp_name_name1
% 0.19/0.47  thf(fact_124_cp__name__name1,axiom,
% 0.19/0.47      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 0.19/0.47        = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cp_name_name1
% 0.19/0.47  thf(fact_125_cp__name__name1,axiom,
% 0.19/0.47      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 0.19/0.47        = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cp_name_name1
% 0.19/0.47  thf(fact_126_name__perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_perm_compose
% 0.19/0.47  thf(fact_127_name__perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_perm_compose
% 0.19/0.47  thf(fact_128_name__perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_perm_compose
% 0.19/0.47  thf(fact_129_name__perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_perm_compose
% 0.19/0.47  thf(fact_130_name__perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_perm_compose
% 0.19/0.47  thf(fact_131_perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_compose
% 0.19/0.47  thf(fact_132_perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_compose
% 0.19/0.47  thf(fact_133_perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.47        ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_compose
% 0.19/0.47  thf(fact_134_perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_compose
% 0.19/0.47  thf(fact_135_perm__compose,axiom,
% 0.19/0.47      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.19/0.47        ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.19/0.47        = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_compose
% 0.19/0.47  thf(fact_136_perm__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( ( perm_n1559866809ubject @ Pi @ X )
% 0.19/0.47          = ( perm_n1559866809ubject @ Pi @ Y4 ) )
% 0.19/0.47        = ( X = Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_bij
% 0.19/0.47  thf(fact_137_perm__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( ( perm_n336613537reeRes @ Pi @ X )
% 0.19/0.47          = ( perm_n336613537reeRes @ Pi @ Y4 ) )
% 0.19/0.47        = ( X = Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_bij
% 0.19/0.47  thf(fact_138_perm__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 0.19/0.47        ( ( ( perm_name_pi_Rep @ Pi @ X )
% 0.19/0.47          = ( perm_name_pi_Rep @ Pi @ Y4 ) )
% 0.19/0.47        = ( X = Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_bij
% 0.19/0.47  thf(fact_139_perm__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.19/0.47        ( ( ( perm_name_name @ Pi @ X )
% 0.19/0.47          = ( perm_name_name @ Pi @ Y4 ) )
% 0.19/0.47        = ( X = Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_bij
% 0.19/0.47  thf(fact_140_perm__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 0.19/0.47        ( ( ( perm_name_pi @ Pi @ X )
% 0.19/0.47          = ( perm_name_pi @ Pi @ Y4 ) )
% 0.19/0.47        = ( X = Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_bij
% 0.19/0.47  thf(fact_141_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_142_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_143_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_144_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_145_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_146_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_147_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_148_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_149_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_150_perm__app,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.47        = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_app
% 0.19/0.47  thf(fact_151_in__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X3: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X3 ) )
% 0.19/0.47        = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % in_eqvt
% 0.19/0.47  thf(fact_152_in__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,X3: set_Late_subject] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X3 ) )
% 0.19/0.47        = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % in_eqvt
% 0.19/0.47  thf(fact_153_in__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,X3: set_Late_freeRes] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X3 ) )
% 0.19/0.47        = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % in_eqvt
% 0.19/0.47  thf(fact_154_in__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi_Rep,X3: set_pi_Rep] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X3 ) )
% 0.19/0.47        = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % in_eqvt
% 0.19/0.47  thf(fact_155_in__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: name,X3: set_name] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( member_name @ X @ X3 ) )
% 0.19/0.47        = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % in_eqvt
% 0.19/0.47  thf(fact_156_in__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi,X3: set_pi] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( member_pi @ X @ X3 ) )
% 0.19/0.47        = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % in_eqvt
% 0.19/0.47  thf(fact_157_eq__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.19/0.47        = ( ( perm_n1559866809ubject @ Pi @ X )
% 0.19/0.47          = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_eqvt
% 0.19/0.47  thf(fact_158_eq__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.19/0.47        = ( ( perm_n336613537reeRes @ Pi @ X )
% 0.19/0.47          = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_eqvt
% 0.19/0.47  thf(fact_159_eq__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.19/0.47        = ( ( perm_name_pi_Rep @ Pi @ X )
% 0.19/0.47          = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_eqvt
% 0.19/0.47  thf(fact_160_eq__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.19/0.47        = ( ( perm_name_name @ Pi @ X )
% 0.19/0.47          = ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_eqvt
% 0.19/0.47  thf(fact_161_eq__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 0.19/0.47        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.19/0.47        = ( ( perm_name_pi @ Pi @ X )
% 0.19/0.47          = ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_eqvt
% 0.19/0.47  thf(fact_162_map__tailrec__rev_Oinduct,axiom,
% 0.19/0.47      ! [P2: ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name,A1: list_P227219501e_name,A22: list_P227219501e_name] :
% 0.19/0.47        ( ! [F2: produc367475239e_name > produc367475239e_name,X_1: list_P227219501e_name] : ( P2 @ F2 @ nil_Pr743626285e_name @ X_1 )
% 0.19/0.47       => ( ! [F2: produc367475239e_name > produc367475239e_name,A3: produc367475239e_name,As: list_P227219501e_name,Bs: list_P227219501e_name] :
% 0.19/0.47              ( ( P2 @ F2 @ As @ ( cons_P1213805021e_name @ ( F2 @ A3 ) @ Bs ) )
% 0.19/0.47             => ( P2 @ F2 @ ( cons_P1213805021e_name @ A3 @ As ) @ Bs ) )
% 0.19/0.47         => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % map_tailrec_rev.induct
% 0.19/0.47  thf(fact_163_list__nonempty__induct,axiom,
% 0.19/0.47      ! [Xs2: list_P227219501e_name,P2: list_P227219501e_name > $o] :
% 0.19/0.47        ( ( Xs2 != nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.19/0.47         => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.19/0.47                ( ( Xs != nil_Pr743626285e_name )
% 0.19/0.47               => ( ( P2 @ Xs )
% 0.19/0.47                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) ) )
% 0.19/0.47           => ( P2 @ Xs2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list_nonempty_induct
% 0.19/0.47  thf(fact_164_successively_Oinduct,axiom,
% 0.19/0.47      ! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 0.19/0.47        ( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] : ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.19/0.47         => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.19/0.47                ( ( P2 @ P @ ( cons_P1213805021e_name @ Y3 @ Xs ) )
% 0.19/0.47               => ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) )
% 0.19/0.47           => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % successively.induct
% 0.19/0.47  thf(fact_165_remdups__adj_Oinduct,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > $o,A0: list_P227219501e_name] :
% 0.19/0.47        ( ( P2 @ nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.19/0.47         => ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.19/0.47                ( ( ( X4 = Y3 )
% 0.19/0.47                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) )
% 0.19/0.47               => ( ( ( X4 != Y3 )
% 0.19/0.47                   => ( P2 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) )
% 0.19/0.47                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) )
% 0.19/0.47           => ( P2 @ A0 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % remdups_adj.induct
% 0.19/0.47  thf(fact_166_sorted__wrt_Oinduct,axiom,
% 0.19/0.47      ! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 0.19/0.47        ( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.47              ( ( P2 @ P @ Ys )
% 0.19/0.47             => ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) )
% 0.19/0.47         => ( P2 @ A0 @ A1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sorted_wrt.induct
% 0.19/0.47  thf(fact_167_remdups__adj_Ocases,axiom,
% 0.19/0.47      ! [X: list_P227219501e_name] :
% 0.19/0.47        ( ( X != nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [X4: produc367475239e_name] :
% 0.19/0.47              ( X
% 0.19/0.47             != ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.19/0.47         => ~ ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.19/0.47                ( X
% 0.19/0.47               != ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % remdups_adj.cases
% 0.19/0.47  thf(fact_168_transpose_Ocases,axiom,
% 0.19/0.47      ! [X: list_l1406151091e_name] :
% 0.19/0.47        ( ( X != nil_li29751603e_name )
% 0.19/0.47       => ( ! [Xss: list_l1406151091e_name] :
% 0.19/0.47              ( X
% 0.19/0.47             != ( cons_l798145763e_name @ nil_Pr743626285e_name @ Xss ) )
% 0.19/0.47         => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Xss: list_l1406151091e_name] :
% 0.19/0.47                ( X
% 0.19/0.47               != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Xss ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % transpose.cases
% 0.19/0.47  thf(fact_169_shuffles_Oinduct,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 0.19/0.47        ( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
% 0.19/0.47       => ( ! [Xs: list_P227219501e_name] : ( P2 @ Xs @ nil_Pr743626285e_name )
% 0.19/0.47         => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.47                ( ( P2 @ Xs @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 0.19/0.47               => ( ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys )
% 0.19/0.47                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) )
% 0.19/0.47           => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % shuffles.induct
% 0.19/0.47  thf(fact_170_induct__list012,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > $o,Xs2: list_P227219501e_name] :
% 0.19/0.47        ( ( P2 @ nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.19/0.47         => ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Zs: list_P227219501e_name] :
% 0.19/0.47                ( ( P2 @ Zs )
% 0.19/0.47               => ( ( P2 @ ( cons_P1213805021e_name @ Y3 @ Zs ) )
% 0.19/0.47                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Zs ) ) ) ) )
% 0.19/0.47           => ( P2 @ Xs2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % induct_list012
% 0.19/0.47  thf(fact_171_splice_Oinduct,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 0.19/0.47        ( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
% 0.19/0.47       => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
% 0.19/0.47              ( ( P2 @ Ys @ Xs )
% 0.19/0.47             => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) )
% 0.19/0.47         => ( P2 @ A0 @ A1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % splice.induct
% 0.19/0.47  thf(fact_172_list__induct2_H,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > list_P227219501e_name > $o,Xs2: list_P227219501e_name,Ys2: list_P227219501e_name] :
% 0.19/0.47        ( ( P2 @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ nil_Pr743626285e_name )
% 0.19/0.47         => ( ! [Y3: produc367475239e_name,Ys: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 0.19/0.47           => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.47                  ( ( P2 @ Xs @ Ys )
% 0.19/0.47                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) )
% 0.19/0.47             => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list_induct2'
% 0.19/0.47  thf(fact_173_neq__Nil__conv,axiom,
% 0.19/0.47      ! [Xs2: list_P227219501e_name] :
% 0.19/0.47        ( ( Xs2 != nil_Pr743626285e_name )
% 0.19/0.47        = ( ? [Y5: produc367475239e_name,Ys3: list_P227219501e_name] :
% 0.19/0.47              ( Xs2
% 0.19/0.47              = ( cons_P1213805021e_name @ Y5 @ Ys3 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % neq_Nil_conv
% 0.19/0.47  thf(fact_174_list_Oinducts,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > $o,List: list_P227219501e_name] :
% 0.19/0.47        ( ( P2 @ nil_Pr743626285e_name )
% 0.19/0.47       => ( ! [X12: produc367475239e_name,X23: list_P227219501e_name] :
% 0.19/0.47              ( ( P2 @ X23 )
% 0.19/0.47             => ( P2 @ ( cons_P1213805021e_name @ X12 @ X23 ) ) )
% 0.19/0.47         => ( P2 @ List ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list.inducts
% 0.19/0.47  thf(fact_175_list_Oexhaust,axiom,
% 0.19/0.47      ! [Y4: list_P227219501e_name] :
% 0.19/0.47        ( ( Y4 != nil_Pr743626285e_name )
% 0.19/0.47       => ~ ! [X212: produc367475239e_name,X222: list_P227219501e_name] :
% 0.19/0.47              ( Y4
% 0.19/0.47             != ( cons_P1213805021e_name @ X212 @ X222 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list.exhaust
% 0.19/0.47  thf(fact_176_list_OdiscI,axiom,
% 0.19/0.47      ! [List: list_P227219501e_name,X21: produc367475239e_name,X22: list_P227219501e_name] :
% 0.19/0.47        ( ( List
% 0.19/0.47          = ( cons_P1213805021e_name @ X21 @ X22 ) )
% 0.19/0.47       => ( List != nil_Pr743626285e_name ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list.discI
% 0.19/0.47  thf(fact_177_list_Odistinct_I1_J,axiom,
% 0.19/0.47      ! [X21: produc367475239e_name,X22: list_P227219501e_name] :
% 0.19/0.47        ( nil_Pr743626285e_name
% 0.19/0.47       != ( cons_P1213805021e_name @ X21 @ X22 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % list.distinct(1)
% 0.19/0.47  thf(fact_178__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.19/0.47      fresh_name_pi @ y @ q ).
% 0.19/0.47  
% 0.19/0.47  % \<open>y \<sharp> Q\<close>
% 0.19/0.47  thf(fact_179_pair__in__Id__conv,axiom,
% 0.19/0.47      ! [A: name,B: name] :
% 0.19/0.47        ( ( member695284560e_name @ ( produc1570949143e_name @ A @ B ) @ id_name )
% 0.19/0.47        = ( A = B ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pair_in_Id_conv
% 0.19/0.47  thf(fact_180_pair__in__Id__conv,axiom,
% 0.19/0.47      ! [A: pi,B: pi] :
% 0.19/0.47        ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 0.19/0.47        = ( A = B ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pair_in_Id_conv
% 0.19/0.47  thf(fact_181_IdI,axiom,
% 0.19/0.47      ! [A: name] : ( member695284560e_name @ ( produc1570949143e_name @ A @ A ) @ id_name ) ).
% 0.19/0.47  
% 0.19/0.47  % IdI
% 0.19/0.47  thf(fact_182_IdI,axiom,
% 0.19/0.47      ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 0.19/0.47  
% 0.19/0.47  % IdI
% 0.19/0.47  thf(fact_183_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47          & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_184_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,Y4: late_freeRes] :
% 0.19/0.47        ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47          & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_185_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,Y4: name] :
% 0.19/0.47        ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47          & ( fresh_name_name @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_186_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,Y4: pi] :
% 0.19/0.47        ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47          & ( fresh_name_pi @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_187_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,Y4: late_subject] :
% 0.19/0.47        ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47          & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_188_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47          & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_189_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,Y4: name] :
% 0.19/0.47        ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47          & ( fresh_name_name @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_190_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,Y4: pi] :
% 0.19/0.47        ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47          & ( fresh_name_pi @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_191_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: name,Y4: late_subject] :
% 0.19/0.47        ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_name_name @ A @ X )
% 0.19/0.47          & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_192_fresh__prod,axiom,
% 0.19/0.47      ! [A: name,X: name,Y4: late_freeRes] :
% 0.19/0.47        ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y4 ) )
% 0.19/0.47        = ( ( fresh_name_name @ A @ X )
% 0.19/0.47          & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prod
% 0.19/0.47  thf(fact_193__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.19/0.47      fresh_name_pi @ y @ p ).
% 0.19/0.47  
% 0.19/0.47  % \<open>y \<sharp> P\<close>
% 0.19/0.47  thf(fact_194_derivativeReflexive,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,A: late_subject,X: name] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong2129052853vative @ P2 @ P2 @ A @ X @ Rel ) ) ).
% 0.19/0.47  
% 0.19/0.47  % derivativeReflexive
% 0.19/0.47  thf(fact_195_derivativeEqvtI,axiom,
% 0.19/0.47      ! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
% 0.19/0.47       => ( ( eqvt_pi @ Rel )
% 0.19/0.47         => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % derivativeEqvtI
% 0.19/0.47  thf(fact_196_derivativeEqvtI2,axiom,
% 0.19/0.47      ! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
% 0.19/0.47       => ( ( eqvt_pi @ Rel )
% 0.19/0.47         => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % derivativeEqvtI2
% 0.19/0.47  thf(fact_197_eqvtRelI,axiom,
% 0.19/0.47      ! [Rel: set_Pr806375235ubject,P2: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( eqvt_Late_subject @ Rel )
% 0.19/0.47       => ( ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel )
% 0.19/0.47         => ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelI
% 0.19/0.47  thf(fact_198_eqvtRelI,axiom,
% 0.19/0.47      ! [Rel: set_Pr1780909331reeRes,P2: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( eqvt_Late_freeRes @ Rel )
% 0.19/0.47       => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel )
% 0.19/0.47         => ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelI
% 0.19/0.47  thf(fact_199_eqvtRelI,axiom,
% 0.19/0.47      ! [Rel: set_Pr1131282415pi_Rep,P2: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( eqvt_pi_Rep @ Rel )
% 0.19/0.47       => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel )
% 0.19/0.47         => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelI
% 0.19/0.47  thf(fact_200_eqvtRelI,axiom,
% 0.19/0.47      ! [Rel: set_Pr443758855e_name,P2: name,Q: name,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( eqvt_name @ Rel )
% 0.19/0.47       => ( ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel )
% 0.19/0.47         => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelI
% 0.19/0.47  thf(fact_201_eqvtRelI,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( eqvt_pi @ Rel )
% 0.19/0.47       => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel )
% 0.19/0.47         => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelI
% 0.19/0.47  thf(fact_202_Bound_Ohyps_I5_J,axiom,
% 0.19/0.47      fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Bound.hyps(5)
% 0.19/0.47  thf(fact_203_subject_Ofresh_I2_J,axiom,
% 0.19/0.47      ! [A: name,X1: name] :
% 0.19/0.47        ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.47        = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subject.fresh(2)
% 0.19/0.47  thf(fact_204_name__bij,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.19/0.47        ( ( ( perm_name_name @ Pi @ X )
% 0.19/0.47          = ( perm_name_name @ Pi @ Y4 ) )
% 0.19/0.47        = ( X = Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_bij
% 0.19/0.47  thf(fact_205_allE__Nil,axiom,
% 0.19/0.47      ! [P2: list_P227219501e_name > $o] :
% 0.19/0.47        ( ! [X_1: list_P227219501e_name] : ( P2 @ X_1 )
% 0.19/0.47       => ( P2 @ nil_Pr743626285e_name ) ) ).
% 0.19/0.47  
% 0.19/0.47  % allE_Nil
% 0.19/0.47  thf(fact_206_if__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 0.19/0.47        ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 0.19/0.47        & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % if_eqvt
% 0.19/0.47  thf(fact_207_if__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 0.19/0.47        ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 0.19/0.47        & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % if_eqvt
% 0.19/0.47  thf(fact_208_if__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 0.19/0.47        ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 0.19/0.47        & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % if_eqvt
% 0.19/0.47  thf(fact_209_if__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 0.19/0.47        ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_name_name @ Pi @ C1 ) ) )
% 0.19/0.47        & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % if_eqvt
% 0.19/0.47  thf(fact_210_if__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 0.19/0.47        ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_name_pi @ Pi @ C1 ) ) )
% 0.19/0.47        & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.47         => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.19/0.47            = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % if_eqvt
% 0.19/0.47  thf(fact_211_pt__bij3,axiom,
% 0.19/0.47      ! [X: late_subject,Y4: late_subject,Pi: list_P227219501e_name] :
% 0.19/0.47        ( ( X = Y4 )
% 0.19/0.47       => ( ( perm_n1559866809ubject @ Pi @ X )
% 0.19/0.47          = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_bij3
% 0.19/0.47  thf(fact_212_pt__bij3,axiom,
% 0.19/0.47      ! [X: late_freeRes,Y4: late_freeRes,Pi: list_P227219501e_name] :
% 0.19/0.47        ( ( X = Y4 )
% 0.19/0.47       => ( ( perm_n336613537reeRes @ Pi @ X )
% 0.19/0.47          = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_bij3
% 0.19/0.47  thf(fact_213_pt__bij3,axiom,
% 0.19/0.47      ! [X: pi_Rep,Y4: pi_Rep,Pi: list_P227219501e_name] :
% 0.19/0.47        ( ( X = Y4 )
% 0.19/0.47       => ( ( perm_name_pi_Rep @ Pi @ X )
% 0.19/0.47          = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_bij3
% 0.19/0.47  thf(fact_214_pt__bij3,axiom,
% 0.19/0.47      ! [X: name,Y4: name,Pi: list_P227219501e_name] :
% 0.19/0.47        ( ( X = Y4 )
% 0.19/0.47       => ( ( perm_name_name @ Pi @ X )
% 0.19/0.47          = ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_bij3
% 0.19/0.47  thf(fact_215_pt__bij3,axiom,
% 0.19/0.47      ! [X: pi,Y4: pi,Pi: list_P227219501e_name] :
% 0.19/0.47        ( ( X = Y4 )
% 0.19/0.47       => ( ( perm_name_pi @ Pi @ X )
% 0.19/0.47          = ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pt_bij3
% 0.19/0.47  thf(fact_216_abs__fun__if,axiom,
% 0.19/0.47      ! [C2: $o,Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( C2
% 0.19/0.47         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 0.19/0.47        & ( ~ C2
% 0.19/0.47         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % abs_fun_if
% 0.19/0.47  thf(fact_217_abs__fun__if,axiom,
% 0.19/0.47      ! [C2: $o,Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( C2
% 0.19/0.47         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 0.19/0.47        & ( ~ C2
% 0.19/0.47         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % abs_fun_if
% 0.19/0.47  thf(fact_218_abs__fun__if,axiom,
% 0.19/0.47      ! [C2: $o,Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 0.19/0.47        ( ( C2
% 0.19/0.47         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 0.19/0.47        & ( ~ C2
% 0.19/0.47         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % abs_fun_if
% 0.19/0.47  thf(fact_219_abs__fun__if,axiom,
% 0.19/0.47      ! [C2: $o,Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.19/0.47        ( ( C2
% 0.19/0.47         => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_name_name @ Pi @ X ) ) )
% 0.19/0.47        & ( ~ C2
% 0.19/0.47         => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_name_name @ Pi @ Y4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % abs_fun_if
% 0.19/0.47  thf(fact_220_abs__fun__if,axiom,
% 0.19/0.47      ! [C2: $o,Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 0.19/0.47        ( ( C2
% 0.19/0.47         => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_name_pi @ Pi @ X ) ) )
% 0.19/0.47        & ( ~ C2
% 0.19/0.47         => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
% 0.19/0.47            = ( perm_name_pi @ Pi @ Y4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % abs_fun_if
% 0.19/0.47  thf(fact_221_eqvt__def,axiom,
% 0.19/0.47      ( eqvt_pi
% 0.19/0.47      = ( ^ [Rel2: set_Pr1834926343_pi_pi] :
% 0.19/0.47          ! [X5: product_prod_pi_pi,Perm2: list_P227219501e_name] :
% 0.19/0.47            ( ( member558706512_pi_pi @ X5 @ Rel2 )
% 0.19/0.47           => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X5 ) @ Rel2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvt_def
% 0.19/0.47  thf(fact_222_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y4 ) )
% 0.19/0.47        = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_223_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_freeRes] :
% 0.19/0.47        ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y4 ) )
% 0.19/0.47        = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_224_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: pi_Rep] :
% 0.19/0.47        ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y4 ) )
% 0.19/0.47        = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_225_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: name] :
% 0.19/0.47        ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y4 ) )
% 0.19/0.47        = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_226_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Y4: pi] :
% 0.19/0.47        ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y4 ) )
% 0.19/0.47        = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_227_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_subject] :
% 0.19/0.47        ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y4 ) )
% 0.19/0.47        = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_228_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y4 ) )
% 0.19/0.47        = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_229_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi_Rep] :
% 0.19/0.47        ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y4 ) )
% 0.19/0.47        = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_230_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: name] :
% 0.19/0.47        ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y4 ) )
% 0.19/0.47        = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_231_perm__prod_Osimps,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi] :
% 0.19/0.47        ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y4 ) )
% 0.19/0.47        = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % perm_prod.simps
% 0.19/0.47  thf(fact_232_cons__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_subject,Xs2: list_Late_subject] :
% 0.19/0.47        ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs2 ) )
% 0.19/0.47        = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cons_eqvt
% 0.19/0.47  thf(fact_233_cons__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: late_freeRes,Xs2: list_Late_freeRes] :
% 0.19/0.47        ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs2 ) )
% 0.19/0.47        = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cons_eqvt
% 0.19/0.47  thf(fact_234_cons__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi_Rep,Xs2: list_pi_Rep] :
% 0.19/0.47        ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs2 ) )
% 0.19/0.47        = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cons_eqvt
% 0.19/0.47  thf(fact_235_cons__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: name,Xs2: list_name] :
% 0.19/0.47        ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs2 ) )
% 0.19/0.47        = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cons_eqvt
% 0.19/0.47  thf(fact_236_cons__eqvt,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X: pi,Xs2: list_pi] :
% 0.19/0.47        ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs2 ) )
% 0.19/0.47        = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % cons_eqvt
% 0.19/0.47  thf(fact_237_fresh__prodD_I1_J,axiom,
% 0.19/0.47      ! [A: name,X: name,Y4: name] :
% 0.19/0.47        ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
% 0.19/0.47       => ( fresh_name_name @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prodD(1)
% 0.19/0.47  thf(fact_238_fresh__prodD_I1_J,axiom,
% 0.19/0.47      ! [A: name,X: name,Y4: product_prod_pi_pi] :
% 0.19/0.47        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
% 0.19/0.47       => ( fresh_name_name @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prodD(1)
% 0.19/0.47  thf(fact_239_fresh__prodD_I1_J,axiom,
% 0.19/0.47      ! [A: name,X: pi,Y4: pi] :
% 0.19/0.47        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
% 0.19/0.47       => ( fresh_name_pi @ A @ X ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prodD(1)
% 0.19/0.47  thf(fact_240_fresh__prodD_I2_J,axiom,
% 0.19/0.47      ! [A: name,X: name,Y4: name] :
% 0.19/0.47        ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
% 0.19/0.47       => ( fresh_name_name @ A @ Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prodD(2)
% 0.19/0.47  thf(fact_241_fresh__prodD_I2_J,axiom,
% 0.19/0.47      ! [A: name,X: name,Y4: product_prod_pi_pi] :
% 0.19/0.47        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
% 0.19/0.47       => ( fresh_1627595501_pi_pi @ A @ Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prodD(2)
% 0.19/0.47  thf(fact_242_fresh__prodD_I2_J,axiom,
% 0.19/0.47      ! [A: name,X: pi,Y4: pi] :
% 0.19/0.47        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
% 0.19/0.47       => ( fresh_name_pi @ A @ Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_prodD(2)
% 0.19/0.47  thf(fact_243_fresh__list__cons,axiom,
% 0.19/0.47      ! [A: name,X: late_subject,Xs2: list_Late_subject] :
% 0.19/0.47        ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ X @ Xs2 ) )
% 0.19/0.47        = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47          & ( fresh_838462539ubject @ A @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_list_cons
% 0.19/0.47  thf(fact_244_fresh__list__cons,axiom,
% 0.19/0.47      ! [A: name,X: late_freeRes,Xs2: list_Late_freeRes] :
% 0.19/0.47        ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ X @ Xs2 ) )
% 0.19/0.47        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47          & ( fresh_1981651763reeRes @ A @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_list_cons
% 0.19/0.47  thf(fact_245_fresh__list__cons,axiom,
% 0.19/0.47      ! [A: name,X: produc1141751126_pi_pi,Xs2: list_P431515740_pi_pi] :
% 0.19/0.47        ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs2 ) )
% 0.19/0.47        = ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.19/0.47          & ( fresh_1958133282_pi_pi @ A @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_list_cons
% 0.19/0.47  thf(fact_246_fresh__list__cons,axiom,
% 0.19/0.47      ! [A: name,X: name,Xs2: list_name] :
% 0.19/0.47        ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs2 ) )
% 0.19/0.47        = ( ( fresh_name_name @ A @ X )
% 0.19/0.47          & ( fresh_name_list_name @ A @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_list_cons
% 0.19/0.47  thf(fact_247_fresh__list__cons,axiom,
% 0.19/0.47      ! [A: name,X: pi,Xs2: list_pi] :
% 0.19/0.47        ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs2 ) )
% 0.19/0.47        = ( ( fresh_name_pi @ A @ X )
% 0.19/0.47          & ( fresh_name_list_pi @ A @ Xs2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % fresh_list_cons
% 0.19/0.47  thf(fact_248_subrelI,axiom,
% 0.19/0.47      ! [R: set_Pr443758855e_name,S: set_Pr443758855e_name] :
% 0.19/0.47        ( ! [X4: name,Y3: name] :
% 0.19/0.47            ( ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ R )
% 0.19/0.47           => ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ S ) )
% 0.19/0.47       => ( ord_le793202855e_name @ R @ S ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subrelI
% 0.19/0.47  thf(fact_249_subrelI,axiom,
% 0.19/0.47      ! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
% 0.19/0.47        ( ! [X4: name,Y3: product_prod_pi_pi] :
% 0.19/0.47            ( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ R )
% 0.19/0.47           => ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ S ) )
% 0.19/0.47       => ( ord_le797229014_pi_pi @ R @ S ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subrelI
% 0.19/0.47  thf(fact_250_subrelI,axiom,
% 0.19/0.47      ! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ! [X4: pi,Y3: pi] :
% 0.19/0.47            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ R )
% 0.19/0.47           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ S ) )
% 0.19/0.47       => ( ord_le630093991_pi_pi @ R @ S ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subrelI
% 0.19/0.47  thf(fact_251_IdE,axiom,
% 0.19/0.47      ! [P3: produc367475239e_name] :
% 0.19/0.47        ( ( member695284560e_name @ P3 @ id_name )
% 0.19/0.47       => ~ ! [X4: name] :
% 0.19/0.47              ( P3
% 0.19/0.47             != ( produc1570949143e_name @ X4 @ X4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % IdE
% 0.19/0.47  thf(fact_252_IdE,axiom,
% 0.19/0.47      ! [P3: product_prod_pi_pi] :
% 0.19/0.47        ( ( member558706512_pi_pi @ P3 @ id_pi )
% 0.19/0.47       => ~ ! [X4: pi] :
% 0.19/0.47              ( P3
% 0.19/0.47             != ( product_Pair_pi_pi @ X4 @ X4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % IdE
% 0.19/0.47  thf(fact_253_derivativeMonotonic,axiom,
% 0.19/0.47      ! [P2: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( strong2129052853vative @ P2 @ Q @ A @ X @ A4 )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.19/0.47         => ( strong2129052853vative @ P2 @ Q @ A @ X @ B4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % derivativeMonotonic
% 0.19/0.47  thf(fact_254_eqvtRelE,axiom,
% 0.19/0.47      ! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P2: late_subject,Q: late_subject] :
% 0.19/0.47        ( ( eqvt_Late_subject @ Rel )
% 0.19/0.47       => ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
% 0.19/0.47         => ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelE
% 0.19/0.47  thf(fact_255_eqvtRelE,axiom,
% 0.19/0.47      ! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P2: late_freeRes,Q: late_freeRes] :
% 0.19/0.47        ( ( eqvt_Late_freeRes @ Rel )
% 0.19/0.47       => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
% 0.19/0.47         => ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelE
% 0.19/0.47  thf(fact_256_eqvtRelE,axiom,
% 0.19/0.47      ! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P2: pi_Rep,Q: pi_Rep] :
% 0.19/0.47        ( ( eqvt_pi_Rep @ Rel )
% 0.19/0.47       => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
% 0.19/0.47         => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelE
% 0.19/0.47  thf(fact_257_eqvtRelE,axiom,
% 0.19/0.47      ! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P2: name,Q: name] :
% 0.19/0.47        ( ( eqvt_name @ Rel )
% 0.19/0.47       => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
% 0.19/0.47         => ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelE
% 0.19/0.47  thf(fact_258_eqvtRelE,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P2: pi,Q: pi] :
% 0.19/0.47        ( ( eqvt_pi @ Rel )
% 0.19/0.47       => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
% 0.19/0.47         => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtRelE
% 0.19/0.47  thf(fact_259_Bound_Ohyps_I3_J,axiom,
% 0.19/0.47      fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Bound.hyps(3)
% 0.19/0.47  thf(fact_260_Bound_Ohyps_I2_J,axiom,
% 0.19/0.47      fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Bound.hyps(2)
% 0.19/0.47  thf(fact_261_subset__antisym,axiom,
% 0.19/0.47      ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ B4 @ A4 )
% 0.19/0.47         => ( A4 = B4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subset_antisym
% 0.19/0.47  thf(fact_262_subsetI,axiom,
% 0.19/0.47      ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ! [X4: product_prod_pi_pi] :
% 0.19/0.47            ( ( member558706512_pi_pi @ X4 @ A4 )
% 0.19/0.47           => ( member558706512_pi_pi @ X4 @ B4 ) )
% 0.19/0.47       => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subsetI
% 0.19/0.47  thf(fact_263_order__refl,axiom,
% 0.19/0.47      ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 0.19/0.47  
% 0.19/0.47  % order_refl
% 0.19/0.47  thf(fact_264_name__fresh,axiom,
% 0.19/0.47      ( fresh_name_name
% 0.19/0.47      = ( ^ [A5: name,B5: name] : ( A5 != B5 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_fresh
% 0.19/0.47  thf(fact_265_pi_Ofresh_I7_J,axiom,
% 0.19/0.47      ! [A: name,X2: pi,X1: pi] :
% 0.19/0.47        ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.19/0.47        = ( ( fresh_name_pi @ A @ X2 )
% 0.19/0.47          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.fresh(7)
% 0.19/0.47  thf(fact_266_pi_Operm_I7_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 0.19/0.47        ( ( perm_name_pi @ Pi @ ( sum @ X2 @ X1 ) )
% 0.19/0.47        = ( sum @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.perm(7)
% 0.19/0.47  thf(fact_267_pi_Operm_I9_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 0.19/0.47        ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 0.19/0.47        = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.perm(9)
% 0.19/0.47  thf(fact_268_pi_Odistinct_I81_J,axiom,
% 0.19/0.47      ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 0.19/0.47        ( ( sum @ Pi1 @ Pi2 )
% 0.19/0.47       != ( res @ Name @ Pi3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.distinct(81)
% 0.19/0.47  thf(fact_269_pi_Oinject_I6_J,axiom,
% 0.19/0.47      ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.47        ( ( ( sum @ X2 @ X1 )
% 0.19/0.47          = ( sum @ Y2 @ Y1 ) )
% 0.19/0.47        = ( ( X2 = Y2 )
% 0.19/0.47          & ( X1 = Y1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.inject(6)
% 0.19/0.47  thf(fact_270_freshRes,axiom,
% 0.19/0.47      ! [A: name,P2: pi] : ( fresh_name_pi @ A @ ( res @ A @ P2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freshRes
% 0.19/0.47  thf(fact_271_order__subst1,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A @ ( F @ B ) )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.19/0.47         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.19/0.47                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.19/0.47               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.19/0.47           => ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % order_subst1
% 0.19/0.47  thf(fact_272_order__subst2,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A @ B )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ ( F @ B ) @ C2 )
% 0.19/0.47         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.19/0.47                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.19/0.47               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.19/0.47           => ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % order_subst2
% 0.19/0.47  thf(fact_273_ord__eq__le__subst,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( A
% 0.19/0.47          = ( F @ B ) )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.19/0.47         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.19/0.47                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.19/0.47               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.19/0.47           => ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ord_eq_le_subst
% 0.19/0.47  thf(fact_274_ord__le__eq__subst,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A @ B )
% 0.19/0.47       => ( ( ( F @ B )
% 0.19/0.47            = C2 )
% 0.19/0.47         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.19/0.47                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.19/0.47               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.19/0.47           => ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ord_le_eq_subst
% 0.19/0.47  thf(fact_275_eq__iff,axiom,
% 0.19/0.47      ( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : ( Y6 = Z ) )
% 0.19/0.47      = ( ^ [X5: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 0.19/0.47            ( ( ord_le630093991_pi_pi @ X5 @ Y5 )
% 0.19/0.47            & ( ord_le630093991_pi_pi @ Y5 @ X5 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_iff
% 0.19/0.47  thf(fact_276_antisym,axiom,
% 0.19/0.47      ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ Y4 @ X )
% 0.19/0.47         => ( X = Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % antisym
% 0.19/0.47  thf(fact_277_eq__refl,axiom,
% 0.19/0.47      ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( X = Y4 )
% 0.19/0.47       => ( ord_le630093991_pi_pi @ X @ Y4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eq_refl
% 0.19/0.47  thf(fact_278_order_Otrans,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A @ B )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.19/0.47         => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % order.trans
% 0.19/0.47  thf(fact_279_antisym__conv,axiom,
% 0.19/0.47      ! [Y4: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ Y4 @ X )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 0.19/0.47          = ( X = Y4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % antisym_conv
% 0.19/0.47  thf(fact_280_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.47      ( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : ( Y6 = Z ) )
% 0.19/0.47      = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 0.19/0.47            ( ( ord_le630093991_pi_pi @ A5 @ B5 )
% 0.19/0.47            & ( ord_le630093991_pi_pi @ B5 @ A5 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % order_class.order.eq_iff
% 0.19/0.47  thf(fact_281_ord__eq__le__trans,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( A = B )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.19/0.47         => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ord_eq_le_trans
% 0.19/0.47  thf(fact_282_ord__le__eq__trans,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A @ B )
% 0.19/0.47       => ( ( B = C2 )
% 0.19/0.47         => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ord_le_eq_trans
% 0.19/0.47  thf(fact_283_order__class_Oorder_Oantisym,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ A @ B )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ B @ A )
% 0.19/0.47         => ( A = B ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % order_class.order.antisym
% 0.19/0.47  thf(fact_284_order__trans,axiom,
% 0.19/0.47      ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi,Z2: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ Y4 @ Z2 )
% 0.19/0.47         => ( ord_le630093991_pi_pi @ X @ Z2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % order_trans
% 0.19/0.47  thf(fact_285_dual__order_Orefl,axiom,
% 0.19/0.47      ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 0.19/0.47  
% 0.19/0.47  % dual_order.refl
% 0.19/0.47  thf(fact_286_alphaRes,axiom,
% 0.19/0.47      ! [C2: name,P2: pi,A: name] :
% 0.19/0.47        ( ( fresh_name_pi @ C2 @ P2 )
% 0.19/0.47       => ( ( res @ A @ P2 )
% 0.19/0.47          = ( res @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % alphaRes
% 0.19/0.47  thf(fact_287_calculation,axiom,
% 0.19/0.47      late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % calculation
% 0.19/0.47  thf(fact_288_Bound_Ohyps_I1_J,axiom,
% 0.19/0.47      late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.19/0.47  
% 0.19/0.47  % Bound.hyps(1)
% 0.19/0.47  thf(fact_289__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 0.19/0.47      late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ) ).
% 0.19/0.47  
% 0.19/0.47  % \<open><\<nu>x>(P \<oplus> Q) \<longmapsto> a<\<nu>x> \<prec> P'\<close>
% 0.19/0.47  thf(fact_290_sumResLeft,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,X: name,P2: pi,Q: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( ( eqvt_pi @ Rel )
% 0.19/0.47         => ( strong743114133lation @ ( sum @ ( res @ X @ P2 ) @ ( res @ X @ Q ) ) @ Rel @ ( res @ X @ ( sum @ P2 @ Q ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumResLeft
% 0.19/0.47  thf(fact_291_cSum1_Ohyps,axiom,
% 0.19/0.47      late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.19/0.47  
% 0.19/0.47  % cSum1.hyps
% 0.19/0.47  thf(fact_292_residual_Operm_I1_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 0.19/0.47        ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.19/0.47        = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual.perm(1)
% 0.19/0.47  thf(fact_293_freshBoundDerivative_I1_J,axiom,
% 0.19/0.47      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.19/0.47       => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.19/0.47         => ( fresh_717452603ubject @ Y4 @ A ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freshBoundDerivative(1)
% 0.19/0.47  thf(fact_294_Late__Semantics_OResB,axiom,
% 0.19/0.47      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.19/0.47       => ( ( fresh_717452603ubject @ Y4 @ A )
% 0.19/0.47         => ( ( Y4 != X )
% 0.19/0.47           => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics.ResB
% 0.19/0.47  thf(fact_295_freshBoundDerivative_I2_J,axiom,
% 0.19/0.47      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.19/0.47       => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.19/0.47         => ( ( Y4 != X )
% 0.19/0.47           => ( fresh_name_pi @ Y4 @ P4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freshBoundDerivative(2)
% 0.19/0.47  thf(fact_296_simE_I1_J,axiom,
% 0.19/0.47      ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.19/0.47        ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.19/0.47       => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.47         => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47           => ? [P5: pi] :
% 0.19/0.47                ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
% 0.19/0.47                & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % simE(1)
% 0.19/0.47  thf(fact_297_Sum2,axiom,
% 0.19/0.47      ! [Q: pi,Rs: late_residual,P2: pi] :
% 0.19/0.47        ( ( late_transitions @ Q @ Rs )
% 0.19/0.47       => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Sum2
% 0.19/0.47  thf(fact_298_Sum1,axiom,
% 0.19/0.47      ! [P2: pi,Rs: late_residual,Q: pi] :
% 0.19/0.47        ( ( late_transitions @ P2 @ Rs )
% 0.19/0.47       => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Sum1
% 0.19/0.47  thf(fact_299_sumCases_H,axiom,
% 0.19/0.47      ! [P2: pi,Q: pi,Rs: late_residual] :
% 0.19/0.47        ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 0.19/0.47       => ( ~ ( late_transitions @ P2 @ Rs )
% 0.19/0.47         => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumCases'
% 0.19/0.47  thf(fact_300_sumCases,axiom,
% 0.19/0.47      ! [P2: pi,Q: pi,Rs: late_residual] :
% 0.19/0.47        ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 0.19/0.47       => ( ~ ( late_transitions @ P2 @ Rs )
% 0.19/0.47         => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumCases
% 0.19/0.47  thf(fact_301_freshResidual,axiom,
% 0.19/0.47      ! [P2: pi,Rs: late_residual,X: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ Rs )
% 0.19/0.47       => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47         => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freshResidual
% 0.19/0.47  thf(fact_302_eqvt,axiom,
% 0.19/0.47      ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 0.19/0.47        ( ( late_transitions @ X1 @ X2 )
% 0.19/0.47       => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvt
% 0.19/0.47  thf(fact_303_transitions_OResB,axiom,
% 0.19/0.47      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.19/0.47       => ( ( fresh_717452603ubject @ Y4 @ A )
% 0.19/0.47         => ( ( Y4 != X )
% 0.19/0.47           => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47             => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47               => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % transitions.ResB
% 0.19/0.47  thf(fact_304_monotonic,axiom,
% 0.19/0.47      ! [P2: pi,A4: set_Pr1834926343_pi_pi,P4: pi,B4: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ( strong743114133lation @ P2 @ A4 @ P4 )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.19/0.47         => ( strong743114133lation @ P2 @ B4 @ P4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % monotonic
% 0.19/0.47  thf(fact_305_Strong__Late__Sim_Oreflexive,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong743114133lation @ P2 @ Rel @ P2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Strong_Late_Sim.reflexive
% 0.19/0.47  thf(fact_306_sumIdempRight,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong743114133lation @ ( sum @ P2 @ P2 ) @ Rel @ P2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumIdempRight
% 0.19/0.47  thf(fact_307_sumAssocRight,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong743114133lation @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumAssocRight
% 0.19/0.47  thf(fact_308_sumIdempLeft,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong743114133lation @ P2 @ Rel @ ( sum @ P2 @ P2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumIdempLeft
% 0.19/0.47  thf(fact_309_sumAssocLeft,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong743114133lation @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) @ Rel @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumAssocLeft
% 0.19/0.47  thf(fact_310_sumSym,axiom,
% 0.19/0.47      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi] :
% 0.19/0.47        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.19/0.47       => ( strong743114133lation @ ( sum @ P2 @ Q ) @ Rel @ ( sum @ Q @ P2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % sumSym
% 0.19/0.47  thf(fact_311_eqvtI,axiom,
% 0.19/0.47      ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Rel3: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.19/0.47        ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.19/0.47       => ( ( ord_le630093991_pi_pi @ Rel @ Rel3 )
% 0.19/0.47         => ( ( eqvt_pi @ Rel3 )
% 0.19/0.47           => ( strong743114133lation @ ( perm_name_pi @ Perm @ P2 ) @ Rel3 @ ( perm_name_pi @ Perm @ Q ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % eqvtI
% 0.19/0.47  thf(fact_312_alphaBoundResidual,axiom,
% 0.19/0.47      ! [X6: name,P2: pi,A: late_subject,X: name] :
% 0.19/0.47        ( ( fresh_name_pi @ X6 @ P2 )
% 0.19/0.47       => ( ( late_BoundR @ A @ X @ P2 )
% 0.19/0.47          = ( late_BoundR @ A @ X6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X6 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % alphaBoundResidual
% 0.19/0.47  thf(fact_313_cOpen_Ohyps_I1_J,axiom,
% 0.19/0.47      late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 0.19/0.47  
% 0.19/0.47  % cOpen.hyps(1)
% 0.19/0.47  thf(fact_314__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 0.19/0.47      late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 0.19/0.47  
% 0.19/0.47  % \<open>P \<oplus> Q \<longmapsto> a[x] \<prec> P'\<close>
% 0.19/0.47  thf(fact_315_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.19/0.47      ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.19/0.47        ( ( ( late_OutputR @ X11 @ X122 )
% 0.19/0.47          = ( late_OutputR @ Y11 @ Y12 ) )
% 0.19/0.47        = ( ( X11 = Y11 )
% 0.19/0.47          & ( X122 = Y12 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics1.freeRes.inject
% 0.19/0.47  thf(fact_316_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.19/0.47      ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.19/0.47        ( ( ( late_OutputR @ X2 @ X1 )
% 0.19/0.47          = ( late_OutputR @ Y2 @ Y1 ) )
% 0.19/0.47        = ( ( X2 = Y2 )
% 0.19/0.47          & ( X1 = Y1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics.freeRes.inject
% 0.19/0.47  thf(fact_317_freeRes_Operm_I1_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 0.19/0.47        ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.47        = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freeRes.perm(1)
% 0.19/0.47  thf(fact_318_freeRes_Ofresh_I1_J,axiom,
% 0.19/0.47      ! [A: name,X2: name,X1: name] :
% 0.19/0.47        ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.47        = ( ( fresh_name_name @ A @ X2 )
% 0.19/0.47          & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freeRes.fresh(1)
% 0.19/0.47  thf(fact_319_residual_Operm_I2_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 0.19/0.47        ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.47        = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual.perm(2)
% 0.19/0.47  thf(fact_320_residual_Ofresh_I2_J,axiom,
% 0.19/0.47      ! [A: name,X2: late_freeRes,X1: pi] :
% 0.19/0.47        ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.47        = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.19/0.47          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual.fresh(2)
% 0.19/0.47  thf(fact_321_residual_Odistinct_I1_J,axiom,
% 0.19/0.47      ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 0.19/0.47        ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 0.19/0.47       != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual.distinct(1)
% 0.19/0.47  thf(fact_322_residual_Oinducts,axiom,
% 0.19/0.47      ! [P2: late_residual > $o,Residual: late_residual] :
% 0.19/0.47        ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.19/0.47       => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.19/0.47         => ( P2 @ Residual ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual.inducts
% 0.19/0.47  thf(fact_323_residual_Oinject_I2_J,axiom,
% 0.19/0.47      ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.19/0.47        ( ( ( late_FreeR @ X2 @ X1 )
% 0.19/0.47          = ( late_FreeR @ Y2 @ Y1 ) )
% 0.19/0.47        = ( ( X2 = Y2 )
% 0.19/0.47          & ( X1 = Y1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual.inject(2)
% 0.19/0.47  thf(fact_324_ResF,axiom,
% 0.19/0.47      ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.19/0.47       => ( ( fresh_1641682979reeRes @ Y4 @ Alpha )
% 0.19/0.47         => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_FreeR @ Alpha @ ( res @ Y4 @ P4 ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ResF
% 0.19/0.47  thf(fact_325_resCasesF_H,axiom,
% 0.19/0.47      ! [X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 0.19/0.47        ( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) )
% 0.19/0.47       => ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.19/0.47              ( ( ( res @ X @ P2 )
% 0.19/0.47                = ( res @ Y3 @ P ) )
% 0.19/0.47             => ( ( ( late_FreeR @ Alpha @ P4 )
% 0.19/0.47                  = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.19/0.47               => ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.19/0.47                 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resCasesF'
% 0.19/0.47  thf(fact_326_resCasesF,axiom,
% 0.19/0.47      ! [X: name,P2: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 0.19/0.47        ( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.19/0.47       => ( ! [P5: pi] :
% 0.19/0.47              ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
% 0.19/0.47             => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.19/0.47               => ( F3 @ ( res @ X @ P5 ) ) ) )
% 0.19/0.47         => ( F3 @ XP ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resCasesF
% 0.19/0.47  thf(fact_327_freshFreeDerivative_I2_J,axiom,
% 0.19/0.47      ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.19/0.47       => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.19/0.47         => ( fresh_name_pi @ Y4 @ P4 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freshFreeDerivative(2)
% 0.19/0.47  thf(fact_328_freshFreeDerivative_I1_J,axiom,
% 0.19/0.47      ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.19/0.47       => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.19/0.47         => ( fresh_1641682979reeRes @ Y4 @ Alpha ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % freshFreeDerivative(1)
% 0.19/0.47  thf(fact_329_Open,axiom,
% 0.19/0.47      ! [P2: pi,A: name,B: name,P4: pi] :
% 0.19/0.47        ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P4 ) )
% 0.19/0.47       => ( ( A != B )
% 0.19/0.47         => ( late_transitions @ ( res @ B @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P4 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Open
% 0.19/0.47  thf(fact_330_simE_I2_J,axiom,
% 0.19/0.47      ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.19/0.47        ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.19/0.47       => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.19/0.47         => ? [P5: pi] :
% 0.19/0.47              ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
% 0.19/0.47              & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % simE(2)
% 0.19/0.47  thf(fact_331_resCasesB_H,axiom,
% 0.19/0.47      ! [X6: name,P2: pi,A: late_subject,Y7: name,P4: pi] :
% 0.19/0.47        ( ( late_transitions @ ( res @ X6 @ P2 ) @ ( late_BoundR @ A @ Y7 @ P4 ) )
% 0.19/0.47       => ( ! [P: pi,A3: name,B3: name] :
% 0.19/0.47              ( ( ( res @ X6 @ P2 )
% 0.19/0.47                = ( res @ B3 @ P ) )
% 0.19/0.47             => ! [P5: pi] :
% 0.19/0.47                  ( ( ( late_BoundR @ A @ Y7 @ P4 )
% 0.19/0.47                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.19/0.47                 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.19/0.47                   => ( A3 = B3 ) ) ) )
% 0.19/0.47         => ~ ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 0.19/0.47                ( ( ( res @ X6 @ P2 )
% 0.19/0.47                  = ( res @ Y3 @ P ) )
% 0.19/0.47               => ( ( ( late_BoundR @ A @ Y7 @ P4 )
% 0.19/0.47                    = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.19/0.47                 => ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.19/0.47                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.19/0.47                     => ( ( Y3 != X4 )
% 0.19/0.47                       => ( ( fresh_name_pi @ X4 @ P )
% 0.19/0.47                         => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resCasesB'
% 0.19/0.47  thf(fact_332_resCases_H,axiom,
% 0.19/0.47      ! [X: name,P2: pi,Rs: late_residual] :
% 0.19/0.47        ( ( late_transitions @ ( res @ X @ P2 ) @ Rs )
% 0.19/0.47       => ( ! [P: pi,A3: name,B3: name] :
% 0.19/0.47              ( ( ( res @ X @ P2 )
% 0.19/0.47                = ( res @ B3 @ P ) )
% 0.19/0.47             => ! [P5: pi] :
% 0.19/0.47                  ( ( Rs
% 0.19/0.47                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.19/0.47                 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.19/0.47                   => ( A3 = B3 ) ) ) )
% 0.19/0.47         => ( ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 0.19/0.47                ( ( ( res @ X @ P2 )
% 0.19/0.47                  = ( res @ Y3 @ P ) )
% 0.19/0.47               => ( ( Rs
% 0.19/0.47                    = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.19/0.47                 => ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.19/0.47                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.19/0.47                     => ( ( Y3 != X4 )
% 0.19/0.47                       => ( ( fresh_name_pi @ X4 @ P )
% 0.19/0.47                         => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 0.19/0.47           => ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.19/0.47                  ( ( ( res @ X @ P2 )
% 0.19/0.47                    = ( res @ Y3 @ P ) )
% 0.19/0.47                 => ( ( Rs
% 0.19/0.47                      = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.19/0.47                   => ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.19/0.47                     => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resCases'
% 0.19/0.47  thf(fact_333_resCasesB,axiom,
% 0.19/0.47      ! [Y4: name,P2: pi,A: late_subject,X: name,YP: pi,F3: late_subject > pi > $o] :
% 0.19/0.47        ( ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ YP ) )
% 0.19/0.47       => ( ( X != Y4 )
% 0.19/0.47         => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47           => ( ! [B3: name,P5: pi] :
% 0.19/0.47                  ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ B3 @ Y4 ) @ P5 ) )
% 0.19/0.47                 => ( ( B3 != Y4 )
% 0.19/0.47                   => ( ( A
% 0.19/0.47                        = ( late_BoundOutputS @ B3 ) )
% 0.19/0.47                     => ( F3 @ ( late_BoundOutputS @ B3 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P5 ) ) ) ) )
% 0.19/0.47             => ( ! [P5: pi] :
% 0.19/0.47                    ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
% 0.19/0.47                   => ( ( fresh_717452603ubject @ Y4 @ A )
% 0.19/0.47                     => ( F3 @ A @ ( res @ Y4 @ P5 ) ) ) )
% 0.19/0.47               => ( F3 @ A @ YP ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resCasesB
% 0.19/0.47  thf(fact_334_simulation__def,axiom,
% 0.19/0.47      ( strong743114133lation
% 0.19/0.47      = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q3: pi] :
% 0.19/0.47            ( ! [A5: late_subject,X5: name,Q4: pi] :
% 0.19/0.47                ( ( ( late_transitions @ Q3 @ ( late_BoundR @ A5 @ X5 @ Q4 ) )
% 0.19/0.47                  & ( fresh_name_pi @ X5 @ P6 ) )
% 0.19/0.47               => ? [P7: pi] :
% 0.19/0.47                    ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X5 @ P7 ) )
% 0.19/0.47                    & ( strong2129052853vative @ P7 @ Q4 @ A5 @ X5 @ Rel2 ) ) )
% 0.19/0.47            & ! [Alpha3: late_freeRes,Q4: pi] :
% 0.19/0.47                ( ( late_transitions @ Q3 @ ( late_FreeR @ Alpha3 @ Q4 ) )
% 0.19/0.47               => ? [P7: pi] :
% 0.19/0.47                    ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.19/0.47                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q4 ) @ Rel2 ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % simulation_def
% 0.19/0.47  thf(fact_335_simCases,axiom,
% 0.19/0.47      ! [Q: pi,P2: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.19/0.47        ( ! [A3: late_subject,Y3: name,Q5: pi] :
% 0.19/0.47            ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q5 ) )
% 0.19/0.47           => ( ( fresh_name_pi @ Y3 @ P2 )
% 0.19/0.47             => ? [P8: pi] :
% 0.19/0.47                  ( ( late_transitions @ P2 @ ( late_BoundR @ A3 @ Y3 @ P8 ) )
% 0.19/0.47                  & ( strong2129052853vative @ P8 @ Q5 @ A3 @ Y3 @ Rel ) ) ) )
% 0.19/0.47       => ( ! [Alpha2: late_freeRes,Q5: pi] :
% 0.19/0.47              ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q5 ) )
% 0.19/0.47             => ? [P8: pi] :
% 0.19/0.47                  ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q5 ) @ Rel ) ) )
% 0.19/0.47         => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % simCases
% 0.19/0.47  thf(fact_336_residual__Rep_Oinject_I2_J,axiom,
% 0.19/0.47      ! [X21: late_freeRes,X22: pi,Y21: late_freeRes,Y22: pi] :
% 0.19/0.47        ( ( ( late_r347633188eR_Rep @ X21 @ X22 )
% 0.19/0.47          = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.19/0.47        = ( ( X21 = Y21 )
% 0.19/0.47          & ( X22 = Y22 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % residual_Rep.inject(2)
% 0.19/0.47  thf(fact_337_alphaInput,axiom,
% 0.19/0.47      ! [C2: name,P2: pi,A: name,X: name] :
% 0.19/0.47        ( ( fresh_name_pi @ C2 @ P2 )
% 0.19/0.47       => ( ( input @ A @ X @ P2 )
% 0.19/0.47          = ( input @ A @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % alphaInput
% 0.19/0.47  thf(fact_338_pi_Operm_I4_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 0.19/0.47        ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 0.19/0.47        = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.perm(4)
% 0.19/0.47  thf(fact_339_resTrans_I2_J,axiom,
% 0.19/0.47      ! [X: name,Y4: name,P2: pi,Rs: late_residual] :
% 0.19/0.47        ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y4 @ P2 ) ) @ Rs ) ).
% 0.19/0.47  
% 0.19/0.47  % resTrans(2)
% 0.19/0.47  thf(fact_340_pi_Odistinct_I53_J,axiom,
% 0.19/0.47      ! [Name1: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47        ( ( input @ Name1 @ Name22 @ Pi )
% 0.19/0.47       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.distinct(53)
% 0.19/0.47  thf(fact_341_pi_Odistinct_I57_J,axiom,
% 0.19/0.47      ! [Name1: name,Name22: name,Pi: pi,Name: name,Pi3: pi] :
% 0.19/0.47        ( ( input @ Name1 @ Name22 @ Pi )
% 0.19/0.47       != ( res @ Name @ Pi3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % pi.distinct(57)
% 0.19/0.47  thf(fact_342_inputFreeTrans,axiom,
% 0.19/0.47      ! [A: name,X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 0.19/0.47        ~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % inputFreeTrans
% 0.19/0.47  thf(fact_343_resInputFreeTrans,axiom,
% 0.19/0.47      ! [X: name,A: name,Y4: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 0.19/0.47        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resInputFreeTrans
% 0.19/0.47  thf(fact_344_inputBoundOutputTrans,axiom,
% 0.19/0.47      ! [A: name,X: name,P2: pi,B: name,Y4: name,P4: pi] :
% 0.19/0.47        ~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y4 @ P4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % inputBoundOutputTrans
% 0.19/0.47  thf(fact_345_inputIneqTrans,axiom,
% 0.19/0.47      ! [A: name,X: name,P2: pi,B: late_subject,Y4: name,P4: pi] :
% 0.19/0.47        ( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ P4 ) )
% 0.19/0.47       => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.19/0.47  
% 0.19/0.47  % inputIneqTrans
% 0.19/0.47  thf(fact_346_resInputBoundOutputTrans,axiom,
% 0.19/0.47      ! [X: name,A: name,Y4: name,P2: pi,B: name,Z2: name,P4: pi] :
% 0.19/0.47        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z2 @ P4 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % resInputBoundOutputTrans
% 0.19/0.47  thf(fact_347_inputCases,axiom,
% 0.19/0.47      ! [A: name,X: name,P2: pi,B: late_subject,Y4: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.19/0.47        ( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ YP ) )
% 0.19/0.47       => ( ( Y4 != A )
% 0.19/0.47         => ( ( Y4 != X )
% 0.19/0.47           => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.19/0.47             => ( ( ( B
% 0.19/0.47                    = ( late_InputS @ A ) )
% 0.19/0.47                 => ( ( YP
% 0.19/0.47                      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) )
% 0.19/0.47                   => ( Prop @ ( late_InputS @ A ) @ Y4 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) )
% 0.19/0.47               => ( Prop @ B @ Y4 @ YP ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % inputCases
% 0.19/0.47  thf(fact_348_name__calc_I1_J,axiom,
% 0.19/0.47      ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 0.19/0.47        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 0.19/0.47        = ( swap_name @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % name_calc(1)
% 0.19/0.47  thf(fact_349_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.19/0.47      ! [X1: name,Y1: name] :
% 0.19/0.47        ( ( ( late_InputS @ X1 )
% 0.19/0.47          = ( late_InputS @ Y1 ) )
% 0.19/0.47        = ( X1 = Y1 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics1.subject.inject(1)
% 0.19/0.47  thf(fact_350_subject_Ofresh_I1_J,axiom,
% 0.19/0.47      ! [A: name,X1: name] :
% 0.19/0.47        ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.19/0.47        = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subject.fresh(1)
% 0.19/0.47  thf(fact_351_subject_Operm_I1_J,axiom,
% 0.19/0.47      ! [Pi: list_P227219501e_name,X1: name] :
% 0.19/0.47        ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 0.19/0.47        = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % subject.perm(1)
% 0.19/0.47  thf(fact_352_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.47      ! [Name2: name,Name: name] :
% 0.19/0.47        ( ( late_InputS @ Name2 )
% 0.19/0.47       != ( late_BoundOutputS @ Name ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Late_Semantics.subject.distinct(1)
% 0.19/0.47  
% 0.19/0.47  % Helper facts (11)
% 0.19/0.47  thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 0.19/0.47      ! [X: pi,Y4: pi] :
% 0.19/0.47        ( ( if_pi @ $false @ X @ Y4 )
% 0.19/0.47        = Y4 ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 0.19/0.47      ! [X: pi,Y4: pi] :
% 0.19/0.47        ( ( if_pi @ $true @ X @ Y4 )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.47      ! [X: name,Y4: name] :
% 0.19/0.47        ( ( if_name @ $false @ X @ Y4 )
% 0.19/0.47        = Y4 ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.47      ! [X: name,Y4: name] :
% 0.19/0.47        ( ( if_name @ $true @ X @ Y4 )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.19/0.47      ! [X: pi_Rep,Y4: pi_Rep] :
% 0.19/0.47        ( ( if_pi_Rep @ $false @ X @ Y4 )
% 0.19/0.47        = Y4 ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.19/0.47      ! [X: pi_Rep,Y4: pi_Rep] :
% 0.19/0.47        ( ( if_pi_Rep @ $true @ X @ Y4 )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.19/0.47      ! [X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( if_Late_freeRes @ $false @ X @ Y4 )
% 0.19/0.47        = Y4 ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.19/0.47      ! [X: late_freeRes,Y4: late_freeRes] :
% 0.19/0.47        ( ( if_Late_freeRes @ $true @ X @ Y4 )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.19/0.47      ! [P2: $o] :
% 0.19/0.47        ( ( P2 = $true )
% 0.19/0.47        | ( P2 = $false ) ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.19/0.47      ! [X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( if_Late_subject @ $false @ X @ Y4 )
% 0.19/0.47        = Y4 ) ).
% 0.19/0.47  
% 0.19/0.47  thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.19/0.47      ! [X: late_subject,Y4: late_subject] :
% 0.19/0.47        ( ( if_Late_subject @ $true @ X @ Y4 )
% 0.19/0.47        = X ) ).
% 0.19/0.47  
% 0.19/0.47  % Conjectures (1)
% 0.19/0.47  thf(conj_0,conjecture,
% 0.19/0.47      strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ).
% 0.19/0.47  
% 0.19/0.47  %------------------------------------------------------------------------------
% 0.19/0.47  ------------------------
% 2.89/1.58  ---- Embedded in THF ---
% 2.89/1.58  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.89/1.58  %%% Generated on Tue Feb 24 08:29:01 EST 2026
% 2.89/1.58  %%% using '$$dhol' embedding, version 1.3.0.
% 2.89/1.58  %%% Logic specification used:
% 2.89/1.58  %%% thf(spec, logic, $$dhol).
% 2.89/1.58  
% 2.89/1.58  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2DTF19857.p
% See solution above
% 2.89/1.58  ------------------------
% 3.16/1.61  ---- Cleaned THF ---
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 3.16/1.61      produc1872410278e_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 3.16/1.61      produc890461031e_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 3.16/1.61      list_P431515740_pi_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 3.16/1.61      set_Pr1654044726_pi_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J,type,
% 3.16/1.61      set_Pr806375235ubject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J,type,
% 3.16/1.61      set_Pr1780909331reeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.16/1.61      produc1141751126_pi_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 3.16/1.61      list_l1406151091e_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 3.16/1.61      produc1359399907ubject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      produc355105483reeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 3.16/1.61      produc214645451ubject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      produc1357834675reeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J_J,type,
% 3.16/1.61      set_Pr1131282415pi_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 3.16/1.61      produc257012921pi_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 3.16/1.61      produc1777919905pi_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 3.16/1.61      list_P227219501e_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 3.16/1.61      set_Pr443758855e_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 3.16/1.61      produc1998742700t_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 3.16/1.61      produc2052722628s_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 3.16/1.61      produc865358760ubject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      produc2008547984reeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 3.16/1.61      produc140253050ect_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 3.16/1.61      produc992857746Res_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.16/1.61      set_Pr1834926343_pi_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 3.16/1.61      produc1212344719pi_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 3.16/1.61      produc367475239e_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.16/1.61      product_prod_pi_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Late____Semantics__Osubject_J,type,
% 3.16/1.61      list_Late_subject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      list_Late_freeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 3.16/1.61      set_Late_subject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      set_Late_freeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Agent__Opi____Rep_J,type,
% 3.16/1.61      list_pi_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Late____Semantics__Oresidual____Rep,type,
% 3.16/1.61      late_residual_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Late____Semantics__Osubject____Rep,type,
% 3.16/1.61      late_subject_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Late____Semantics__OfreeRes____Rep,type,
% 3.16/1.61      late_freeRes_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 3.16/1.61      set_pi_Rep: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Agent__Oname_J,type,
% 3.16/1.61      list_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 3.16/1.61      set_name: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__List__Olist_It__Agent__Opi_J,type,
% 3.16/1.61      list_pi: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Late____Semantics__Oresidual,type,
% 3.16/1.61      late_residual: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Late____Semantics__Osubject,type,
% 3.16/1.61      late_subject: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 3.16/1.61      late_freeRes: $tType ).
% 3.16/1.61  
% 3.16/1.61  thf(ty_n_t__Set__Oset_It__Agent__Opi_J,type,
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% 3.16/1.61      perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 3.16/1.61      perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 3.16/1.61      perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 3.16/1.61      perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 3.16/1.61      perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 3.16/1.61      perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 3.16/1.61      perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Oname_J,type,
% 3.16/1.61      perm_name_set_name: list_P227219501e_name > set_name > set_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
% 3.16/1.61      perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 3.16/1.61      perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 3.16/1.61      perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.16/1.61      perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
% 3.16/1.61      swap_name: produc367475239e_name > name > name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
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% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 3.16/1.61      ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
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% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 3.16/1.61      produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 3.16/1.61      produc1570949143e_name: name > name > produc367475239e_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 3.16/1.61      produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 3.16/1.61      produc607574050ubject: name > late_subject > produc865358760ubject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.16/1.61      produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 3.16/1.61      product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Agent__Opi____Rep_001t__Agent__Opi____Rep,type,
% 3.16/1.61      produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 3.16/1.61      produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 3.16/1.61      produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi____Rep,type,
% 3.16/1.61      produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 3.16/1.61      produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 3.16/1.61      produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 3.16/1.61      produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 3.16/1.61      produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
% 3.16/1.61      produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 3.16/1.61      produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 3.16/1.61      produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 3.16/1.61      produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
% 3.16/1.61      eqvt_name: set_Pr443758855e_name > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 3.16/1.61      eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
% 3.16/1.61      eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
% 3.16/1.61      eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
% 3.16/1.61      eqvt_Late_subject: set_Pr806375235ubject > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Relation_OId_001t__Agent__Oname,type,
% 3.16/1.61      id_name: set_Pr443758855e_name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Relation_OId_001t__Agent__Opi,type,
% 3.16/1.61      id_pi: set_Pr1834926343_pi_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.16/1.61      collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 3.16/1.61      strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 3.16/1.61      strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Agent__Oname,type,
% 3.16/1.61      member_name: name > set_name > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Agent__Opi,type,
% 3.16/1.61      member_pi: pi > set_pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Agent__Opi____Rep,type,
% 3.16/1.61      member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
% 3.16/1.61      member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Late____Semantics__Osubject,type,
% 3.16/1.61      member_Late_subject: late_subject > set_Late_subject > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 3.16/1.61      member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.16/1.61      member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.16/1.61      member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 3.16/1.61      member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 3.16/1.61      member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 3.16/1.61      member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_P,type,
% 3.16/1.61      p: pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_PQ____,type,
% 3.16/1.61      pq: pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_P_H____,type,
% 3.16/1.61      p2: pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_Q,type,
% 3.16/1.61      q: pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_Rel,type,
% 3.16/1.61      rel: set_Pr1834926343_pi_pi ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_a____,type,
% 3.16/1.61      a: late_subject ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_aa____,type,
% 3.16/1.61      aa: name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_x,type,
% 3.16/1.61      x: name ).
% 3.16/1.61  
% 3.16/1.61  thf(sy_v_y____,type,
% 3.16/1.61      y: name ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_0_Id,axiom,
% 3.16/1.61      ord_le630093991_pi_pi @ id_pi @ rel ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 3.16/1.61      aa != x ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_2_cOpen_Ohyps_I3_J,axiom,
% 3.16/1.61      ( a
% 3.16/1.61      = ( late_BoundOutputS @ aa ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 3.16/1.61      y != x ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_4_Eqvt,axiom,
% 3.16/1.61      eqvt_pi @ rel ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_5_perm__swap_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_6_perm__swap_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_7_perm__swap_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_8_perm__swap_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_9_perm__swap_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_10_name__id,axiom,
% 3.16/1.61      ! [A: name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_11_name__id,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_12_name__id,axiom,
% 3.16/1.61      ! [A: name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_13_name__id,axiom,
% 3.16/1.61      ! [A: name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_14_name__id,axiom,
% 3.16/1.61      ! [A: name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_15_name__swap,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_16_name__swap,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_17_name__swap,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_18_name__swap,axiom,
% 3.16/1.61      ! [A: name,B: name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_19_name__swap,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61        = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_20_name__swap__bij,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_21_name__swap__bij,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_22_name__swap__bij,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_23_name__swap__bij,axiom,
% 3.16/1.61      ! [A: name,B: name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_24_name__swap__bij,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_25_pt__name1,axiom,
% 3.16/1.61      ! [X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_26_pt__name1,axiom,
% 3.16/1.61      ! [X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_27_pt__name1,axiom,
% 3.16/1.61      ! [X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_28_pt__name1,axiom,
% 3.16/1.61      ! [X: name] :
% 3.16/1.61        ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_29_pt__name1,axiom,
% 3.16/1.61      ! [X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_30_perm__swap_I2_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_31_perm__swap_I2_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_32_perm__swap_I2_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_33_perm__swap_I2_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_34_perm__swap_I2_J,axiom,
% 3.16/1.61      ! [A: name,B: name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_35_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.16/1.61      ! [X1: name,Y1: name] :
% 3.16/1.61        ( ( ( late_BoundOutputS @ X1 )
% 3.16/1.61          = ( late_BoundOutputS @ Y1 ) )
% 3.16/1.61        = ( X1 = Y1 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_36_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.16/1.61      ! [X2: name,Y2: name] :
% 3.16/1.61        ( ( ( late_BoundOutputS @ X2 )
% 3.16/1.61          = ( late_BoundOutputS @ Y2 ) )
% 3.16/1.61        = ( X2 = Y2 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_37__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 3.16/1.61      fresh_name_pi @ y @ p2 ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_38_list_Oinject,axiom,
% 3.16/1.61      ! [X21: produc367475239e_name,X22: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 3.16/1.61        ( ( ( cons_P1213805021e_name @ X21 @ X22 )
% 3.16/1.61          = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 3.16/1.61        = ( ( X21 = Y21 )
% 3.16/1.61          & ( X22 = Y22 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_39_prod_Oinject,axiom,
% 3.16/1.61      ! [X1: name,X2: name,Y1: name,Y2: name] :
% 3.16/1.61        ( ( ( produc1570949143e_name @ X1 @ X2 )
% 3.16/1.61          = ( produc1570949143e_name @ Y1 @ Y2 ) )
% 3.16/1.61        = ( ( X1 = Y1 )
% 3.16/1.61          & ( X2 = Y2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_40_prod_Oinject,axiom,
% 3.16/1.61      ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 3.16/1.61        ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 3.16/1.61          = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 3.16/1.61        = ( ( X1 = Y1 )
% 3.16/1.61          & ( X2 = Y2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_41_prod_Oinject,axiom,
% 3.16/1.61      ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 3.16/1.61        ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 3.16/1.61          = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 3.16/1.61        = ( ( X1 = Y1 )
% 3.16/1.61          & ( X2 = Y2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_42_old_Oprod_Oinject,axiom,
% 3.16/1.61      ! [A: name,B: name,A2: name,B2: name] :
% 3.16/1.61        ( ( ( produc1570949143e_name @ A @ B )
% 3.16/1.61          = ( produc1570949143e_name @ A2 @ B2 ) )
% 3.16/1.61        = ( ( A = A2 )
% 3.16/1.61          & ( B = B2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_43_old_Oprod_Oinject,axiom,
% 3.16/1.61      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 3.16/1.61        ( ( ( produc235456326_pi_pi @ A @ B )
% 3.16/1.61          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 3.16/1.61        = ( ( A = A2 )
% 3.16/1.61          & ( B = B2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_44_old_Oprod_Oinject,axiom,
% 3.16/1.61      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 3.16/1.61        ( ( ( product_Pair_pi_pi @ A @ B )
% 3.16/1.61          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 3.16/1.61        = ( ( A = A2 )
% 3.16/1.61          & ( B = B2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_45_residual__perm__empty,axiom,
% 3.16/1.61      ! [Residual_Rep: late_residual_Rep] :
% 3.16/1.61        ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 3.16/1.61        = Residual_Rep ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_46_subject__perm__empty,axiom,
% 3.16/1.61      ! [Subject_Rep: late_subject_Rep] :
% 3.16/1.61        ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 3.16/1.61        = Subject_Rep ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_47_freeRes__perm__empty,axiom,
% 3.16/1.61      ! [FreeRes_Rep: late_freeRes_Rep] :
% 3.16/1.61        ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 3.16/1.61        = FreeRes_Rep ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_48_pi__perm__empty,axiom,
% 3.16/1.61      ! [Pi_Rep: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 3.16/1.61        = Pi_Rep ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_49_subject_Operm_I2_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X1: name] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 3.16/1.61        = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_50_perm__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: pi_Rep,B: name] :
% 3.16/1.61        ( ( fresh_name_pi_Rep @ A @ X )
% 3.16/1.61       => ( ( fresh_name_pi_Rep @ B @ X )
% 3.16/1.61         => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_51_perm__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,B: name] :
% 3.16/1.61        ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61       => ( ( fresh_717452603ubject @ B @ X )
% 3.16/1.61         => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_52_perm__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,B: name] :
% 3.16/1.61        ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61       => ( ( fresh_1641682979reeRes @ B @ X )
% 3.16/1.61         => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_53_perm__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 3.16/1.61        ( ( fresh_1376661020_pi_pi @ A @ X )
% 3.16/1.61       => ( ( fresh_1376661020_pi_pi @ B @ X )
% 3.16/1.61         => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_54_perm__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: name,B: name] :
% 3.16/1.61        ( ( fresh_name_name @ A @ X )
% 3.16/1.61       => ( ( fresh_name_name @ B @ X )
% 3.16/1.61         => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_55_perm__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: pi,B: name] :
% 3.16/1.61        ( ( fresh_name_pi @ A @ X )
% 3.16/1.61       => ( ( fresh_name_pi @ B @ X )
% 3.16/1.61         => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_56_name__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: pi_Rep,B: name] :
% 3.16/1.61        ( ( fresh_name_pi_Rep @ A @ X )
% 3.16/1.61       => ( ( fresh_name_pi_Rep @ B @ X )
% 3.16/1.61         => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_57_name__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,B: name] :
% 3.16/1.61        ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61       => ( ( fresh_717452603ubject @ B @ X )
% 3.16/1.61         => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_58_name__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,B: name] :
% 3.16/1.61        ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61       => ( ( fresh_1641682979reeRes @ B @ X )
% 3.16/1.61         => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_59_name__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 3.16/1.61        ( ( fresh_1376661020_pi_pi @ A @ X )
% 3.16/1.61       => ( ( fresh_1376661020_pi_pi @ B @ X )
% 3.16/1.61         => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_60_name__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: name,B: name] :
% 3.16/1.61        ( ( fresh_name_name @ A @ X )
% 3.16/1.61       => ( ( fresh_name_name @ B @ X )
% 3.16/1.61         => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_61_name__fresh__fresh,axiom,
% 3.16/1.61      ! [A: name,X: pi,B: name] :
% 3.16/1.61        ( ( fresh_name_pi @ A @ X )
% 3.16/1.61       => ( ( fresh_name_pi @ B @ X )
% 3.16/1.61         => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.16/1.61            = X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_62_Bound_Ohyps_I4_J,axiom,
% 3.16/1.61      fresh_717452603ubject @ y @ a ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_63_subseteq__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X3: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( ord_le630093991_pi_pi @ X3 @ Y ) )
% 3.16/1.61        = ( ord_le630093991_pi_pi @ ( perm_n675238095_pi_pi @ Pi @ X3 ) @ ( perm_n675238095_pi_pi @ Pi @ Y ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_64_fresh__perm__app,axiom,
% 3.16/1.61      ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 3.16/1.61        ( ( fresh_922791155e_name @ A @ Pi )
% 3.16/1.61       => ( ( fresh_name_pi_Rep @ A @ X )
% 3.16/1.61         => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_65_fresh__perm__app,axiom,
% 3.16/1.61      ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 3.16/1.61        ( ( fresh_922791155e_name @ A @ Pi )
% 3.16/1.61       => ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61         => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_66_fresh__perm__app,axiom,
% 3.16/1.61      ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 3.16/1.61        ( ( fresh_922791155e_name @ A @ Pi )
% 3.16/1.61       => ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61         => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_67_fresh__perm__app,axiom,
% 3.16/1.61      ! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
% 3.16/1.61        ( ( fresh_922791155e_name @ A @ Pi )
% 3.16/1.61       => ( ( fresh_1376661020_pi_pi @ A @ X )
% 3.16/1.61         => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_68_fresh__perm__app,axiom,
% 3.16/1.61      ! [A: name,Pi: list_P227219501e_name,X: name] :
% 3.16/1.61        ( ( fresh_922791155e_name @ A @ Pi )
% 3.16/1.61       => ( ( fresh_name_name @ A @ X )
% 3.16/1.61         => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_69_fresh__perm__app,axiom,
% 3.16/1.61      ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 3.16/1.61        ( ( fresh_922791155e_name @ A @ Pi )
% 3.16/1.61       => ( ( fresh_name_pi @ A @ X )
% 3.16/1.61         => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_70_name__exists__fresh,axiom,
% 3.16/1.61      ! [X: late_subject] :
% 3.16/1.61        ~ ! [C: name] :
% 3.16/1.61            ~ ( fresh_717452603ubject @ C @ X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_71_name__exists__fresh,axiom,
% 3.16/1.61      ! [X: late_freeRes] :
% 3.16/1.61        ~ ! [C: name] :
% 3.16/1.61            ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_72_name__exists__fresh,axiom,
% 3.16/1.61      ! [X: produc1141751126_pi_pi] :
% 3.16/1.61        ~ ! [C: name] :
% 3.16/1.61            ~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_73_name__exists__fresh,axiom,
% 3.16/1.61      ! [X: name] :
% 3.16/1.61        ~ ! [C: name] :
% 3.16/1.61            ~ ( fresh_name_name @ C @ X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_74_name__exists__fresh,axiom,
% 3.16/1.61      ! [X: pi] :
% 3.16/1.61        ~ ! [C: name] :
% 3.16/1.61            ~ ( fresh_name_pi @ C @ X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_75_fresh__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 3.16/1.61        = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_76_fresh__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 3.16/1.61        = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_77_fresh__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 3.16/1.61        = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_78_fresh__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
% 3.16/1.61        = ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_79_fresh__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: name] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 3.16/1.61        = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_80_fresh__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 3.16/1.61        = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_81_fresh__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 3.16/1.61        ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 3.16/1.61        = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_82_fresh__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 3.16/1.61        ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 3.16/1.61        = ( fresh_717452603ubject @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_83_fresh__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 3.16/1.61        ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 3.16/1.61        = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_84_fresh__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 3.16/1.61        ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
% 3.16/1.61        = ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_85_fresh__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: name] :
% 3.16/1.61        ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 3.16/1.61        = ( fresh_name_name @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_86_fresh__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 3.16/1.61        ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 3.16/1.61        = ( fresh_name_pi @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_87_name__calc_I2_J,axiom,
% 3.16/1.61      ! [X: name] :
% 3.16/1.61        ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_88_successively_Ocases,axiom,
% 3.16/1.61      ! [X: produc1872410278e_name] :
% 3.16/1.61        ( ! [P: produc367475239e_name > produc367475239e_name > $o] :
% 3.16/1.61            ( X
% 3.16/1.61           != ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
% 3.16/1.61       => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] :
% 3.16/1.61              ( X
% 3.16/1.61             != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) ) )
% 3.16/1.61         => ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 3.16/1.61                ( X
% 3.16/1.61               != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_89_sorted__wrt_Ocases,axiom,
% 3.16/1.61      ! [X: produc1872410278e_name] :
% 3.16/1.61        ( ! [P: produc367475239e_name > produc367475239e_name > $o] :
% 3.16/1.61            ( X
% 3.16/1.61           != ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
% 3.16/1.61       => ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.16/1.61              ( X
% 3.16/1.61             != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_90_shuffles_Ocases,axiom,
% 3.16/1.61      ! [X: produc890461031e_name] :
% 3.16/1.61        ( ! [Ys: list_P227219501e_name] :
% 3.16/1.61            ( X
% 3.16/1.61           != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 3.16/1.61       => ( ! [Xs: list_P227219501e_name] :
% 3.16/1.61              ( X
% 3.16/1.61             != ( produc208131031e_name @ Xs @ nil_Pr743626285e_name ) )
% 3.16/1.61         => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.16/1.61                ( X
% 3.16/1.61               != ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_91_splice_Ocases,axiom,
% 3.16/1.61      ! [X: produc890461031e_name] :
% 3.16/1.61        ( ! [Ys: list_P227219501e_name] :
% 3.16/1.61            ( X
% 3.16/1.61           != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 3.16/1.61       => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
% 3.16/1.61              ( X
% 3.16/1.61             != ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_92_swap__simps_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 3.16/1.61        = B ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_93_swap__simps_I2_J,axiom,
% 3.16/1.61      ! [A: name,B: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 3.16/1.61        = A ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_94_swap__simps_I3_J,axiom,
% 3.16/1.61      ! [A: name,C2: name,B: name] :
% 3.16/1.61        ( ( A != C2 )
% 3.16/1.61       => ( ( B != C2 )
% 3.16/1.61         => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C2 )
% 3.16/1.61            = C2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_95_fresh__aux,axiom,
% 3.16/1.61      ! [C2: name,A: name,X: pi_Rep,B: name] :
% 3.16/1.61        ( ( C2 != A )
% 3.16/1.61       => ( ( fresh_name_pi_Rep @ A @ X )
% 3.16/1.61         => ( ( fresh_name_pi_Rep @ C2 @ X )
% 3.16/1.61           => ( fresh_name_pi_Rep @ C2 @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_96_fresh__aux,axiom,
% 3.16/1.61      ! [C2: name,A: name,X: late_subject,B: name] :
% 3.16/1.61        ( ( C2 != A )
% 3.16/1.61       => ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61         => ( ( fresh_717452603ubject @ C2 @ X )
% 3.16/1.61           => ( fresh_717452603ubject @ C2 @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_97_fresh__aux,axiom,
% 3.16/1.61      ! [C2: name,A: name,X: late_freeRes,B: name] :
% 3.16/1.61        ( ( C2 != A )
% 3.16/1.61       => ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61         => ( ( fresh_1641682979reeRes @ C2 @ X )
% 3.16/1.61           => ( fresh_1641682979reeRes @ C2 @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_98_fresh__aux,axiom,
% 3.16/1.61      ! [C2: name,A: name,X: produc1141751126_pi_pi,B: name] :
% 3.16/1.61        ( ( C2 != A )
% 3.16/1.61       => ( ( fresh_1376661020_pi_pi @ A @ X )
% 3.16/1.61         => ( ( fresh_1376661020_pi_pi @ C2 @ X )
% 3.16/1.61           => ( fresh_1376661020_pi_pi @ C2 @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_99_fresh__aux,axiom,
% 3.16/1.61      ! [C2: name,A: name,X: name,B: name] :
% 3.16/1.61        ( ( C2 != A )
% 3.16/1.61       => ( ( fresh_name_name @ A @ X )
% 3.16/1.61         => ( ( fresh_name_name @ C2 @ X )
% 3.16/1.61           => ( fresh_name_name @ C2 @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_100_fresh__aux,axiom,
% 3.16/1.61      ! [C2: name,A: name,X: pi,B: name] :
% 3.16/1.61        ( ( C2 != A )
% 3.16/1.61       => ( ( fresh_name_pi @ A @ X )
% 3.16/1.61         => ( ( fresh_name_pi @ C2 @ X )
% 3.16/1.61           => ( fresh_name_pi @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_101_old_Oprod_Oinducts,axiom,
% 3.16/1.61      ! [P2: produc367475239e_name > $o,Prod: produc367475239e_name] :
% 3.16/1.61        ( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
% 3.16/1.61       => ( P2 @ Prod ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_102_old_Oprod_Oinducts,axiom,
% 3.16/1.61      ! [P2: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 3.16/1.61        ( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 3.16/1.61       => ( P2 @ Prod ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_103_old_Oprod_Oinducts,axiom,
% 3.16/1.61      ! [P2: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 3.16/1.61        ( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 3.16/1.61       => ( P2 @ Prod ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_104_old_Oprod_Oexhaust,axiom,
% 3.16/1.61      ! [Y4: produc367475239e_name] :
% 3.16/1.61        ~ ! [A3: name,B3: name] :
% 3.16/1.61            ( Y4
% 3.16/1.61           != ( produc1570949143e_name @ A3 @ B3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_105_old_Oprod_Oexhaust,axiom,
% 3.16/1.61      ! [Y4: produc1141751126_pi_pi] :
% 3.16/1.61        ~ ! [A3: name,B3: product_prod_pi_pi] :
% 3.16/1.61            ( Y4
% 3.16/1.61           != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_106_old_Oprod_Oexhaust,axiom,
% 3.16/1.61      ! [Y4: product_prod_pi_pi] :
% 3.16/1.61        ~ ! [A3: pi,B3: pi] :
% 3.16/1.61            ( Y4
% 3.16/1.61           != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_107_mem__Collect__eq,axiom,
% 3.16/1.61      ! [A: product_prod_pi_pi,P2: product_prod_pi_pi > $o] :
% 3.16/1.61        ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P2 ) )
% 3.16/1.61        = ( P2 @ A ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_108_Collect__mem__eq,axiom,
% 3.16/1.61      ! [A4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( collec1051790738_pi_pi
% 3.16/1.61          @ ^ [X5: product_prod_pi_pi] : ( member558706512_pi_pi @ X5 @ A4 ) )
% 3.16/1.61        = A4 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_109_prod__induct3,axiom,
% 3.16/1.61      ! [P2: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 3.16/1.61        ( ! [A3: name,B3: pi,C: pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
% 3.16/1.61       => ( P2 @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_110_prod__cases3,axiom,
% 3.16/1.61      ! [Y4: produc1141751126_pi_pi] :
% 3.16/1.61        ~ ! [A3: name,B3: pi,C: pi] :
% 3.16/1.61            ( Y4
% 3.16/1.61           != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_111_Pair__inject,axiom,
% 3.16/1.61      ! [A: name,B: name,A2: name,B2: name] :
% 3.16/1.61        ( ( ( produc1570949143e_name @ A @ B )
% 3.16/1.61          = ( produc1570949143e_name @ A2 @ B2 ) )
% 3.16/1.61       => ~ ( ( A = A2 )
% 3.16/1.61           => ( B != B2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_112_Pair__inject,axiom,
% 3.16/1.61      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 3.16/1.61        ( ( ( produc235456326_pi_pi @ A @ B )
% 3.16/1.61          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 3.16/1.61       => ~ ( ( A = A2 )
% 3.16/1.61           => ( B != B2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_113_Pair__inject,axiom,
% 3.16/1.61      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 3.16/1.61        ( ( ( product_Pair_pi_pi @ A @ B )
% 3.16/1.61          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 3.16/1.61       => ~ ( ( A = A2 )
% 3.16/1.61           => ( B != B2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_114_prod__cases,axiom,
% 3.16/1.61      ! [P2: produc367475239e_name > $o,P3: produc367475239e_name] :
% 3.16/1.61        ( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
% 3.16/1.61       => ( P2 @ P3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_115_prod__cases,axiom,
% 3.16/1.61      ! [P2: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
% 3.16/1.61        ( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 3.16/1.61       => ( P2 @ P3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_116_prod__cases,axiom,
% 3.16/1.61      ! [P2: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 3.16/1.61        ( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 3.16/1.61       => ( P2 @ P3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_117_surj__pair,axiom,
% 3.16/1.61      ! [P3: produc367475239e_name] :
% 3.16/1.61      ? [X4: name,Y3: name] :
% 3.16/1.61        ( P3
% 3.16/1.61        = ( produc1570949143e_name @ X4 @ Y3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_118_surj__pair,axiom,
% 3.16/1.61      ! [P3: produc1141751126_pi_pi] :
% 3.16/1.61      ? [X4: name,Y3: product_prod_pi_pi] :
% 3.16/1.61        ( P3
% 3.16/1.61        = ( produc235456326_pi_pi @ X4 @ Y3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_119_surj__pair,axiom,
% 3.16/1.61      ! [P3: product_prod_pi_pi] :
% 3.16/1.61      ? [X4: pi,Y3: pi] :
% 3.16/1.61        ( P3
% 3.16/1.61        = ( product_Pair_pi_pi @ X4 @ Y3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_120_not__Cons__self2,axiom,
% 3.16/1.61      ! [X: produc367475239e_name,Xs2: list_P227219501e_name] :
% 3.16/1.61        ( ( cons_P1213805021e_name @ X @ Xs2 )
% 3.16/1.61       != Xs2 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_121_cp__name__name1,axiom,
% 3.16/1.61      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 3.16/1.61        = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_122_cp__name__name1,axiom,
% 3.16/1.61      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 3.16/1.61        = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_123_cp__name__name1,axiom,
% 3.16/1.61      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 3.16/1.61        = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_124_cp__name__name1,axiom,
% 3.16/1.61      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 3.16/1.61        = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_125_cp__name__name1,axiom,
% 3.16/1.61      ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 3.16/1.61        = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_126_name__perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_127_name__perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_128_name__perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_129_name__perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_130_name__perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_131_perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_132_perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_133_perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 3.16/1.61        ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_134_perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_135_perm__compose,axiom,
% 3.16/1.61      ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 3.16/1.61        ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 3.16/1.61        = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_136_perm__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( ( perm_n1559866809ubject @ Pi @ X )
% 3.16/1.61          = ( perm_n1559866809ubject @ Pi @ Y4 ) )
% 3.16/1.61        = ( X = Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_137_perm__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( ( perm_n336613537reeRes @ Pi @ X )
% 3.16/1.61          = ( perm_n336613537reeRes @ Pi @ Y4 ) )
% 3.16/1.61        = ( X = Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_138_perm__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 3.16/1.61        ( ( ( perm_name_pi_Rep @ Pi @ X )
% 3.16/1.61          = ( perm_name_pi_Rep @ Pi @ Y4 ) )
% 3.16/1.61        = ( X = Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_139_perm__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 3.16/1.61        ( ( ( perm_name_name @ Pi @ X )
% 3.16/1.61          = ( perm_name_name @ Pi @ Y4 ) )
% 3.16/1.61        = ( X = Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_140_perm__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 3.16/1.61        ( ( ( perm_name_pi @ Pi @ X )
% 3.16/1.61          = ( perm_name_pi @ Pi @ Y4 ) )
% 3.16/1.61        = ( X = Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_141_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_142_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_143_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_144_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_145_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_146_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_147_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_148_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_149_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_150_perm__app,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.16/1.61        = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_151_in__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X3: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X3 ) )
% 3.16/1.61        = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X3 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_152_in__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,X3: set_Late_subject] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X3 ) )
% 3.16/1.61        = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X3 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_153_in__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,X3: set_Late_freeRes] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X3 ) )
% 3.16/1.61        = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X3 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_154_in__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi_Rep,X3: set_pi_Rep] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X3 ) )
% 3.16/1.61        = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X3 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_155_in__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: name,X3: set_name] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( member_name @ X @ X3 ) )
% 3.16/1.61        = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X3 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_156_in__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi,X3: set_pi] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( member_pi @ X @ X3 ) )
% 3.16/1.61        = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X3 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_157_eq__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 3.16/1.61        = ( ( perm_n1559866809ubject @ Pi @ X )
% 3.16/1.61          = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_158_eq__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 3.16/1.61        = ( ( perm_n336613537reeRes @ Pi @ X )
% 3.16/1.61          = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_159_eq__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 3.16/1.61        = ( ( perm_name_pi_Rep @ Pi @ X )
% 3.16/1.61          = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_160_eq__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 3.16/1.61        = ( ( perm_name_name @ Pi @ X )
% 3.16/1.61          = ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_161_eq__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 3.16/1.61        ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 3.16/1.61        = ( ( perm_name_pi @ Pi @ X )
% 3.16/1.61          = ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_162_map__tailrec__rev_Oinduct,axiom,
% 3.16/1.61      ! [P2: ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name,A1: list_P227219501e_name,A22: list_P227219501e_name] :
% 3.16/1.61        ( ! [F2: produc367475239e_name > produc367475239e_name,X_1: list_P227219501e_name] : ( P2 @ F2 @ nil_Pr743626285e_name @ X_1 )
% 3.16/1.61       => ( ! [F2: produc367475239e_name > produc367475239e_name,A3: produc367475239e_name,As: list_P227219501e_name,Bs: list_P227219501e_name] :
% 3.16/1.61              ( ( P2 @ F2 @ As @ ( cons_P1213805021e_name @ ( F2 @ A3 ) @ Bs ) )
% 3.16/1.61             => ( P2 @ F2 @ ( cons_P1213805021e_name @ A3 @ As ) @ Bs ) )
% 3.16/1.61         => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_163_list__nonempty__induct,axiom,
% 3.16/1.61      ! [Xs2: list_P227219501e_name,P2: list_P227219501e_name > $o] :
% 3.16/1.61        ( ( Xs2 != nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 3.16/1.61         => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] :
% 3.16/1.61                ( ( Xs != nil_Pr743626285e_name )
% 3.16/1.61               => ( ( P2 @ Xs )
% 3.16/1.61                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) ) )
% 3.16/1.61           => ( P2 @ Xs2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_164_successively_Oinduct,axiom,
% 3.16/1.61      ! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 3.16/1.61        ( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] : ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 3.16/1.61         => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 3.16/1.61                ( ( P2 @ P @ ( cons_P1213805021e_name @ Y3 @ Xs ) )
% 3.16/1.61               => ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) )
% 3.16/1.61           => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_165_remdups__adj_Oinduct,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > $o,A0: list_P227219501e_name] :
% 3.16/1.61        ( ( P2 @ nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 3.16/1.61         => ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 3.16/1.61                ( ( ( X4 = Y3 )
% 3.16/1.61                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) )
% 3.16/1.61               => ( ( ( X4 != Y3 )
% 3.16/1.61                   => ( P2 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) )
% 3.16/1.61                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) )
% 3.16/1.61           => ( P2 @ A0 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_166_sorted__wrt_Oinduct,axiom,
% 3.16/1.61      ! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 3.16/1.61        ( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.16/1.61              ( ( P2 @ P @ Ys )
% 3.16/1.61             => ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) )
% 3.16/1.61         => ( P2 @ A0 @ A1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_167_remdups__adj_Ocases,axiom,
% 3.16/1.61      ! [X: list_P227219501e_name] :
% 3.16/1.61        ( ( X != nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [X4: produc367475239e_name] :
% 3.16/1.61              ( X
% 3.16/1.61             != ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 3.16/1.61         => ~ ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 3.16/1.61                ( X
% 3.16/1.61               != ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_168_transpose_Ocases,axiom,
% 3.16/1.61      ! [X: list_l1406151091e_name] :
% 3.16/1.61        ( ( X != nil_li29751603e_name )
% 3.16/1.61       => ( ! [Xss: list_l1406151091e_name] :
% 3.16/1.61              ( X
% 3.16/1.61             != ( cons_l798145763e_name @ nil_Pr743626285e_name @ Xss ) )
% 3.16/1.61         => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Xss: list_l1406151091e_name] :
% 3.16/1.61                ( X
% 3.16/1.61               != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Xss ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_169_shuffles_Oinduct,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 3.16/1.61        ( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
% 3.16/1.61       => ( ! [Xs: list_P227219501e_name] : ( P2 @ Xs @ nil_Pr743626285e_name )
% 3.16/1.61         => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.16/1.61                ( ( P2 @ Xs @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 3.16/1.61               => ( ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys )
% 3.16/1.61                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) )
% 3.16/1.61           => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_170_induct__list012,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > $o,Xs2: list_P227219501e_name] :
% 3.16/1.61        ( ( P2 @ nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 3.16/1.61         => ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Zs: list_P227219501e_name] :
% 3.16/1.61                ( ( P2 @ Zs )
% 3.16/1.61               => ( ( P2 @ ( cons_P1213805021e_name @ Y3 @ Zs ) )
% 3.16/1.61                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Zs ) ) ) ) )
% 3.16/1.61           => ( P2 @ Xs2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_171_splice_Oinduct,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 3.16/1.61        ( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
% 3.16/1.61       => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
% 3.16/1.61              ( ( P2 @ Ys @ Xs )
% 3.16/1.61             => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) )
% 3.16/1.61         => ( P2 @ A0 @ A1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_172_list__induct2_H,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > list_P227219501e_name > $o,Xs2: list_P227219501e_name,Ys2: list_P227219501e_name] :
% 3.16/1.61        ( ( P2 @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ nil_Pr743626285e_name )
% 3.16/1.61         => ( ! [Y3: produc367475239e_name,Ys: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 3.16/1.61           => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.16/1.61                  ( ( P2 @ Xs @ Ys )
% 3.16/1.61                 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) )
% 3.16/1.61             => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_173_neq__Nil__conv,axiom,
% 3.16/1.61      ! [Xs2: list_P227219501e_name] :
% 3.16/1.61        ( ( Xs2 != nil_Pr743626285e_name )
% 3.16/1.61        = ( ? [Y5: produc367475239e_name,Ys3: list_P227219501e_name] :
% 3.16/1.61              ( Xs2
% 3.16/1.61              = ( cons_P1213805021e_name @ Y5 @ Ys3 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_174_list_Oinducts,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > $o,List: list_P227219501e_name] :
% 3.16/1.61        ( ( P2 @ nil_Pr743626285e_name )
% 3.16/1.61       => ( ! [X12: produc367475239e_name,X23: list_P227219501e_name] :
% 3.16/1.61              ( ( P2 @ X23 )
% 3.16/1.61             => ( P2 @ ( cons_P1213805021e_name @ X12 @ X23 ) ) )
% 3.16/1.61         => ( P2 @ List ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_175_list_Oexhaust,axiom,
% 3.16/1.61      ! [Y4: list_P227219501e_name] :
% 3.16/1.61        ( ( Y4 != nil_Pr743626285e_name )
% 3.16/1.61       => ~ ! [X212: produc367475239e_name,X222: list_P227219501e_name] :
% 3.16/1.61              ( Y4
% 3.16/1.61             != ( cons_P1213805021e_name @ X212 @ X222 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_176_list_OdiscI,axiom,
% 3.16/1.61      ! [List: list_P227219501e_name,X21: produc367475239e_name,X22: list_P227219501e_name] :
% 3.16/1.61        ( ( List
% 3.16/1.61          = ( cons_P1213805021e_name @ X21 @ X22 ) )
% 3.16/1.61       => ( List != nil_Pr743626285e_name ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_177_list_Odistinct_I1_J,axiom,
% 3.16/1.61      ! [X21: produc367475239e_name,X22: list_P227219501e_name] :
% 3.16/1.61        ( nil_Pr743626285e_name
% 3.16/1.61       != ( cons_P1213805021e_name @ X21 @ X22 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_178__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 3.16/1.61      fresh_name_pi @ y @ q ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_179_pair__in__Id__conv,axiom,
% 3.16/1.61      ! [A: name,B: name] :
% 3.16/1.61        ( ( member695284560e_name @ ( produc1570949143e_name @ A @ B ) @ id_name )
% 3.16/1.61        = ( A = B ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_180_pair__in__Id__conv,axiom,
% 3.16/1.61      ! [A: pi,B: pi] :
% 3.16/1.61        ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 3.16/1.61        = ( A = B ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_181_IdI,axiom,
% 3.16/1.61      ! [A: name] : ( member695284560e_name @ ( produc1570949143e_name @ A @ A ) @ id_name ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_182_IdI,axiom,
% 3.16/1.61      ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_183_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61          & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_184_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,Y4: late_freeRes] :
% 3.16/1.61        ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61          & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_185_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,Y4: name] :
% 3.16/1.61        ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61          & ( fresh_name_name @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_186_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,Y4: pi] :
% 3.16/1.61        ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61          & ( fresh_name_pi @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_187_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,Y4: late_subject] :
% 3.16/1.61        ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61          & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_188_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61          & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_189_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,Y4: name] :
% 3.16/1.61        ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61          & ( fresh_name_name @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_190_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,Y4: pi] :
% 3.16/1.61        ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61          & ( fresh_name_pi @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_191_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: name,Y4: late_subject] :
% 3.16/1.61        ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_name_name @ A @ X )
% 3.16/1.61          & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_192_fresh__prod,axiom,
% 3.16/1.61      ! [A: name,X: name,Y4: late_freeRes] :
% 3.16/1.61        ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y4 ) )
% 3.16/1.61        = ( ( fresh_name_name @ A @ X )
% 3.16/1.61          & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_193__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 3.16/1.61      fresh_name_pi @ y @ p ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_194_derivativeReflexive,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,A: late_subject,X: name] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong2129052853vative @ P2 @ P2 @ A @ X @ Rel ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_195_derivativeEqvtI,axiom,
% 3.16/1.61      ! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
% 3.16/1.61       => ( ( eqvt_pi @ Rel )
% 3.16/1.61         => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_196_derivativeEqvtI2,axiom,
% 3.16/1.61      ! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
% 3.16/1.61       => ( ( eqvt_pi @ Rel )
% 3.16/1.61         => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_197_eqvtRelI,axiom,
% 3.16/1.61      ! [Rel: set_Pr806375235ubject,P2: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( eqvt_Late_subject @ Rel )
% 3.16/1.61       => ( ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel )
% 3.16/1.61         => ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_198_eqvtRelI,axiom,
% 3.16/1.61      ! [Rel: set_Pr1780909331reeRes,P2: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( eqvt_Late_freeRes @ Rel )
% 3.16/1.61       => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel )
% 3.16/1.61         => ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_199_eqvtRelI,axiom,
% 3.16/1.61      ! [Rel: set_Pr1131282415pi_Rep,P2: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( eqvt_pi_Rep @ Rel )
% 3.16/1.61       => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel )
% 3.16/1.61         => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_200_eqvtRelI,axiom,
% 3.16/1.61      ! [Rel: set_Pr443758855e_name,P2: name,Q: name,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( eqvt_name @ Rel )
% 3.16/1.61       => ( ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel )
% 3.16/1.61         => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_201_eqvtRelI,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( eqvt_pi @ Rel )
% 3.16/1.61       => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel )
% 3.16/1.61         => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_202_Bound_Ohyps_I5_J,axiom,
% 3.16/1.61      fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_203_subject_Ofresh_I2_J,axiom,
% 3.16/1.61      ! [A: name,X1: name] :
% 3.16/1.61        ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 3.16/1.61        = ( fresh_name_name @ A @ X1 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_204_name__bij,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 3.16/1.61        ( ( ( perm_name_name @ Pi @ X )
% 3.16/1.61          = ( perm_name_name @ Pi @ Y4 ) )
% 3.16/1.61        = ( X = Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_205_allE__Nil,axiom,
% 3.16/1.61      ! [P2: list_P227219501e_name > $o] :
% 3.16/1.61        ( ! [X_1: list_P227219501e_name] : ( P2 @ X_1 )
% 3.16/1.61       => ( P2 @ nil_Pr743626285e_name ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_206_if__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 3.16/1.61        ( ( ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 3.16/1.61        & ( ~ ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_207_if__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 3.16/1.61        ( ( ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 3.16/1.61        & ( ~ ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_208_if__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 3.16/1.61        ( ( ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 3.16/1.61        & ( ~ ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_209_if__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 3.16/1.61        ( ( ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_name_name @ Pi @ C1 ) ) )
% 3.16/1.61        & ( ~ ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_210_if__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 3.16/1.61        ( ( ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_name_pi @ Pi @ C1 ) ) )
% 3.16/1.61        & ( ~ ( perm_name_o @ Pi @ B )
% 3.16/1.61         => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 3.16/1.61            = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_211_pt__bij3,axiom,
% 3.16/1.61      ! [X: late_subject,Y4: late_subject,Pi: list_P227219501e_name] :
% 3.16/1.61        ( ( X = Y4 )
% 3.16/1.61       => ( ( perm_n1559866809ubject @ Pi @ X )
% 3.16/1.61          = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_212_pt__bij3,axiom,
% 3.16/1.61      ! [X: late_freeRes,Y4: late_freeRes,Pi: list_P227219501e_name] :
% 3.16/1.61        ( ( X = Y4 )
% 3.16/1.61       => ( ( perm_n336613537reeRes @ Pi @ X )
% 3.16/1.61          = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_213_pt__bij3,axiom,
% 3.16/1.61      ! [X: pi_Rep,Y4: pi_Rep,Pi: list_P227219501e_name] :
% 3.16/1.61        ( ( X = Y4 )
% 3.16/1.61       => ( ( perm_name_pi_Rep @ Pi @ X )
% 3.16/1.61          = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_214_pt__bij3,axiom,
% 3.16/1.61      ! [X: name,Y4: name,Pi: list_P227219501e_name] :
% 3.16/1.61        ( ( X = Y4 )
% 3.16/1.61       => ( ( perm_name_name @ Pi @ X )
% 3.16/1.61          = ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_215_pt__bij3,axiom,
% 3.16/1.61      ! [X: pi,Y4: pi,Pi: list_P227219501e_name] :
% 3.16/1.61        ( ( X = Y4 )
% 3.16/1.61       => ( ( perm_name_pi @ Pi @ X )
% 3.16/1.61          = ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_216_abs__fun__if,axiom,
% 3.16/1.61      ! [C2: $o,Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( C2
% 3.16/1.61         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 3.16/1.61        & ( ~ C2
% 3.16/1.61         => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_217_abs__fun__if,axiom,
% 3.16/1.61      ! [C2: $o,Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( C2
% 3.16/1.61         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 3.16/1.61        & ( ~ C2
% 3.16/1.61         => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_218_abs__fun__if,axiom,
% 3.16/1.61      ! [C2: $o,Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 3.16/1.61        ( ( C2
% 3.16/1.61         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 3.16/1.61        & ( ~ C2
% 3.16/1.61         => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_219_abs__fun__if,axiom,
% 3.16/1.61      ! [C2: $o,Pi: list_P227219501e_name,X: name,Y4: name] :
% 3.16/1.61        ( ( C2
% 3.16/1.61         => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_name_name @ Pi @ X ) ) )
% 3.16/1.61        & ( ~ C2
% 3.16/1.61         => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_name_name @ Pi @ Y4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_220_abs__fun__if,axiom,
% 3.16/1.61      ! [C2: $o,Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 3.16/1.61        ( ( C2
% 3.16/1.61         => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_name_pi @ Pi @ X ) ) )
% 3.16/1.61        & ( ~ C2
% 3.16/1.61         => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
% 3.16/1.61            = ( perm_name_pi @ Pi @ Y4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_221_eqvt__def,axiom,
% 3.16/1.61      ( eqvt_pi
% 3.16/1.61      = ( ^ [Rel2: set_Pr1834926343_pi_pi] :
% 3.16/1.61          ! [X5: product_prod_pi_pi,Perm2: list_P227219501e_name] :
% 3.16/1.61            ( ( member558706512_pi_pi @ X5 @ Rel2 )
% 3.16/1.61           => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X5 ) @ Rel2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_222_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y4 ) )
% 3.16/1.61        = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_223_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_freeRes] :
% 3.16/1.61        ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y4 ) )
% 3.16/1.61        = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_224_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: pi_Rep] :
% 3.16/1.61        ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y4 ) )
% 3.16/1.61        = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_225_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: name] :
% 3.16/1.61        ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y4 ) )
% 3.16/1.61        = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_226_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Y4: pi] :
% 3.16/1.61        ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y4 ) )
% 3.16/1.61        = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_227_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_subject] :
% 3.16/1.61        ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y4 ) )
% 3.16/1.61        = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_228_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y4 ) )
% 3.16/1.61        = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_229_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi_Rep] :
% 3.16/1.61        ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y4 ) )
% 3.16/1.61        = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_230_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: name] :
% 3.16/1.61        ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y4 ) )
% 3.16/1.61        = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_231_perm__prod_Osimps,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi] :
% 3.16/1.61        ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y4 ) )
% 3.16/1.61        = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_232_cons__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_subject,Xs2: list_Late_subject] :
% 3.16/1.61        ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs2 ) )
% 3.16/1.61        = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_233_cons__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: late_freeRes,Xs2: list_Late_freeRes] :
% 3.16/1.61        ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs2 ) )
% 3.16/1.61        = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_234_cons__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi_Rep,Xs2: list_pi_Rep] :
% 3.16/1.61        ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs2 ) )
% 3.16/1.61        = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_235_cons__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: name,Xs2: list_name] :
% 3.16/1.61        ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs2 ) )
% 3.16/1.61        = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_236_cons__eqvt,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X: pi,Xs2: list_pi] :
% 3.16/1.61        ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs2 ) )
% 3.16/1.61        = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_237_fresh__prodD_I1_J,axiom,
% 3.16/1.61      ! [A: name,X: name,Y4: name] :
% 3.16/1.61        ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
% 3.16/1.61       => ( fresh_name_name @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_238_fresh__prodD_I1_J,axiom,
% 3.16/1.61      ! [A: name,X: name,Y4: product_prod_pi_pi] :
% 3.16/1.61        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
% 3.16/1.61       => ( fresh_name_name @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_239_fresh__prodD_I1_J,axiom,
% 3.16/1.61      ! [A: name,X: pi,Y4: pi] :
% 3.16/1.61        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
% 3.16/1.61       => ( fresh_name_pi @ A @ X ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_240_fresh__prodD_I2_J,axiom,
% 3.16/1.61      ! [A: name,X: name,Y4: name] :
% 3.16/1.61        ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
% 3.16/1.61       => ( fresh_name_name @ A @ Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_241_fresh__prodD_I2_J,axiom,
% 3.16/1.61      ! [A: name,X: name,Y4: product_prod_pi_pi] :
% 3.16/1.61        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
% 3.16/1.61       => ( fresh_1627595501_pi_pi @ A @ Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_242_fresh__prodD_I2_J,axiom,
% 3.16/1.61      ! [A: name,X: pi,Y4: pi] :
% 3.16/1.61        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
% 3.16/1.61       => ( fresh_name_pi @ A @ Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_243_fresh__list__cons,axiom,
% 3.16/1.61      ! [A: name,X: late_subject,Xs2: list_Late_subject] :
% 3.16/1.61        ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ X @ Xs2 ) )
% 3.16/1.61        = ( ( fresh_717452603ubject @ A @ X )
% 3.16/1.61          & ( fresh_838462539ubject @ A @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_244_fresh__list__cons,axiom,
% 3.16/1.61      ! [A: name,X: late_freeRes,Xs2: list_Late_freeRes] :
% 3.16/1.61        ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ X @ Xs2 ) )
% 3.16/1.61        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.16/1.61          & ( fresh_1981651763reeRes @ A @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_245_fresh__list__cons,axiom,
% 3.16/1.61      ! [A: name,X: produc1141751126_pi_pi,Xs2: list_P431515740_pi_pi] :
% 3.16/1.61        ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs2 ) )
% 3.16/1.61        = ( ( fresh_1376661020_pi_pi @ A @ X )
% 3.16/1.61          & ( fresh_1958133282_pi_pi @ A @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_246_fresh__list__cons,axiom,
% 3.16/1.61      ! [A: name,X: name,Xs2: list_name] :
% 3.16/1.61        ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs2 ) )
% 3.16/1.61        = ( ( fresh_name_name @ A @ X )
% 3.16/1.61          & ( fresh_name_list_name @ A @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_247_fresh__list__cons,axiom,
% 3.16/1.61      ! [A: name,X: pi,Xs2: list_pi] :
% 3.16/1.61        ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs2 ) )
% 3.16/1.61        = ( ( fresh_name_pi @ A @ X )
% 3.16/1.61          & ( fresh_name_list_pi @ A @ Xs2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_248_subrelI,axiom,
% 3.16/1.61      ! [R: set_Pr443758855e_name,S: set_Pr443758855e_name] :
% 3.16/1.61        ( ! [X4: name,Y3: name] :
% 3.16/1.61            ( ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ R )
% 3.16/1.61           => ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ S ) )
% 3.16/1.61       => ( ord_le793202855e_name @ R @ S ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_249_subrelI,axiom,
% 3.16/1.61      ! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
% 3.16/1.61        ( ! [X4: name,Y3: product_prod_pi_pi] :
% 3.16/1.61            ( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ R )
% 3.16/1.61           => ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ S ) )
% 3.16/1.61       => ( ord_le797229014_pi_pi @ R @ S ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_250_subrelI,axiom,
% 3.16/1.61      ! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ! [X4: pi,Y3: pi] :
% 3.16/1.61            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ R )
% 3.16/1.61           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ S ) )
% 3.16/1.61       => ( ord_le630093991_pi_pi @ R @ S ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_251_IdE,axiom,
% 3.16/1.61      ! [P3: produc367475239e_name] :
% 3.16/1.61        ( ( member695284560e_name @ P3 @ id_name )
% 3.16/1.61       => ~ ! [X4: name] :
% 3.16/1.61              ( P3
% 3.16/1.61             != ( produc1570949143e_name @ X4 @ X4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_252_IdE,axiom,
% 3.16/1.61      ! [P3: product_prod_pi_pi] :
% 3.16/1.61        ( ( member558706512_pi_pi @ P3 @ id_pi )
% 3.16/1.61       => ~ ! [X4: pi] :
% 3.16/1.61              ( P3
% 3.16/1.61             != ( product_Pair_pi_pi @ X4 @ X4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_253_derivativeMonotonic,axiom,
% 3.16/1.61      ! [P2: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( strong2129052853vative @ P2 @ Q @ A @ X @ A4 )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 3.16/1.61         => ( strong2129052853vative @ P2 @ Q @ A @ X @ B4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_254_eqvtRelE,axiom,
% 3.16/1.61      ! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P2: late_subject,Q: late_subject] :
% 3.16/1.61        ( ( eqvt_Late_subject @ Rel )
% 3.16/1.61       => ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
% 3.16/1.61         => ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_255_eqvtRelE,axiom,
% 3.16/1.61      ! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P2: late_freeRes,Q: late_freeRes] :
% 3.16/1.61        ( ( eqvt_Late_freeRes @ Rel )
% 3.16/1.61       => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
% 3.16/1.61         => ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_256_eqvtRelE,axiom,
% 3.16/1.61      ! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P2: pi_Rep,Q: pi_Rep] :
% 3.16/1.61        ( ( eqvt_pi_Rep @ Rel )
% 3.16/1.61       => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
% 3.16/1.61         => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_257_eqvtRelE,axiom,
% 3.16/1.61      ! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P2: name,Q: name] :
% 3.16/1.61        ( ( eqvt_name @ Rel )
% 3.16/1.61       => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
% 3.16/1.61         => ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_258_eqvtRelE,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P2: pi,Q: pi] :
% 3.16/1.61        ( ( eqvt_pi @ Rel )
% 3.16/1.61       => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
% 3.16/1.61         => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_259_Bound_Ohyps_I3_J,axiom,
% 3.16/1.61      fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_260_Bound_Ohyps_I2_J,axiom,
% 3.16/1.61      fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_261_subset__antisym,axiom,
% 3.16/1.61      ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ B4 @ A4 )
% 3.16/1.61         => ( A4 = B4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_262_subsetI,axiom,
% 3.16/1.61      ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ! [X4: product_prod_pi_pi] :
% 3.16/1.61            ( ( member558706512_pi_pi @ X4 @ A4 )
% 3.16/1.61           => ( member558706512_pi_pi @ X4 @ B4 ) )
% 3.16/1.61       => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_263_order__refl,axiom,
% 3.16/1.61      ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_264_name__fresh,axiom,
% 3.16/1.61      ( fresh_name_name
% 3.16/1.61      = ( ^ [A5: name,B5: name] : ( A5 != B5 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_265_pi_Ofresh_I7_J,axiom,
% 3.16/1.61      ! [A: name,X2: pi,X1: pi] :
% 3.16/1.61        ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 3.16/1.61        = ( ( fresh_name_pi @ A @ X2 )
% 3.16/1.61          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_266_pi_Operm_I7_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 3.16/1.61        ( ( perm_name_pi @ Pi @ ( sum @ X2 @ X1 ) )
% 3.16/1.61        = ( sum @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_267_pi_Operm_I9_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 3.16/1.61        ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 3.16/1.61        = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_268_pi_Odistinct_I81_J,axiom,
% 3.16/1.61      ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 3.16/1.61        ( ( sum @ Pi1 @ Pi2 )
% 3.16/1.61       != ( res @ Name @ Pi3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_269_pi_Oinject_I6_J,axiom,
% 3.16/1.61      ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 3.16/1.61        ( ( ( sum @ X2 @ X1 )
% 3.16/1.61          = ( sum @ Y2 @ Y1 ) )
% 3.16/1.61        = ( ( X2 = Y2 )
% 3.16/1.61          & ( X1 = Y1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_270_freshRes,axiom,
% 3.16/1.61      ! [A: name,P2: pi] : ( fresh_name_pi @ A @ ( res @ A @ P2 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_271_order__subst1,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A @ ( F @ B ) )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.16/1.61         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 3.16/1.61                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 3.16/1.61               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 3.16/1.61           => ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_272_order__subst2,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A @ B )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ ( F @ B ) @ C2 )
% 3.16/1.61         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 3.16/1.61                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 3.16/1.61               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 3.16/1.61           => ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_273_ord__eq__le__subst,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( A
% 3.16/1.61          = ( F @ B ) )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.16/1.61         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 3.16/1.61                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 3.16/1.61               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 3.16/1.61           => ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_274_ord__le__eq__subst,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A @ B )
% 3.16/1.61       => ( ( ( F @ B )
% 3.16/1.61            = C2 )
% 3.16/1.61         => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 3.16/1.61                ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 3.16/1.61               => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 3.16/1.61           => ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_275_eq__iff,axiom,
% 3.16/1.61      ( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : ( Y6 = Z ) )
% 3.16/1.61      = ( ^ [X5: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 3.16/1.61            ( ( ord_le630093991_pi_pi @ X5 @ Y5 )
% 3.16/1.61            & ( ord_le630093991_pi_pi @ Y5 @ X5 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_276_antisym,axiom,
% 3.16/1.61      ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ Y4 @ X )
% 3.16/1.61         => ( X = Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_277_eq__refl,axiom,
% 3.16/1.61      ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( X = Y4 )
% 3.16/1.61       => ( ord_le630093991_pi_pi @ X @ Y4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_278_order_Otrans,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A @ B )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.16/1.61         => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_279_antisym__conv,axiom,
% 3.16/1.61      ! [Y4: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ Y4 @ X )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 3.16/1.61          = ( X = Y4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_280_order__class_Oorder_Oeq__iff,axiom,
% 3.16/1.61      ( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : ( Y6 = Z ) )
% 3.16/1.61      = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 3.16/1.61            ( ( ord_le630093991_pi_pi @ A5 @ B5 )
% 3.16/1.61            & ( ord_le630093991_pi_pi @ B5 @ A5 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_281_ord__eq__le__trans,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( A = B )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.16/1.61         => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_282_ord__le__eq__trans,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A @ B )
% 3.16/1.61       => ( ( B = C2 )
% 3.16/1.61         => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_283_order__class_Oorder_Oantisym,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ A @ B )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ B @ A )
% 3.16/1.61         => ( A = B ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_284_order__trans,axiom,
% 3.16/1.61      ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi,Z2: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ Y4 @ Z2 )
% 3.16/1.61         => ( ord_le630093991_pi_pi @ X @ Z2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_285_dual__order_Orefl,axiom,
% 3.16/1.61      ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_286_alphaRes,axiom,
% 3.16/1.61      ! [C2: name,P2: pi,A: name] :
% 3.16/1.61        ( ( fresh_name_pi @ C2 @ P2 )
% 3.16/1.61       => ( ( res @ A @ P2 )
% 3.16/1.61          = ( res @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_287_calculation,axiom,
% 3.16/1.61      late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_288_Bound_Ohyps_I1_J,axiom,
% 3.16/1.61      late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_289__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 3.16/1.61      late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_290_sumResLeft,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,X: name,P2: pi,Q: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( ( eqvt_pi @ Rel )
% 3.16/1.61         => ( strong743114133lation @ ( sum @ ( res @ X @ P2 ) @ ( res @ X @ Q ) ) @ Rel @ ( res @ X @ ( sum @ P2 @ Q ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_291_cSum1_Ohyps,axiom,
% 3.16/1.61      late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_292_residual_Operm_I1_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 3.16/1.61        ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 3.16/1.61        = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_293_freshBoundDerivative_I1_J,axiom,
% 3.16/1.61      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 3.16/1.61       => ( ( fresh_name_pi @ Y4 @ P2 )
% 3.16/1.61         => ( fresh_717452603ubject @ Y4 @ A ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_294_Late__Semantics_OResB,axiom,
% 3.16/1.61      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 3.16/1.61       => ( ( fresh_717452603ubject @ Y4 @ A )
% 3.16/1.61         => ( ( Y4 != X )
% 3.16/1.61           => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_295_freshBoundDerivative_I2_J,axiom,
% 3.16/1.61      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 3.16/1.61       => ( ( fresh_name_pi @ Y4 @ P2 )
% 3.16/1.61         => ( ( Y4 != X )
% 3.16/1.61           => ( fresh_name_pi @ Y4 @ P4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_296_simE_I1_J,axiom,
% 3.16/1.61      ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 3.16/1.61        ( ( strong743114133lation @ P2 @ Rel @ Q )
% 3.16/1.61       => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.16/1.61         => ( ( fresh_name_pi @ X @ P2 )
% 3.16/1.61           => ? [P5: pi] :
% 3.16/1.61                ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
% 3.16/1.61                & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_297_Sum2,axiom,
% 3.16/1.61      ! [Q: pi,Rs: late_residual,P2: pi] :
% 3.16/1.61        ( ( late_transitions @ Q @ Rs )
% 3.16/1.61       => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_298_Sum1,axiom,
% 3.16/1.61      ! [P2: pi,Rs: late_residual,Q: pi] :
% 3.16/1.61        ( ( late_transitions @ P2 @ Rs )
% 3.16/1.61       => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_299_sumCases_H,axiom,
% 3.16/1.61      ! [P2: pi,Q: pi,Rs: late_residual] :
% 3.16/1.61        ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 3.16/1.61       => ( ~ ( late_transitions @ P2 @ Rs )
% 3.16/1.61         => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_300_sumCases,axiom,
% 3.16/1.61      ! [P2: pi,Q: pi,Rs: late_residual] :
% 3.16/1.61        ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 3.16/1.61       => ( ~ ( late_transitions @ P2 @ Rs )
% 3.16/1.61         => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_301_freshResidual,axiom,
% 3.16/1.61      ! [P2: pi,Rs: late_residual,X: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ Rs )
% 3.16/1.61       => ( ( fresh_name_pi @ X @ P2 )
% 3.16/1.61         => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_302_eqvt,axiom,
% 3.16/1.61      ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 3.16/1.61        ( ( late_transitions @ X1 @ X2 )
% 3.16/1.61       => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_303_transitions_OResB,axiom,
% 3.16/1.61      ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 3.16/1.61       => ( ( fresh_717452603ubject @ Y4 @ A )
% 3.16/1.61         => ( ( Y4 != X )
% 3.16/1.61           => ( ( fresh_name_pi @ X @ P2 )
% 3.16/1.61             => ( ( fresh_717452603ubject @ X @ A )
% 3.16/1.61               => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_304_monotonic,axiom,
% 3.16/1.61      ! [P2: pi,A4: set_Pr1834926343_pi_pi,P4: pi,B4: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ( strong743114133lation @ P2 @ A4 @ P4 )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 3.16/1.61         => ( strong743114133lation @ P2 @ B4 @ P4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_305_Strong__Late__Sim_Oreflexive,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong743114133lation @ P2 @ Rel @ P2 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_306_sumIdempRight,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong743114133lation @ ( sum @ P2 @ P2 ) @ Rel @ P2 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_307_sumAssocRight,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong743114133lation @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_308_sumIdempLeft,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong743114133lation @ P2 @ Rel @ ( sum @ P2 @ P2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_309_sumAssocLeft,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong743114133lation @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) @ Rel @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_310_sumSym,axiom,
% 3.16/1.61      ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi] :
% 3.16/1.61        ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.16/1.61       => ( strong743114133lation @ ( sum @ P2 @ Q ) @ Rel @ ( sum @ Q @ P2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_311_eqvtI,axiom,
% 3.16/1.61      ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Rel3: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 3.16/1.61        ( ( strong743114133lation @ P2 @ Rel @ Q )
% 3.16/1.61       => ( ( ord_le630093991_pi_pi @ Rel @ Rel3 )
% 3.16/1.61         => ( ( eqvt_pi @ Rel3 )
% 3.16/1.61           => ( strong743114133lation @ ( perm_name_pi @ Perm @ P2 ) @ Rel3 @ ( perm_name_pi @ Perm @ Q ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_312_alphaBoundResidual,axiom,
% 3.16/1.61      ! [X6: name,P2: pi,A: late_subject,X: name] :
% 3.16/1.61        ( ( fresh_name_pi @ X6 @ P2 )
% 3.16/1.61       => ( ( late_BoundR @ A @ X @ P2 )
% 3.16/1.61          = ( late_BoundR @ A @ X6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X6 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_313_cOpen_Ohyps_I1_J,axiom,
% 3.16/1.61      late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_314__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 3.16/1.61      late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_315_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.16/1.61      ! [X11: name,X122: name,Y11: name,Y12: name] :
% 3.16/1.61        ( ( ( late_OutputR @ X11 @ X122 )
% 3.16/1.61          = ( late_OutputR @ Y11 @ Y12 ) )
% 3.16/1.61        = ( ( X11 = Y11 )
% 3.16/1.61          & ( X122 = Y12 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_316_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.16/1.61      ! [X2: name,X1: name,Y2: name,Y1: name] :
% 3.16/1.61        ( ( ( late_OutputR @ X2 @ X1 )
% 3.16/1.61          = ( late_OutputR @ Y2 @ Y1 ) )
% 3.16/1.61        = ( ( X2 = Y2 )
% 3.16/1.61          & ( X1 = Y1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_317_freeRes_Operm_I1_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 3.16/1.61        ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 3.16/1.61        = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_318_freeRes_Ofresh_I1_J,axiom,
% 3.16/1.61      ! [A: name,X2: name,X1: name] :
% 3.16/1.61        ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 3.16/1.61        = ( ( fresh_name_name @ A @ X2 )
% 3.16/1.61          & ( fresh_name_name @ A @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_319_residual_Operm_I2_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 3.16/1.61        ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 3.16/1.61        = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_320_residual_Ofresh_I2_J,axiom,
% 3.16/1.61      ! [A: name,X2: late_freeRes,X1: pi] :
% 3.16/1.61        ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 3.16/1.61        = ( ( fresh_1641682979reeRes @ A @ X2 )
% 3.16/1.61          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_321_residual_Odistinct_I1_J,axiom,
% 3.16/1.61      ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 3.16/1.61        ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 3.16/1.61       != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_322_residual_Oinducts,axiom,
% 3.16/1.61      ! [P2: late_residual > $o,Residual: late_residual] :
% 3.16/1.61        ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 3.16/1.61       => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.16/1.61         => ( P2 @ Residual ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_323_residual_Oinject_I2_J,axiom,
% 3.16/1.61      ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 3.16/1.61        ( ( ( late_FreeR @ X2 @ X1 )
% 3.16/1.61          = ( late_FreeR @ Y2 @ Y1 ) )
% 3.16/1.61        = ( ( X2 = Y2 )
% 3.16/1.61          & ( X1 = Y1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_324_ResF,axiom,
% 3.16/1.61      ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 3.16/1.61       => ( ( fresh_1641682979reeRes @ Y4 @ Alpha )
% 3.16/1.61         => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_FreeR @ Alpha @ ( res @ Y4 @ P4 ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_325_resCasesF_H,axiom,
% 3.16/1.61      ! [X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 3.16/1.61        ( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) )
% 3.16/1.61       => ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 3.16/1.61              ( ( ( res @ X @ P2 )
% 3.16/1.61                = ( res @ Y3 @ P ) )
% 3.16/1.61             => ( ( ( late_FreeR @ Alpha @ P4 )
% 3.16/1.61                  = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 3.16/1.61               => ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.16/1.61                 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_326_resCasesF,axiom,
% 3.16/1.61      ! [X: name,P2: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 3.16/1.61        ( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ XP ) )
% 3.16/1.61       => ( ! [P5: pi] :
% 3.16/1.61              ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
% 3.16/1.61             => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.16/1.61               => ( F3 @ ( res @ X @ P5 ) ) ) )
% 3.16/1.61         => ( F3 @ XP ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_327_freshFreeDerivative_I2_J,axiom,
% 3.16/1.61      ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 3.16/1.61       => ( ( fresh_name_pi @ Y4 @ P2 )
% 3.16/1.61         => ( fresh_name_pi @ Y4 @ P4 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_328_freshFreeDerivative_I1_J,axiom,
% 3.16/1.61      ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 3.16/1.61       => ( ( fresh_name_pi @ Y4 @ P2 )
% 3.16/1.61         => ( fresh_1641682979reeRes @ Y4 @ Alpha ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_329_Open,axiom,
% 3.16/1.61      ! [P2: pi,A: name,B: name,P4: pi] :
% 3.16/1.61        ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P4 ) )
% 3.16/1.61       => ( ( A != B )
% 3.16/1.61         => ( late_transitions @ ( res @ B @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P4 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_330_simE_I2_J,axiom,
% 3.16/1.61      ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 3.16/1.61        ( ( strong743114133lation @ P2 @ Rel @ Q )
% 3.16/1.61       => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.16/1.61         => ? [P5: pi] :
% 3.16/1.61              ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
% 3.16/1.61              & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_331_resCasesB_H,axiom,
% 3.16/1.61      ! [X6: name,P2: pi,A: late_subject,Y7: name,P4: pi] :
% 3.16/1.61        ( ( late_transitions @ ( res @ X6 @ P2 ) @ ( late_BoundR @ A @ Y7 @ P4 ) )
% 3.16/1.61       => ( ! [P: pi,A3: name,B3: name] :
% 3.16/1.61              ( ( ( res @ X6 @ P2 )
% 3.16/1.61                = ( res @ B3 @ P ) )
% 3.16/1.61             => ! [P5: pi] :
% 3.16/1.61                  ( ( ( late_BoundR @ A @ Y7 @ P4 )
% 3.16/1.61                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 3.16/1.61                 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 3.16/1.61                   => ( A3 = B3 ) ) ) )
% 3.16/1.61         => ~ ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 3.16/1.61                ( ( ( res @ X6 @ P2 )
% 3.16/1.61                  = ( res @ Y3 @ P ) )
% 3.16/1.61               => ( ( ( late_BoundR @ A @ Y7 @ P4 )
% 3.16/1.61                    = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 3.16/1.61                 => ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 3.16/1.61                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 3.16/1.61                     => ( ( Y3 != X4 )
% 3.16/1.61                       => ( ( fresh_name_pi @ X4 @ P )
% 3.16/1.61                         => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_332_resCases_H,axiom,
% 3.16/1.61      ! [X: name,P2: pi,Rs: late_residual] :
% 3.16/1.61        ( ( late_transitions @ ( res @ X @ P2 ) @ Rs )
% 3.16/1.61       => ( ! [P: pi,A3: name,B3: name] :
% 3.16/1.61              ( ( ( res @ X @ P2 )
% 3.16/1.61                = ( res @ B3 @ P ) )
% 3.16/1.61             => ! [P5: pi] :
% 3.16/1.61                  ( ( Rs
% 3.16/1.61                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 3.16/1.61                 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 3.16/1.61                   => ( A3 = B3 ) ) ) )
% 3.16/1.61         => ( ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 3.16/1.61                ( ( ( res @ X @ P2 )
% 3.16/1.61                  = ( res @ Y3 @ P ) )
% 3.16/1.61               => ( ( Rs
% 3.16/1.61                    = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 3.16/1.61                 => ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 3.16/1.61                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 3.16/1.61                     => ( ( Y3 != X4 )
% 3.16/1.61                       => ( ( fresh_name_pi @ X4 @ P )
% 3.16/1.61                         => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 3.16/1.61           => ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 3.16/1.61                  ( ( ( res @ X @ P2 )
% 3.16/1.61                    = ( res @ Y3 @ P ) )
% 3.16/1.61                 => ( ( Rs
% 3.16/1.61                      = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 3.16/1.61                   => ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.16/1.61                     => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_333_resCasesB,axiom,
% 3.16/1.61      ! [Y4: name,P2: pi,A: late_subject,X: name,YP: pi,F3: late_subject > pi > $o] :
% 3.16/1.61        ( ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ YP ) )
% 3.16/1.61       => ( ( X != Y4 )
% 3.16/1.61         => ( ( fresh_name_pi @ X @ P2 )
% 3.16/1.61           => ( ! [B3: name,P5: pi] :
% 3.16/1.61                  ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ B3 @ Y4 ) @ P5 ) )
% 3.16/1.61                 => ( ( B3 != Y4 )
% 3.16/1.61                   => ( ( A
% 3.16/1.61                        = ( late_BoundOutputS @ B3 ) )
% 3.16/1.61                     => ( F3 @ ( late_BoundOutputS @ B3 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P5 ) ) ) ) )
% 3.16/1.61             => ( ! [P5: pi] :
% 3.16/1.61                    ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
% 3.16/1.61                   => ( ( fresh_717452603ubject @ Y4 @ A )
% 3.16/1.61                     => ( F3 @ A @ ( res @ Y4 @ P5 ) ) ) )
% 3.16/1.61               => ( F3 @ A @ YP ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_334_simulation__def,axiom,
% 3.16/1.61      ( strong743114133lation
% 3.16/1.61      = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q3: pi] :
% 3.16/1.61            ( ! [A5: late_subject,X5: name,Q4: pi] :
% 3.16/1.61                ( ( ( late_transitions @ Q3 @ ( late_BoundR @ A5 @ X5 @ Q4 ) )
% 3.16/1.61                  & ( fresh_name_pi @ X5 @ P6 ) )
% 3.16/1.61               => ? [P7: pi] :
% 3.16/1.61                    ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X5 @ P7 ) )
% 3.16/1.61                    & ( strong2129052853vative @ P7 @ Q4 @ A5 @ X5 @ Rel2 ) ) )
% 3.16/1.61            & ! [Alpha3: late_freeRes,Q4: pi] :
% 3.16/1.61                ( ( late_transitions @ Q3 @ ( late_FreeR @ Alpha3 @ Q4 ) )
% 3.16/1.61               => ? [P7: pi] :
% 3.16/1.61                    ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 3.16/1.61                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q4 ) @ Rel2 ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_335_simCases,axiom,
% 3.16/1.61      ! [Q: pi,P2: pi,Rel: set_Pr1834926343_pi_pi] :
% 3.16/1.61        ( ! [A3: late_subject,Y3: name,Q5: pi] :
% 3.16/1.61            ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q5 ) )
% 3.16/1.61           => ( ( fresh_name_pi @ Y3 @ P2 )
% 3.16/1.61             => ? [P8: pi] :
% 3.16/1.61                  ( ( late_transitions @ P2 @ ( late_BoundR @ A3 @ Y3 @ P8 ) )
% 3.16/1.61                  & ( strong2129052853vative @ P8 @ Q5 @ A3 @ Y3 @ Rel ) ) ) )
% 3.16/1.61       => ( ! [Alpha2: late_freeRes,Q5: pi] :
% 3.16/1.61              ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q5 ) )
% 3.16/1.61             => ? [P8: pi] :
% 3.16/1.61                  ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P8 ) )
% 3.16/1.61                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q5 ) @ Rel ) ) )
% 3.16/1.61         => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_336_residual__Rep_Oinject_I2_J,axiom,
% 3.16/1.61      ! [X21: late_freeRes,X22: pi,Y21: late_freeRes,Y22: pi] :
% 3.16/1.61        ( ( ( late_r347633188eR_Rep @ X21 @ X22 )
% 3.16/1.61          = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 3.16/1.61        = ( ( X21 = Y21 )
% 3.16/1.61          & ( X22 = Y22 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_337_alphaInput,axiom,
% 3.16/1.61      ! [C2: name,P2: pi,A: name,X: name] :
% 3.16/1.61        ( ( fresh_name_pi @ C2 @ P2 )
% 3.16/1.61       => ( ( input @ A @ X @ P2 )
% 3.16/1.61          = ( input @ A @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_338_pi_Operm_I4_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 3.16/1.61        ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 3.16/1.61        = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_339_resTrans_I2_J,axiom,
% 3.16/1.61      ! [X: name,Y4: name,P2: pi,Rs: late_residual] :
% 3.16/1.61        ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y4 @ P2 ) ) @ Rs ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_340_pi_Odistinct_I53_J,axiom,
% 3.16/1.61      ! [Name1: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 3.16/1.61        ( ( input @ Name1 @ Name22 @ Pi )
% 3.16/1.61       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_341_pi_Odistinct_I57_J,axiom,
% 3.16/1.61      ! [Name1: name,Name22: name,Pi: pi,Name: name,Pi3: pi] :
% 3.16/1.61        ( ( input @ Name1 @ Name22 @ Pi )
% 3.16/1.61       != ( res @ Name @ Pi3 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_342_inputFreeTrans,axiom,
% 3.16/1.61      ! [A: name,X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 3.16/1.61        ~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_343_resInputFreeTrans,axiom,
% 3.16/1.61      ! [X: name,A: name,Y4: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 3.16/1.61        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_344_inputBoundOutputTrans,axiom,
% 3.16/1.61      ! [A: name,X: name,P2: pi,B: name,Y4: name,P4: pi] :
% 3.16/1.61        ~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y4 @ P4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_345_inputIneqTrans,axiom,
% 3.16/1.61      ! [A: name,X: name,P2: pi,B: late_subject,Y4: name,P4: pi] :
% 3.16/1.61        ( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ P4 ) )
% 3.16/1.61       => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_346_resInputBoundOutputTrans,axiom,
% 3.16/1.61      ! [X: name,A: name,Y4: name,P2: pi,B: name,Z2: name,P4: pi] :
% 3.16/1.61        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z2 @ P4 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_347_inputCases,axiom,
% 3.16/1.61      ! [A: name,X: name,P2: pi,B: late_subject,Y4: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 3.16/1.61        ( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ YP ) )
% 3.16/1.61       => ( ( Y4 != A )
% 3.16/1.61         => ( ( Y4 != X )
% 3.16/1.61           => ( ( fresh_name_pi @ Y4 @ P2 )
% 3.16/1.61             => ( ( ( B
% 3.16/1.61                    = ( late_InputS @ A ) )
% 3.16/1.61                 => ( ( YP
% 3.16/1.61                      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) )
% 3.16/1.61                   => ( Prop @ ( late_InputS @ A ) @ Y4 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) )
% 3.16/1.61               => ( Prop @ B @ Y4 @ YP ) ) ) ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_348_name__calc_I1_J,axiom,
% 3.16/1.61      ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 3.16/1.61        ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 3.16/1.61        = ( swap_name @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_349_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.16/1.61      ! [X1: name,Y1: name] :
% 3.16/1.61        ( ( ( late_InputS @ X1 )
% 3.16/1.61          = ( late_InputS @ Y1 ) )
% 3.16/1.61        = ( X1 = Y1 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_350_subject_Ofresh_I1_J,axiom,
% 3.16/1.61      ! [A: name,X1: name] :
% 3.16/1.61        ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 3.16/1.61        = ( fresh_name_name @ A @ X1 ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_351_subject_Operm_I1_J,axiom,
% 3.16/1.61      ! [Pi: list_P227219501e_name,X1: name] :
% 3.16/1.61        ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 3.16/1.61        = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(fact_352_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.16/1.61      ! [Name2: name,Name: name] :
% 3.16/1.61        ( ( late_InputS @ Name2 )
% 3.16/1.61       != ( late_BoundOutputS @ Name ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 3.16/1.61      ! [X: pi,Y4: pi] :
% 3.16/1.61        ( ( if_pi @ $false @ X @ Y4 )
% 3.16/1.61        = Y4 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 3.16/1.61      ! [X: pi,Y4: pi] :
% 3.16/1.61        ( ( if_pi @ $true @ X @ Y4 )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 3.16/1.61      ! [X: name,Y4: name] :
% 3.16/1.61        ( ( if_name @ $false @ X @ Y4 )
% 3.16/1.61        = Y4 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 3.16/1.61      ! [X: name,Y4: name] :
% 3.16/1.61        ( ( if_name @ $true @ X @ Y4 )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 3.16/1.61      ! [X: pi_Rep,Y4: pi_Rep] :
% 3.16/1.61        ( ( if_pi_Rep @ $false @ X @ Y4 )
% 3.16/1.61        = Y4 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 3.16/1.61      ! [X: pi_Rep,Y4: pi_Rep] :
% 3.16/1.61        ( ( if_pi_Rep @ $true @ X @ Y4 )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 3.16/1.61      ! [X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( if_Late_freeRes @ $false @ X @ Y4 )
% 3.16/1.61        = Y4 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 3.16/1.61      ! [X: late_freeRes,Y4: late_freeRes] :
% 3.16/1.61        ( ( if_Late_freeRes @ $true @ X @ Y4 )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 3.16/1.61      ! [P2: $o] :
% 3.16/1.61        ( ( P2 = $true )
% 3.16/1.61        | ( P2 = $false ) ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 3.16/1.61      ! [X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( if_Late_subject @ $false @ X @ Y4 )
% 3.16/1.61        = Y4 ) ).
% 3.16/1.61  
% 3.16/1.61  thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 3.16/1.61      ! [X: late_subject,Y4: late_subject] :
% 3.16/1.61        ( ( if_Late_subject @ $true @ X @ Y4 )
% 3.16/1.61        = X ) ).
% 3.16/1.61  
% 3.16/1.61  thf(conj_0,conjecture,
% 3.16/1.61      strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ).
% 3.16/1.62  ------------------------
% 3.16/1.65  % (19969)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19857 for (2999ds/183Mi)
% 3.16/1.65  % (19971)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_19857 for (2999ds/27Mi)
% 3.16/1.65  % (19972)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19857 for (2999ds/2Mi)
% 3.16/1.65  % (19974)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_19857 for (2999ds/275Mi)
% 3.16/1.66  % (19972)Instruction limit reached!
% 3.16/1.66  % (19972)------------------------------
% 3.16/1.66  % (19972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66  % (19972)Termination reason: Unknown
% 3.16/1.66  % (19972)Termination phase: shuffling
% 3.16/1.66  
% 3.16/1.66  % (19972)Memory used [KB]: 1535
% 3.16/1.66  % (19972)Time elapsed: 0.002 s
% 3.16/1.66  % (19972)Instructions burned: 2 (million)
% 3.16/1.66  % (19972)------------------------------
% 3.16/1.66  % (19972)------------------------------
% 3.16/1.66  % (19975)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19857 for (2999ds/18Mi)
% 3.16/1.66  % (19970)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_19857 for (2999ds/4Mi)
% 3.16/1.66  % (19973)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_19857 for (2999ds/2Mi)
% 3.16/1.66  % (19971)Instruction limit reached!
% 3.16/1.66  % (19971)------------------------------
% 3.16/1.66  % (19971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66  % (19971)Termination reason: Unknown
% 3.16/1.66  % (19971)Termination phase: Property scanning
% 3.16/1.66  
% 3.16/1.66  % (19971)Memory used [KB]: 2046
% 3.16/1.66  % (19971)Time elapsed: 0.010 s
% 3.16/1.66  % (19971)Instructions burned: 27 (million)
% 3.16/1.66  % (19971)------------------------------
% 3.16/1.66  % (19971)------------------------------
% 3.16/1.66  % (19973)Instruction limit reached!
% 3.16/1.66  % (19973)------------------------------
% 3.16/1.66  % (19973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66  % (19973)Termination reason: Unknown
% 3.16/1.66  % (19973)Termination phase: shuffling
% 3.16/1.66  
% 3.16/1.66  % (19973)Memory used [KB]: 1663
% 3.16/1.66  % (19973)Time elapsed: 0.004 s
% 3.16/1.66  % (19973)Instructions burned: 3 (million)
% 3.16/1.66  % (19973)------------------------------
% 3.16/1.66  % (19973)------------------------------
% 3.16/1.66  % (19976)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19857 for (2999ds/3Mi)
% 3.16/1.67  % (19970)Instruction limit reached!
% 3.16/1.67  % (19970)------------------------------
% 3.16/1.67  % (19970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67  % (19970)Termination reason: Unknown
% 3.16/1.67  % (19970)Termination phase: shuffling
% 3.16/1.67  
% 3.16/1.67  % (19970)Memory used [KB]: 1663
% 3.16/1.67  % (19970)Time elapsed: 0.005 s
% 3.16/1.67  % (19970)Instructions burned: 5 (million)
% 3.16/1.67  % (19970)------------------------------
% 3.16/1.67  % (19970)------------------------------
% 3.16/1.67  % (19976)Instruction limit reached!
% 3.16/1.67  % (19976)------------------------------
% 3.16/1.67  % (19976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67  % (19976)Termination reason: Unknown
% 3.16/1.67  % (19976)Termination phase: shuffling
% 3.16/1.67  
% 3.16/1.67  % (19976)Memory used [KB]: 1535
% 3.16/1.67  % (19976)Time elapsed: 0.002 s
% 3.16/1.67  % (19976)Instructions burned: 3 (million)
% 3.16/1.67  % (19976)------------------------------
% 3.16/1.67  % (19976)------------------------------
% 3.16/1.67  % (19975)Instruction limit reached!
% 3.16/1.67  % (19975)------------------------------
% 3.16/1.67  % (19975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67  % (19975)Termination reason: Unknown
% 3.16/1.67  % (19975)Termination phase: shuffling
% 3.16/1.67  
% 3.16/1.67  % (19975)Memory used [KB]: 1918
% 3.16/1.67  % (19975)Time elapsed: 0.010 s
% 3.16/1.67  % (19975)Instructions burned: 20 (million)
% 3.16/1.67  % (19975)------------------------------
% 3.16/1.67  % (19975)------------------------------
% 3.16/1.67  % (19977)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_19857 for (2999ds/37Mi)
% 3.16/1.68  % (19980)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_19857 for (2999ds/1041Mi)
% 3.16/1.68  % (19981)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19857 for (2999ds/7Mi)
% 3.16/1.68  % (19978)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_19857 for (2999ds/15Mi)
% 3.16/1.68  % (19979)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_19857 for (2999ds/3Mi)
% 3.16/1.68  % (19977)Instruction limit reached!
% 3.16/1.68  % (19977)------------------------------
% 3.16/1.68  % (19977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68  % (19977)Termination reason: Unknown
% 3.16/1.68  % (19977)Termination phase: shuffling
% 3.16/1.68  
% 3.16/1.68  % (19977)Memory used [KB]: 2302
% 3.16/1.68  % (19977)Time elapsed: 0.011 s
% 3.16/1.68  % (19977)Instructions burned: 37 (million)
% 3.16/1.68  % (19977)------------------------------
% 3.16/1.68  % (19977)------------------------------
% 3.16/1.68  % (19981)Instruction limit reached!
% 3.16/1.68  % (19981)------------------------------
% 3.16/1.68  % (19981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68  % (19981)Termination reason: Unknown
% 3.16/1.68  % (19981)Termination phase: shuffling
% 3.16/1.68  
% 3.16/1.68  % (19981)Memory used [KB]: 1791
% 3.16/1.68  % (19981)Time elapsed: 0.004 s
% 3.16/1.68  % (19981)Instructions burned: 8 (million)
% 3.16/1.68  % (19981)------------------------------
% 3.16/1.68  % (19981)------------------------------
% 3.16/1.68  % (19979)Instruction limit reached!
% 3.16/1.68  % (19979)------------------------------
% 3.16/1.68  % (19979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68  % (19979)Termination reason: Unknown
% 3.16/1.68  % (19979)Termination phase: shuffling
% 3.16/1.68  
% 3.16/1.68  % (19979)Memory used [KB]: 1663
% 3.16/1.68  % (19979)Time elapsed: 0.004 s
% 3.16/1.68  % (19979)Instructions burned: 4 (million)
% 3.16/1.68  % (19979)------------------------------
% 3.16/1.68  % (19979)------------------------------
% 3.16/1.69  % (19974)First to succeed.
% 3.16/1.69  % (19978)Instruction limit reached!
% 3.16/1.69  % (19978)------------------------------
% 3.16/1.69  % (19978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69  % (19982)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19857 for (2999ds/16Mi)
% 3.16/1.69  % (19978)Termination reason: Unknown
% 3.16/1.69  % (19978)Termination phase: shuffling
% 3.16/1.69  
% 3.16/1.69  % (19978)Memory used [KB]: 1918
% 3.16/1.69  % (19978)Time elapsed: 0.012 s
% 3.16/1.69  % (19978)Instructions burned: 16 (million)
% 3.16/1.69  % (19978)------------------------------
% 3.16/1.69  % (19978)------------------------------
% 3.16/1.69  % (19974)Refutation found. Thanks to Tanya!
% 3.16/1.69  % SZS status Theorem for DTF2THF_19857
% 3.16/1.69  % SZS output start Proof for DTF2THF_19857
% 3.16/1.69  thf(type_def_5, type, name: $tType).
% 3.16/1.69  thf(type_def_6, type, pi: $tType).
% 3.16/1.69  thf(type_def_8, type, pi_Rep: $tType).
% 3.16/1.69  thf(type_def_9, type, late_freeRes: $tType).
% 3.16/1.69  thf(type_def_10, type, late_subject: $tType).
% 3.16/1.69  thf(type_def_11, type, late_residual: $tType).
% 3.16/1.69  thf(type_def_12, type, late_residual_Rep: $tType).
% 3.16/1.69  thf(type_def_13, type, list_name: $tType).
% 3.16/1.69  thf(type_def_14, type, list_pi: $tType).
% 3.16/1.69  thf(type_def_15, type, list_pi_Rep: $tType).
% 3.16/1.69  thf(type_def_16, type, list_Late_freeRes: $tType).
% 3.16/1.69  thf(type_def_17, type, list_Late_subject: $tType).
% 3.16/1.69  thf(type_def_18, type, list_P227219501e_name: $tType).
% 3.16/1.69  thf(type_def_19, type, list_l1406151091e_name: $tType).
% 3.16/1.69  thf(type_def_20, type, produc367475239e_name: $tType).
% 3.16/1.69  thf(type_def_21, type, produc1141751126_pi_pi: $tType).
% 3.16/1.69  thf(type_def_22, type, list_P431515740_pi_pi: $tType).
% 3.16/1.69  thf(type_def_23, type, produc2008547984reeRes: $tType).
% 3.16/1.69  thf(type_def_24, type, produc865358760ubject: $tType).
% 3.16/1.69  thf(type_def_25, type, product_prod_pi_pi: $tType).
% 3.16/1.69  thf(type_def_26, type, produc2052722628s_name: $tType).
% 3.16/1.69  thf(type_def_27, type, produc992857746Res_pi: $tType).
% 3.16/1.69  thf(type_def_28, type, produc1357834675reeRes: $tType).
% 3.16/1.69  thf(type_def_29, type, produc214645451ubject: $tType).
% 3.16/1.69  thf(type_def_30, type, produc1998742700t_name: $tType).
% 3.16/1.69  thf(type_def_31, type, produc140253050ect_pi: $tType).
% 3.16/1.69  thf(type_def_32, type, produc355105483reeRes: $tType).
% 3.16/1.69  thf(type_def_33, type, produc1359399907ubject: $tType).
% 3.16/1.69  thf(type_def_34, type, late_freeRes_Rep: $tType).
% 3.16/1.69  thf(type_def_35, type, late_subject_Rep: $tType).
% 3.16/1.69  thf(type_def_36, type, produc1777919905pi_Rep: $tType).
% 3.16/1.69  thf(type_def_37, type, produc257012921pi_Rep: $tType).
% 3.16/1.69  thf(type_def_38, type, set_name: $tType).
% 3.16/1.69  thf(type_def_39, type, set_pi: $tType).
% 3.16/1.69  thf(type_def_40, type, set_pi_Rep: $tType).
% 3.16/1.69  thf(type_def_41, type, set_Late_freeRes: $tType).
% 3.16/1.69  thf(type_def_42, type, set_Late_subject: $tType).
% 3.16/1.69  thf(type_def_43, type, set_Pr1834926343_pi_pi: $tType).
% 3.16/1.69  thf(type_def_44, type, set_Pr443758855e_name: $tType).
% 3.16/1.69  thf(type_def_45, type, set_Pr1654044726_pi_pi: $tType).
% 3.16/1.69  thf(type_def_46, type, produc1872410278e_name: $tType).
% 3.16/1.69  thf(type_def_47, type, produc1212344719pi_Rep: $tType).
% 3.16/1.69  thf(type_def_48, type, produc890461031e_name: $tType).
% 3.16/1.69  thf(type_def_49, type, set_Pr1131282415pi_Rep: $tType).
% 3.16/1.69  thf(type_def_50, type, set_Pr1780909331reeRes: $tType).
% 3.16/1.69  thf(type_def_51, type, set_Pr806375235ubject: $tType).
% 3.16/1.69  thf(func_def_0, type, produc1872410278e_name: $tType).
% 3.16/1.69  thf(func_def_1, type, produc890461031e_name: $tType).
% 3.16/1.69  thf(func_def_2, type, list_P431515740_pi_pi: $tType).
% 3.16/1.69  thf(func_def_3, type, set_Pr1654044726_pi_pi: $tType).
% 3.16/1.69  thf(func_def_4, type, set_Pr806375235ubject: $tType).
% 3.16/1.69  thf(func_def_5, type, set_Pr1780909331reeRes: $tType).
% 3.16/1.69  thf(func_def_6, type, produc1141751126_pi_pi: $tType).
% 3.16/1.69  thf(func_def_7, type, list_l1406151091e_name: $tType).
% 3.16/1.69  thf(func_def_8, type, produc1359399907ubject: $tType).
% 3.16/1.69  thf(func_def_9, type, produc355105483reeRes: $tType).
% 3.16/1.69  thf(func_def_10, type, produc214645451ubject: $tType).
% 3.16/1.69  thf(func_def_11, type, produc1357834675reeRes: $tType).
% 3.16/1.69  thf(func_def_12, type, set_Pr1131282415pi_Rep: $tType).
% 3.16/1.69  thf(func_def_13, type, produc257012921pi_Rep: $tType).
% 3.16/1.69  thf(func_def_14, type, produc1777919905pi_Rep: $tType).
% 3.16/1.69  thf(func_def_15, type, list_P227219501e_name: $tType).
% 3.16/1.69  thf(func_def_16, type, set_Pr443758855e_name: $tType).
% 3.16/1.69  thf(func_def_17, type, produc1998742700t_name: $tType).
% 3.16/1.69  thf(func_def_18, type, produc2052722628s_name: $tType).
% 3.16/1.69  thf(func_def_19, type, produc865358760ubject: $tType).
% 3.16/1.69  thf(func_def_20, type, produc2008547984reeRes: $tType).
% 3.16/1.69  thf(func_def_21, type, produc140253050ect_pi: $tType).
% 3.16/1.69  thf(func_def_22, type, produc992857746Res_pi: $tType).
% 3.16/1.69  thf(func_def_23, type, set_Pr1834926343_pi_pi: $tType).
% 3.16/1.69  thf(func_def_24, type, produc1212344719pi_Rep: $tType).
% 3.16/1.69  thf(func_def_25, type, produc367475239e_name: $tType).
% 3.16/1.69  thf(func_def_26, type, product_prod_pi_pi: $tType).
% 3.16/1.69  thf(func_def_27, type, list_Late_subject: $tType).
% 3.16/1.69  thf(func_def_28, type, list_Late_freeRes: $tType).
% 3.16/1.69  thf(func_def_29, type, set_Late_subject: $tType).
% 3.16/1.69  thf(func_def_30, type, set_Late_freeRes: $tType).
% 3.16/1.69  thf(func_def_31, type, list_pi_Rep: $tType).
% 3.16/1.69  thf(func_def_32, type, late_residual_Rep: $tType).
% 3.16/1.69  thf(func_def_33, type, late_subject_Rep: $tType).
% 3.16/1.69  thf(func_def_34, type, late_freeRes_Rep: $tType).
% 3.16/1.69  thf(func_def_35, type, set_pi_Rep: $tType).
% 3.16/1.69  thf(func_def_36, type, list_name: $tType).
% 3.16/1.69  thf(func_def_37, type, set_name: $tType).
% 3.16/1.69  thf(func_def_38, type, list_pi: $tType).
% 3.16/1.69  thf(func_def_39, type, late_residual: $tType).
% 3.16/1.69  thf(func_def_40, type, late_subject: $tType).
% 3.16/1.69  thf(func_def_41, type, late_freeRes: $tType).
% 3.16/1.69  thf(func_def_42, type, set_pi: $tType).
% 3.16/1.69  thf(func_def_43, type, pi_Rep: $tType).
% 3.16/1.69  thf(func_def_44, type, name: $tType).
% 3.16/1.69  thf(func_def_45, type, pi: $tType).
% 3.16/1.69  thf(func_def_46, type, input: name > name > pi > pi).
% 3.16/1.69  thf(func_def_47, type, res: name > pi > pi).
% 3.16/1.69  thf(func_def_48, type, sum: pi > pi > pi).
% 3.16/1.69  thf(func_def_49, type, if_name: $o > name > name > name).
% 3.16/1.69  thf(func_def_50, type, if_pi: $o > pi > pi > pi).
% 3.16/1.69  thf(func_def_51, type, if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep).
% 3.16/1.69  thf(func_def_52, type, if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes).
% 3.16/1.69  thf(func_def_53, type, if_Late_subject: $o > late_subject > late_subject > late_subject).
% 3.16/1.69  thf(func_def_54, type, late_OutputR: name > name > late_freeRes).
% 3.16/1.69  thf(func_def_55, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.16/1.69  thf(func_def_56, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.16/1.69  thf(func_def_57, type, late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep).
% 3.16/1.69  thf(func_def_58, type, late_BoundOutputS: name > late_subject).
% 3.16/1.69  thf(func_def_59, type, late_InputS: name > late_subject).
% 3.16/1.69  thf(func_def_60, type, late_transitions: pi > late_residual > $o).
% 3.16/1.69  thf(func_def_61, type, cons_name: name > list_name > list_name).
% 3.16/1.69  thf(func_def_62, type, cons_pi: pi > list_pi > list_pi).
% 3.16/1.69  thf(func_def_63, type, cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep).
% 3.16/1.69  thf(func_def_64, type, cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes).
% 3.16/1.69  thf(func_def_65, type, cons_Late_subject: late_subject > list_Late_subject > list_Late_subject).
% 3.16/1.69  thf(func_def_66, type, cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name).
% 3.16/1.69  thf(func_def_67, type, cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name).
% 3.16/1.69  thf(func_def_68, type, cons_P749510156_pi_pi: produc1141751126_pi_pi > list_P431515740_pi_pi > list_P431515740_pi_pi).
% 3.16/1.69  thf(func_def_69, type, nil_li29751603e_name: list_l1406151091e_name).
% 3.16/1.69  thf(func_def_70, type, nil_Pr743626285e_name: list_P227219501e_name).
% 3.16/1.69  thf(func_def_71, type, fresh_name_name: name > name > $o).
% 3.16/1.69  thf(func_def_72, type, fresh_name_pi: name > pi > $o).
% 3.16/1.69  thf(func_def_73, type, fresh_name_pi_Rep: name > pi_Rep > $o).
% 3.16/1.69  thf(func_def_74, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 3.16/1.69  thf(func_def_75, type, fresh_81631222sidual: name > late_residual > $o).
% 3.16/1.69  thf(func_def_76, type, fresh_717452603ubject: name > late_subject > $o).
% 3.16/1.69  thf(func_def_77, type, fresh_name_list_name: name > list_name > $o).
% 3.16/1.69  thf(func_def_78, type, fresh_name_list_pi: name > list_pi > $o).
% 3.16/1.69  thf(func_def_79, type, fresh_1981651763reeRes: name > list_Late_freeRes > $o).
% 3.16/1.69  thf(func_def_80, type, fresh_838462539ubject: name > list_Late_subject > $o).
% 3.16/1.69  thf(func_def_81, type, fresh_922791155e_name: name > list_P227219501e_name > $o).
% 3.16/1.69  thf(func_def_82, type, fresh_1958133282_pi_pi: name > list_P431515740_pi_pi > $o).
% 3.16/1.69  thf(func_def_83, type, fresh_441084397e_name: name > produc367475239e_name > $o).
% 3.16/1.69  thf(func_def_84, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 3.16/1.69  thf(func_def_85, type, fresh_820177506ubject: name > produc865358760ubject > $o).
% 3.16/1.69  thf(func_def_86, type, fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o).
% 3.16/1.69  thf(func_def_87, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 3.16/1.69  thf(func_def_88, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 3.16/1.69  thf(func_def_89, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 3.16/1.69  thf(func_def_90, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 3.16/1.69  thf(func_def_91, type, fresh_1498103185ubject: name > produc214645451ubject > $o).
% 3.16/1.69  thf(func_def_92, type, fresh_1953561446t_name: name > produc1998742700t_name > $o).
% 3.16/1.69  thf(func_def_93, type, fresh_994896692ect_pi: name > produc140253050ect_pi > $o).
% 3.16/1.69  thf(func_def_94, type, fresh_1638563217reeRes: name > produc355105483reeRes > $o).
% 3.16/1.69  thf(func_def_95, type, fresh_495373993ubject: name > produc1359399907ubject > $o).
% 3.16/1.69  thf(func_def_96, type, perm_n382765978reeRes: list_P227219501e_name > (name > late_freeRes) > name > late_freeRes).
% 3.16/1.69  thf(func_def_97, type, perm_n1387060402ubject: list_P227219501e_name > (name > late_subject) > name > late_subject).
% 3.16/1.69  thf(func_def_98, type, perm_n1333244520reeRes: list_P227219501e_name > (pi > late_freeRes) > pi > late_freeRes).
% 3.16/1.69  thf(func_def_99, type, perm_n190055296ubject: list_P227219501e_name > (pi > late_subject) > pi > late_subject).
% 3.16/1.69  thf(func_def_100, type, perm_n1841560599reeRes: list_P227219501e_name > (pi_Rep > late_freeRes) > pi_Rep > late_freeRes).
% 3.16/1.69  thf(func_def_101, type, perm_n698371375ubject: list_P227219501e_name > (pi_Rep > late_subject) > pi_Rep > late_subject).
% 3.16/1.69  thf(func_def_102, type, perm_n1446290985reeRes: list_P227219501e_name > (late_freeRes > late_freeRes) > late_freeRes > late_freeRes).
% 3.16/1.69  thf(func_def_103, type, perm_n303101761ubject: list_P227219501e_name > (late_freeRes > late_subject) > late_freeRes > late_subject).
% 3.16/1.69  thf(func_def_104, type, perm_n443561793reeRes: list_P227219501e_name > (late_subject > late_freeRes) > late_subject > late_freeRes).
% 3.16/1.69  thf(func_def_105, type, perm_n1447856217ubject: list_P227219501e_name > (late_subject > late_subject) > late_subject > late_subject).
% 3.16/1.69  thf(func_def_106, type, perm_name_o: list_P227219501e_name > $o > $o).
% 3.16/1.69  thf(func_def_107, type, perm_name_name: list_P227219501e_name > name > name).
% 3.16/1.69  thf(func_def_108, type, perm_name_pi: list_P227219501e_name > pi > pi).
% 3.16/1.69  thf(func_def_109, type, perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep).
% 3.16/1.69  thf(func_def_110, type, perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes).
% 3.16/1.69  thf(func_def_111, type, perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep).
% 3.16/1.69  thf(func_def_112, type, perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual).
% 3.16/1.69  thf(func_def_113, type, perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep).
% 3.16/1.69  thf(func_def_114, type, perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject).
% 3.16/1.69  thf(func_def_115, type, perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep).
% 3.16/1.69  thf(func_def_116, type, perm_name_list_name: list_P227219501e_name > list_name > list_name).
% 3.16/1.69  thf(func_def_117, type, perm_name_list_pi: list_P227219501e_name > list_pi > list_pi).
% 3.16/1.69  thf(func_def_118, type, perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep).
% 3.16/1.69  thf(func_def_119, type, perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes).
% 3.16/1.69  thf(func_def_120, type, perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject).
% 3.16/1.69  thf(func_def_121, type, perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name).
% 3.16/1.69  thf(func_def_122, type, perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi).
% 3.16/1.69  thf(func_def_123, type, perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi).
% 3.16/1.69  thf(func_def_124, type, perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name).
% 3.16/1.69  thf(func_def_125, type, perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi).
% 3.16/1.69  thf(func_def_126, type, perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep).
% 3.16/1.69  thf(func_def_127, type, perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes).
% 3.16/1.69  thf(func_def_128, type, perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject).
% 3.16/1.69  thf(func_def_129, type, perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name).
% 3.16/1.69  thf(func_def_130, type, perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi).
% 3.16/1.69  thf(func_def_131, type, perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep).
% 3.16/1.69  thf(func_def_132, type, perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes).
% 3.16/1.69  thf(func_def_133, type, perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject).
% 3.16/1.69  thf(func_def_134, type, perm_name_set_name: list_P227219501e_name > set_name > set_name).
% 3.16/1.69  thf(func_def_135, type, perm_name_set_pi: list_P227219501e_name > set_pi > set_pi).
% 3.16/1.69  thf(func_def_136, type, perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep).
% 3.16/1.69  thf(func_def_137, type, perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes).
% 3.16/1.69  thf(func_def_138, type, perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject).
% 3.16/1.69  thf(func_def_139, type, perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_140, type, swap_name: produc367475239e_name > name > name).
% 3.16/1.69  thf(func_def_141, type, ord_le793202855e_name: set_Pr443758855e_name > set_Pr443758855e_name > $o).
% 3.16/1.69  thf(func_def_142, type, ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o).
% 3.16/1.69  thf(func_def_143, type, ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.16/1.69  thf(func_def_144, type, produc1069608854e_name: (produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > produc1872410278e_name).
% 3.16/1.69  thf(func_def_145, type, produc1570949143e_name: name > name > produc367475239e_name).
% 3.16/1.69  thf(func_def_146, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 3.16/1.69  thf(func_def_147, type, produc607574050ubject: name > late_subject > produc865358760ubject).
% 3.16/1.69  thf(func_def_148, type, produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi).
% 3.16/1.69  thf(func_def_149, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 3.16/1.69  thf(func_def_150, type, produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep).
% 3.16/1.69  thf(func_def_151, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 3.16/1.69  thf(func_def_152, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 3.16/1.69  thf(func_def_153, type, produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep).
% 3.16/1.69  thf(func_def_154, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 3.16/1.69  thf(func_def_155, type, produc320590723ubject: late_freeRes > late_subject > produc214645451ubject).
% 3.16/1.69  thf(func_def_156, type, produc1647375838t_name: late_subject > name > produc1998742700t_name).
% 3.16/1.69  thf(func_def_157, type, produc324947500ect_pi: late_subject > pi > produc140253050ect_pi).
% 3.16/1.69  thf(func_def_158, type, produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep).
% 3.16/1.69  thf(func_def_159, type, produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes).
% 3.16/1.69  thf(func_def_160, type, produc1465345179ubject: late_subject > late_subject > produc1359399907ubject).
% 3.16/1.69  thf(func_def_161, type, produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name).
% 3.16/1.69  thf(func_def_162, type, eqvt_name: set_Pr443758855e_name > $o).
% 3.16/1.69  thf(func_def_163, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 3.16/1.69  thf(func_def_164, type, eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o).
% 3.16/1.69  thf(func_def_165, type, eqvt_Late_freeRes: set_Pr1780909331reeRes > $o).
% 3.16/1.69  thf(func_def_166, type, eqvt_Late_subject: set_Pr806375235ubject > $o).
% 3.16/1.69  thf(func_def_167, type, id_name: set_Pr443758855e_name).
% 3.16/1.69  thf(func_def_168, type, id_pi: set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_169, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_170, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 3.16/1.69  thf(func_def_171, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 3.16/1.69  thf(func_def_172, type, member_name: name > set_name > $o).
% 3.16/1.69  thf(func_def_173, type, member_pi: pi > set_pi > $o).
% 3.16/1.69  thf(func_def_174, type, member_pi_Rep: pi_Rep > set_pi_Rep > $o).
% 3.16/1.69  thf(func_def_175, type, member_Late_freeRes: late_freeRes > set_Late_freeRes > $o).
% 3.16/1.69  thf(func_def_176, type, member_Late_subject: late_subject > set_Late_subject > $o).
% 3.16/1.69  thf(func_def_177, type, member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o).
% 3.16/1.69  thf(func_def_178, type, member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o).
% 3.16/1.69  thf(func_def_179, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.16/1.69  thf(func_def_180, type, member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o).
% 3.16/1.69  thf(func_def_181, type, member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o).
% 3.16/1.69  thf(func_def_182, type, member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o).
% 3.16/1.69  thf(func_def_183, type, p: pi).
% 3.16/1.69  thf(func_def_184, type, pq: pi).
% 3.16/1.69  thf(func_def_185, type, p2: pi).
% 3.16/1.69  thf(func_def_186, type, q: pi).
% 3.16/1.69  thf(func_def_187, type, rel: set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_188, type, a: late_subject).
% 3.16/1.69  thf(func_def_189, type, aa: name).
% 3.16/1.69  thf(func_def_190, type, x: name).
% 3.16/1.69  thf(func_def_191, type, y: name).
% 3.16/1.69  thf(func_def_209, type, sP0: pi > (late_subject > pi > $o) > name > name > late_subject > $o).
% 3.16/1.69  thf(func_def_210, type, sP1: late_subject > name > pi > name > pi > $o).
% 3.16/1.69  thf(func_def_211, type, sP2: name > pi > late_residual > $o).
% 3.16/1.69  thf(func_def_212, type, sP3: name > pi > late_residual > $o).
% 3.16/1.69  thf(func_def_213, type, sK4: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_214, type, sK5: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_215, type, sK6: pi > (late_subject > pi > $o) > name > name > late_subject > name).
% 3.16/1.69  thf(func_def_216, type, sK7: pi > (late_subject > pi > $o) > name > name > late_subject > pi).
% 3.16/1.69  thf(func_def_217, type, sK8: pi > (late_subject > pi > $o) > name > late_subject > name > pi).
% 3.16/1.69  thf(func_def_218, type, sK9: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_219, type, sK10: (list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_220, type, sK11: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_221, type, sK12: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_222, type, sK13: (list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_223, type, sK14: (produc367475239e_name > $o) > name).
% 3.16/1.69  thf(func_def_224, type, sK15: (produc367475239e_name > $o) > name).
% 3.16/1.69  thf(func_def_225, type, sK16: list_P227219501e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_226, type, sK17: list_P227219501e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_227, type, sK18: list_P227219501e_name > list_P227219501e_name).
% 3.16/1.69  thf(func_def_228, type, sK19: list_P227219501e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_229, type, sK20: pi > late_freeRes > (pi > $o) > name > pi).
% 3.16/1.69  thf(func_def_230, type, sK21: product_prod_pi_pi > pi).
% 3.16/1.69  thf(func_def_231, type, sK22: product_prod_pi_pi > pi).
% 3.16/1.69  thf(func_def_232, type, sK23: (list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_233, type, sK24: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_234, type, sK25: product_prod_pi_pi > pi).
% 3.16/1.69  thf(func_def_235, type, sK26: produc367475239e_name > name).
% 3.16/1.69  thf(func_def_236, type, sK27: produc367475239e_name > name).
% 3.16/1.69  thf(func_def_237, type, sK28: list_P227219501e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_238, type, sK29: list_P227219501e_name > list_P227219501e_name).
% 3.16/1.69  thf(func_def_239, type, sK30: late_subject > name).
% 3.16/1.69  thf(func_def_240, type, sK31: (product_prod_pi_pi > $o) > pi).
% 3.16/1.69  thf(func_def_241, type, sK32: (product_prod_pi_pi > $o) > pi).
% 3.16/1.69  thf(func_def_242, type, sK33: product_prod_pi_pi > pi).
% 3.16/1.69  thf(func_def_243, type, sK34: product_prod_pi_pi > pi).
% 3.16/1.69  thf(func_def_244, type, sK35: late_subject > name > pi > name > pi > pi).
% 3.16/1.69  thf(func_def_245, type, sK36: late_subject > name > pi > name > pi > name).
% 3.16/1.69  thf(func_def_246, type, sK37: late_subject > name > pi > name > pi > late_subject).
% 3.16/1.69  thf(func_def_247, type, sK38: late_subject > name > pi > name > pi > pi).
% 3.16/1.69  thf(func_def_248, type, sK39: late_subject > name > pi > name > pi > name).
% 3.16/1.69  thf(func_def_249, type, sK40: name > pi > late_subject > pi > name > name).
% 3.16/1.69  thf(func_def_250, type, sK41: name > pi > late_subject > pi > name > name).
% 3.16/1.69  thf(func_def_251, type, sK42: name > pi > late_subject > pi > name > pi).
% 3.16/1.69  thf(func_def_252, type, sK43: name > pi > late_subject > pi > name > pi).
% 3.16/1.69  thf(func_def_253, type, sK44: name > pi > pi > late_subject > set_Pr1834926343_pi_pi > pi).
% 3.16/1.69  thf(func_def_254, type, sK45: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_255, type, sK46: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_256, type, sK47: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_257, type, sK48: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_258, type, sK49: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_259, type, sK50: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_260, type, sK51: produc367475239e_name > name).
% 3.16/1.69  thf(func_def_261, type, sK52: produc367475239e_name > name).
% 3.16/1.69  thf(func_def_262, type, sK53: (produc367475239e_name > $o) > name).
% 3.16/1.69  thf(func_def_263, type, sK54: (produc367475239e_name > $o) > name).
% 3.16/1.69  thf(func_def_264, type, sK55: name > late_freeRes > pi > pi > name).
% 3.16/1.69  thf(func_def_265, type, sK56: name > late_freeRes > pi > pi > late_freeRes).
% 3.16/1.69  thf(func_def_266, type, sK57: name > late_freeRes > pi > pi > pi).
% 3.16/1.69  thf(func_def_267, type, sK58: name > late_freeRes > pi > pi > pi).
% 3.16/1.69  thf(func_def_268, type, sK59: pi > name).
% 3.16/1.69  thf(func_def_269, type, sK60: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name > $o).
% 3.16/1.69  thf(func_def_270, type, sK61: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_271, type, sK62: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_272, type, sK63: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name > $o).
% 3.16/1.69  thf(func_def_273, type, sK64: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_274, type, sK65: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_275, type, sK66: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_276, type, sK67: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_277, type, sK68: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_278, type, sK69: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_279, type, sK70: pi > pi > set_Pr1834926343_pi_pi > late_subject).
% 3.16/1.69  thf(func_def_280, type, sK71: pi > pi > set_Pr1834926343_pi_pi > name).
% 3.16/1.69  thf(func_def_281, type, sK72: pi > pi > set_Pr1834926343_pi_pi > pi).
% 3.16/1.69  thf(func_def_282, type, sK73: pi > pi > set_Pr1834926343_pi_pi > pi).
% 3.16/1.69  thf(func_def_283, type, sK74: pi > pi > set_Pr1834926343_pi_pi > late_freeRes).
% 3.16/1.69  thf(func_def_284, type, sK75: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_285, type, sK76: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_286, type, sK77: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_287, type, sK78: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_288, type, sK79: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_289, type, sK80: (list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_290, type, sK81: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_291, type, sK82: (list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_292, type, sK83: name > name).
% 3.16/1.69  thf(func_def_293, type, sK84: (late_residual > $o) > name).
% 3.16/1.69  thf(func_def_294, type, sK85: (late_residual > $o) > late_subject).
% 3.16/1.69  thf(func_def_295, type, sK86: (late_residual > $o) > pi).
% 3.16/1.69  thf(func_def_296, type, sK87: (late_residual > $o) > late_freeRes).
% 3.16/1.69  thf(func_def_297, type, sK88: (late_residual > $o) > pi).
% 3.16/1.69  thf(func_def_298, type, sK89: set_Pr1834926343_pi_pi > late_freeRes > pi > pi > pi).
% 3.16/1.69  thf(func_def_299, type, sK90: (product_prod_pi_pi > $o) > pi).
% 3.16/1.69  thf(func_def_300, type, sK91: (product_prod_pi_pi > $o) > pi).
% 3.16/1.69  thf(func_def_301, type, sK92: ((produc367475239e_name > produc367475239e_name) > list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_302, type, sK93: ((produc367475239e_name > produc367475239e_name) > list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_303, type, sK94: ((produc367475239e_name > produc367475239e_name) > list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_304, type, sK95: ((produc367475239e_name > produc367475239e_name) > list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_305, type, sK96: ((produc367475239e_name > produc367475239e_name) > list_P227219501e_name > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_306, type, sK97: ((produc367475239e_name > produc367475239e_name) > list_P227219501e_name > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_307, type, sK98: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > product_prod_pi_pi).
% 3.16/1.69  thf(func_def_308, type, sK99: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name > $o).
% 3.16/1.69  thf(func_def_309, type, sK100: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_310, type, sK101: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_311, type, sK102: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_312, type, sK103: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name > $o).
% 3.16/1.69  thf(func_def_313, type, sK104: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_314, type, sK105: ((produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > $o) > produc367475239e_name > produc367475239e_name > $o).
% 3.16/1.69  thf(func_def_315, type, sK106: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi).
% 3.16/1.69  thf(func_def_316, type, sK107: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi).
% 3.16/1.69  thf(func_def_317, type, sK108: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_318, type, sK109: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_319, type, sK110: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_320, type, sK111: (list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_321, type, sK112: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_322, type, sK113: list_P227219501e_name > produc367475239e_name).
% 3.16/1.69  thf(func_def_323, type, sK114: list_P227219501e_name > list_P227219501e_name).
% 3.16/1.69  thf(func_def_324, type, sK115: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_325, type, sK116: (list_P227219501e_name > $o) > list_P227219501e_name).
% 3.16/1.69  thf(func_def_326, type, sK117: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_327, type, sK118: (list_P227219501e_name > $o) > produc367475239e_name).
% 3.16/1.69  thf(func_def_328, type, sK119: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_329, type, sK120: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.16/1.69  thf(func_def_330, type, sK121: name > pi > late_residual > pi).
% 3.16/1.69  thf(func_def_331, type, sK122: name > pi > late_residual > name).
% 3.16/1.69  thf(func_def_332, type, sK123: name > pi > late_residual > name).
% 3.16/1.69  thf(func_def_333, type, sK124: name > pi > late_residual > pi).
% 3.16/1.69  thf(func_def_334, type, sK125: name > pi > late_residual > name).
% 3.16/1.69  thf(func_def_335, type, sK126: name > pi > late_residual > pi).
% 3.16/1.69  thf(func_def_336, type, sK127: name > pi > late_residual > name).
% 3.16/1.69  thf(func_def_337, type, sK128: name > pi > late_residual > pi).
% 3.16/1.69  thf(func_def_338, type, sK129: name > pi > late_residual > late_subject).
% 3.16/1.69  thf(func_def_339, type, sK130: pi > late_residual > name > late_freeRes).
% 3.16/1.69  thf(func_def_340, type, sK131: pi > late_residual > name > pi).
% 3.16/1.69  thf(func_def_341, type, sK132: pi > late_residual > name > pi).
% 3.16/1.69  thf(func_def_342, type, sK133: pi > late_residual > name > name).
% 3.16/1.69  thf(func_def_344, type, ph135: !>[X0: $tType]:(X0)).
% 3.16/1.69  thf(f1490,plain,(
% 3.16/1.69    $false),
% 3.16/1.69    inference(subsumption_resolution,[status(thm)],[f1488,f1426])).
% 3.16/1.69  thf(f1426,plain,(
% 3.16/1.69    ((ord_le630093991_pi_pi @ id_pi @ rel) = $true)),
% 3.16/1.69    inference(cnf_transformation,[status(thm)],[f557])).
% 3.16/1.69  thf(f557,plain,(
% 3.16/1.69    ((ord_le630093991_pi_pi @ id_pi @ rel) = $true)),
% 3.16/1.69    inference(fool_elimination,[status(thm)],[f556])).
% 3.16/1.69  thf(f556,plain,(
% 3.16/1.69    (ord_le630093991_pi_pi @ id_pi @ rel)),
% 3.16/1.69    inference(rectify,[status(thm)],[f1])).
% 3.16/1.69  thf(f1,axiom,(
% 3.16/1.69    (ord_le630093991_pi_pi @ id_pi @ rel)),
% 3.16/1.69    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',fact_0_Id)).
% 3.16/1.69  thf(f1488,plain,(
% 3.16/1.69    ((ord_le630093991_pi_pi @ id_pi @ rel) != $true)),
% 3.16/1.69    inference(trivial_inequality_removal,[status(thm)],[f1486])).
% 3.16/1.69  thf(f1486,plain,(
% 3.16/1.69    ((ord_le630093991_pi_pi @ id_pi @ rel) != $true) | ($true != $true)),
% 3.16/1.69    inference(superposition,[status(thm)],[f1483,f1319])).
% 3.16/1.69  thf(f1319,plain,(
% 3.16/1.69    ( ! [X2 : name,X3 : late_subject,X0 : pi,X1 : set_Pr1834926343_pi_pi] : (((strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1) = $true) | ((ord_le630093991_pi_pi @ id_pi @ X1) != $true)) )),
% 3.16/1.69    inference(cnf_transformation,[status(thm)],[f1010])).
% 3.16/1.69  thf(f1010,plain,(
% 3.16/1.69    ! [X0 : pi,X1 : set_Pr1834926343_pi_pi,X2 : name,X3 : late_subject] : (((ord_le630093991_pi_pi @ id_pi @ X1) != $true) | ((strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1) = $true))),
% 3.16/1.69    inference(ennf_transformation,[status(thm)],[f471])).
% 3.16/1.69  thf(f471,plain,(
% 3.16/1.69    ! [X0 : pi,X1 : set_Pr1834926343_pi_pi,X2 : name,X3 : late_subject] : (((ord_le630093991_pi_pi @ id_pi @ X1) = $true) => ((strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1) = $true))),
% 3.16/1.69    inference(fool_elimination,[status(thm)],[f470])).
% 3.16/1.69  thf(f470,plain,(
% 3.16/1.69    ! [X0 : pi,X1 : set_Pr1834926343_pi_pi,X2 : name,X3 : late_subject] : ((ord_le630093991_pi_pi @ id_pi @ X1) => (strong2129052853vative @ X0 @ X0 @ X3 @ X2 @ X1))),
% 3.16/1.69    inference(rectify,[status(thm)],[f195])).
% 3.16/1.69  thf(f195,axiom,(
% 3.16/1.69    ! [X27 : pi,X56 : set_Pr1834926343_pi_pi,X2 : name,X0 : late_subject] : ((ord_le630093991_pi_pi @ id_pi @ X56) => (strong2129052853vative @ X27 @ X27 @ X0 @ X2 @ X56))),
% 3.16/1.69    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',fact_194_derivativeReflexive)).
% 3.16/1.69  thf(f1483,plain,(
% 3.16/1.69    ($true != (strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ x @ y) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ x @ y) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel))),
% 3.16/1.69    inference(forward_demodulation,[status(thm)],[f1228,f1236])).
% 3.16/1.69  thf(f1236,plain,(
% 3.16/1.69    ( ! [X2 : name,X0 : pi,X1 : name] : (((perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ X2 @ X1) @ nil_Pr743626285e_name) @ X0) = (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ X1 @ X2) @ nil_Pr743626285e_name) @ X0))) )),
% 3.16/1.69    inference(cnf_transformation,[status(thm)],[f828])).
% 3.16/1.69  thf(f828,plain,(
% 3.16/1.69    ! [X0 : pi,X1 : name,X2 : name] : ((perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ X2 @ X1) @ nil_Pr743626285e_name) @ X0) = (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ X1 @ X2) @ nil_Pr743626285e_name) @ X0))),
% 3.16/1.69    inference(rectify,[status(thm)],[f20])).
% 3.16/1.69  thf(f20,axiom,(
% 3.16/1.69    ! [X2 : pi,X1 : name,X0 : name] : ((perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ X0 @ X1) @ nil_Pr743626285e_name) @ X2) = (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ X1 @ X0) @ nil_Pr743626285e_name) @ X2))),
% 3.16/1.69    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',fact_19_name__swap)).
% 3.16/1.69  thf(f1228,plain,(
% 3.16/1.69    ((strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel) != $true)),
% 3.16/1.69    inference(cnf_transformation,[status(thm)],[f814])).
% 3.16/1.69  thf(f814,plain,(
% 3.16/1.69    ((strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel) != $true)),
% 3.16/1.69    inference(flattening,[status(thm)],[f443])).
% 3.16/1.69  thf(f443,plain,(
% 3.16/1.69    ~((strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel) = $true)),
% 3.16/1.69    inference(fool_elimination,[status(thm)],[f442])).
% 3.16/1.69  thf(f442,plain,(
% 3.16/1.69    ~(strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel)),
% 3.16/1.69    inference(rectify,[status(thm)],[f366])).
% 3.16/1.69  thf(f366,negated_conjecture,(
% 3.16/1.69    ~(strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel)),
% 3.16/1.69    inference(negated_conjecture,[status(cth)],[f365])).
% 3.16/1.69  thf(f365,conjecture,(
% 3.16/1.69    (strong2129052853vative @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ y @ x) @ nil_Pr743626285e_name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel)),
% 3.16/1.69    file('/export/starexec/sandbox/tmp/tmp.5lwgaxu5zL/DTF2THF_19857.p',conj_0)).
% 3.16/1.69  % SZS output end Proof for DTF2THF_19857
% 3.16/1.69  % (19974)------------------------------
% 3.16/1.69  % (19974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69  % (19974)Termination reason: Refutation
% 3.16/1.69  
% 3.16/1.69  % (19974)Memory used [KB]: 7675
% 3.16/1.69  % (19974)Time elapsed: 0.038 s
% 3.16/1.69  % (19974)Instructions burned: 120 (million)
% 3.16/1.69  % (19974)------------------------------
% 3.16/1.69  % (19974)------------------------------
% 3.16/1.69  % (19968)Success in time 0.067 s
%------------------------------------------------------------------------------