TSTP Solution File: ITP190^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP190^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Mon May 20 22:55:50 EDT 2024

% Result   : Theorem 7.74s 1.50s
% Output   : Refutation 7.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      : 1412
% Syntax   : Number of formulae    : 3776 ( 935 unt; 457 typ;   0 def)
%            Number of atoms       : 50004 (5827 equ;   0 cnn)
%            Maximal formula atoms :   16 (  15 avg)
%            Number of connectives : 8919 (3284   ~;3400   |; 620   &;   0   @)
%                                         ( 585 <=>;1030  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Number of types       :   41 (  40 usr)
%            Number of type conns  : 1787 (1786   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  969 ( 966 usr; 603 con; 0-6 aty)
%            Number of variables   : 9067 (  12   ^8138   !; 903   ?;9067   :)
%                                         (  14  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_8,type,
    list_P227219501e_name: $tType ).

thf(type_def_9,type,
    produc367475239e_name: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

thf(type_def_22,type,
    list_l1406151091e_name: $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,
    produc1872410278e_name: $tType ).

thf(type_def_45,type,
    produc890461031e_name: $tType ).

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

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

thf(func_def_2,type,
    list_l1406151091e_name: $tType ).

thf(func_def_3,type,
    produc1359399907ubject: $tType ).

thf(func_def_4,type,
    produc355105483reeRes: $tType ).

thf(func_def_5,type,
    produc214645451ubject: $tType ).

thf(func_def_6,type,
    produc1357834675reeRes: $tType ).

thf(func_def_7,type,
    produc257012921pi_Rep: $tType ).

thf(func_def_8,type,
    produc1777919905pi_Rep: $tType ).

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

thf(func_def_10,type,
    list_P227219501e_name: $tType ).

thf(func_def_11,type,
    produc1998742700t_name: $tType ).

thf(func_def_12,type,
    produc2052722628s_name: $tType ).

thf(func_def_13,type,
    produc865358760ubject: $tType ).

thf(func_def_14,type,
    produc2008547984reeRes: $tType ).

thf(func_def_15,type,
    produc140253050ect_pi: $tType ).

thf(func_def_16,type,
    produc992857746Res_pi: $tType ).

thf(func_def_17,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(func_def_18,type,
    produc367475239e_name: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_40,type,
    input: name > name > pi > pi ).

thf(func_def_41,type,
    par: pi > pi > pi ).

thf(func_def_42,type,
    res: name > pi > pi ).

thf(func_def_43,type,
    name_prm_name: list_P227219501e_name > name > name ).

thf(func_def_44,type,
    swap_name: produc367475239e_name > name > name ).

thf(func_def_45,type,
    subs: pi > name > name > pi ).

thf(func_def_46,type,
    if_name: $o > name > name > name ).

thf(func_def_47,type,
    if_pi: $o > pi > pi > pi ).

thf(func_def_48,type,
    if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).

thf(func_def_49,type,
    if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).

thf(func_def_50,type,
    if_Late_subject: $o > late_subject > late_subject > late_subject ).

thf(func_def_51,type,
    late_OutputR: name > name > late_freeRes ).

thf(func_def_52,type,
    late_TauR: late_freeRes ).

thf(func_def_53,type,
    late_BoundR: late_subject > name > pi > late_residual ).

thf(func_def_54,type,
    late_FreeR: late_freeRes > pi > late_residual ).

thf(func_def_55,type,
    late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).

thf(func_def_56,type,
    late_BoundOutputS: name > late_subject ).

thf(func_def_57,type,
    late_InputS: name > late_subject ).

thf(func_def_58,type,
    late_transitions: pi > late_residual > $o ).

thf(func_def_59,type,
    cons_name_noption_pi: ( name > noption_pi ) > list_name_noption_pi > list_name_noption_pi ).

thf(func_def_60,type,
    cons_name: name > list_name > list_name ).

thf(func_def_61,type,
    cons_pi: pi > list_pi > list_pi ).

thf(func_def_62,type,
    cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep ).

thf(func_def_63,type,
    cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes ).

thf(func_def_64,type,
    cons_Late_subject: late_subject > list_Late_subject > list_Late_subject ).

thf(func_def_65,type,
    cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name ).

thf(func_def_66,type,
    cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).

thf(func_def_67,type,
    nil_li29751603e_name: list_l1406151091e_name ).

thf(func_def_68,type,
    nil_Pr743626285e_name: list_P227219501e_name ).

thf(func_def_69,type,
    abs_fun_name_pi: name > pi > name > noption_pi ).

thf(func_def_70,type,
    fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).

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_1135477378ion_pi: name > list_name_noption_pi > $o ).

thf(func_def_78,type,
    fresh_name_list_name: name > list_name > $o ).

thf(func_def_79,type,
    fresh_name_list_pi: name > list_pi > $o ).

thf(func_def_80,type,
    fresh_1981651763reeRes: name > list_Late_freeRes > $o ).

thf(func_def_81,type,
    fresh_838462539ubject: name > list_Late_subject > $o ).

thf(func_def_82,type,
    fresh_922791155e_name: name > list_P227219501e_name > $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_1627595501_pi_pi: name > product_prod_pi_pi > $o ).

thf(func_def_87,type,
    fresh_2007541374s_name: name > produc2052722628s_name > $o ).

thf(func_def_88,type,
    fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).

thf(func_def_89,type,
    fresh_493808761reeRes: name > produc1357834675reeRes > $o ).

thf(func_def_90,type,
    fresh_1498103185ubject: name > produc214645451ubject > $o ).

thf(func_def_91,type,
    fresh_1953561446t_name: name > produc1998742700t_name > $o ).

thf(func_def_92,type,
    fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).

thf(func_def_93,type,
    fresh_1638563217reeRes: name > produc355105483reeRes > $o ).

thf(func_def_94,type,
    fresh_495373993ubject: name > produc1359399907ubject > $o ).

thf(func_def_95,type,
    perm_n382765978reeRes: list_P227219501e_name > ( name > late_freeRes ) > name > late_freeRes ).

thf(func_def_96,type,
    perm_n1387060402ubject: list_P227219501e_name > ( name > late_subject ) > name > late_subject ).

thf(func_def_97,type,
    perm_n1667196784ion_pi: list_P227219501e_name > ( name > noption_pi ) > name > noption_pi ).

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_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).

thf(func_def_123,type,
    perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).

thf(func_def_124,type,
    perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).

thf(func_def_125,type,
    perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).

thf(func_def_126,type,
    perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).

thf(func_def_127,type,
    perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).

thf(func_def_128,type,
    perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).

thf(func_def_129,type,
    perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).

thf(func_def_130,type,
    perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).

thf(func_def_131,type,
    perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).

thf(func_def_132,type,
    perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).

thf(func_def_133,type,
    perm_name_set_name: list_P227219501e_name > set_name > set_name ).

thf(func_def_134,type,
    perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).

thf(func_def_135,type,
    perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).

thf(func_def_136,type,
    perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).

thf(func_def_137,type,
    perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).

thf(func_def_138,type,
    perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).

thf(func_def_139,type,
    swap_name2: produc367475239e_name > name > name ).

thf(func_def_140,type,
    produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).

thf(func_def_141,type,
    produc1570949143e_name: name > name > produc367475239e_name ).

thf(func_def_142,type,
    produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).

thf(func_def_143,type,
    produc607574050ubject: name > late_subject > produc865358760ubject ).

thf(func_def_144,type,
    product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).

thf(func_def_145,type,
    produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).

thf(func_def_146,type,
    produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).

thf(func_def_147,type,
    produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).

thf(func_def_148,type,
    produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).

thf(func_def_149,type,
    produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).

thf(func_def_150,type,
    produc1647375838t_name: late_subject > name > produc1998742700t_name ).

thf(func_def_151,type,
    produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).

thf(func_def_152,type,
    produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).

thf(func_def_153,type,
    produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).

thf(func_def_154,type,
    produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).

thf(func_def_155,type,
    produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).

thf(func_def_156,type,
    eqvt_pi: set_Pr1834926343_pi_pi > $o ).

thf(func_def_157,type,
    collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).

thf(func_def_158,type,
    strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).

thf(func_def_159,type,
    strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).

thf(func_def_160,type,
    member_name: name > set_name > $o ).

thf(func_def_161,type,
    member_pi: pi > set_pi > $o ).

thf(func_def_162,type,
    member_pi_Rep: pi_Rep > set_pi_Rep > $o ).

thf(func_def_163,type,
    member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).

thf(func_def_164,type,
    member_Late_subject: late_subject > set_Late_subject > $o ).

thf(func_def_165,type,
    member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(func_def_166,type,
    p: pi ).

thf(func_def_167,type,
    p2: pi ).

thf(func_def_168,type,
    pxQ: pi ).

thf(func_def_169,type,
    q: pi ).

thf(func_def_170,type,
    q2: pi ).

thf(func_def_171,type,
    q_a: pi ).

thf(func_def_172,type,
    rel: set_Pr1834926343_pi_pi ).

thf(func_def_173,type,
    alpha: late_freeRes ).

thf(func_def_174,type,
    aa: name ).

thf(func_def_175,type,
    b: name ).

thf(func_def_176,type,
    x: name ).

thf(func_def_177,type,
    y: name ).

thf(func_def_178,type,
    z: name ).

thf(func_def_182,type,
    vAND: $o > $o > $o ).

thf(func_def_183,type,
    vIMP: $o > $o > $o ).

thf(func_def_184,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_185,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_186,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_187,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_188,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_189,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_190,type,
    vNOT: $o > $o ).

thf(func_def_191,type,
    sP0: pi > pi > set_Pr1834926343_pi_pi > $o ).

thf(func_def_192,type,
    sP1: name > pi > late_residual > $o ).

thf(func_def_193,type,
    sP2: name > pi > late_residual > $o ).

thf(func_def_194,type,
    sP3: set_Pr1834926343_pi_pi > $o ).

thf(func_def_195,type,
    sP4: name > pi > late_subject > name > pi > $o ).

thf(func_def_196,type,
    sP5: pi > pi > late_subject > name > pi > $o ).

thf(func_def_197,type,
    sP6: pi > pi > late_subject > name > pi > $o ).

thf(func_def_198,type,
    sP7: pi > late_subject > ( late_subject > pi > $o ) > name > name > $o ).

thf(func_def_199,type,
    sK8: list_l1406151091e_name > produc367475239e_name ).

thf(func_def_200,type,
    sK9: list_l1406151091e_name > list_P227219501e_name ).

thf(func_def_201,type,
    sK10: list_l1406151091e_name > list_l1406151091e_name ).

thf(func_def_202,type,
    sK11: list_l1406151091e_name > list_l1406151091e_name ).

thf(func_def_203,type,
    sK12: list_P227219501e_name > produc367475239e_name ).

thf(func_def_204,type,
    sK13: list_P227219501e_name > produc367475239e_name ).

thf(func_def_205,type,
    sK14: list_P227219501e_name > list_P227219501e_name ).

thf(func_def_206,type,
    sK15: list_P227219501e_name > produc367475239e_name ).

thf(func_def_207,type,
    sK16: list_P227219501e_name > produc367475239e_name ).

thf(func_def_208,type,
    sK17: list_P227219501e_name > list_P227219501e_name ).

thf(func_def_209,type,
    sK18: late_subject > name ).

thf(func_def_210,type,
    sK19: late_subject > name ).

thf(func_def_211,type,
    sK20: produc890461031e_name > produc367475239e_name ).

thf(func_def_212,type,
    sK21: produc890461031e_name > list_P227219501e_name ).

thf(func_def_213,type,
    sK22: produc890461031e_name > produc367475239e_name ).

thf(func_def_214,type,
    sK23: produc890461031e_name > list_P227219501e_name ).

thf(func_def_215,type,
    sK24: produc890461031e_name > list_P227219501e_name ).

thf(func_def_216,type,
    sK25: produc890461031e_name > list_P227219501e_name ).

thf(func_def_217,type,
    sK26: produc890461031e_name > produc367475239e_name ).

thf(func_def_218,type,
    sK27: produc890461031e_name > list_P227219501e_name ).

thf(func_def_219,type,
    sK28: produc890461031e_name > list_P227219501e_name ).

thf(func_def_220,type,
    sK29: produc890461031e_name > list_P227219501e_name ).

thf(func_def_221,type,
    sK30: produc1872410278e_name > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_222,type,
    sK31: produc1872410278e_name > produc367475239e_name ).

thf(func_def_223,type,
    sK32: produc1872410278e_name > produc367475239e_name ).

thf(func_def_224,type,
    sK33: produc1872410278e_name > list_P227219501e_name ).

thf(func_def_225,type,
    sK34: produc1872410278e_name > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_226,type,
    sK35: produc1872410278e_name > produc367475239e_name ).

thf(func_def_227,type,
    sK36: produc1872410278e_name > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_228,type,
    sK37: produc1872410278e_name > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_229,type,
    sK38: produc1872410278e_name > produc367475239e_name ).

thf(func_def_230,type,
    sK39: produc1872410278e_name > list_P227219501e_name ).

thf(func_def_231,type,
    sK40: produc1872410278e_name > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_232,type,
    sK41: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_233,type,
    sK42: late_freeRes > name ).

thf(func_def_234,type,
    sK43: late_freeRes > name ).

thf(func_def_235,type,
    sK44: late_freeRes > name ).

thf(func_def_236,type,
    sK45: late_subject > name ).

thf(func_def_237,type,
    sK46: name > name ).

thf(func_def_238,type,
    sK47: pi > name ).

thf(func_def_239,type,
    sK48: produc367475239e_name > name ).

thf(func_def_240,type,
    sK49: produc367475239e_name > name ).

thf(func_def_241,type,
    sK50: product_prod_pi_pi > pi ).

thf(func_def_242,type,
    sK51: product_prod_pi_pi > pi ).

thf(func_def_243,type,
    sK52: produc367475239e_name > name ).

thf(func_def_244,type,
    sK53: produc367475239e_name > name ).

thf(func_def_245,type,
    sK54: product_prod_pi_pi > pi ).

thf(func_def_246,type,
    sK55: product_prod_pi_pi > pi ).

thf(func_def_247,type,
    sK56: ( late_subject > $o ) > name ).

thf(func_def_248,type,
    sK57: ( late_subject > $o ) > name ).

thf(func_def_249,type,
    sK58: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_250,type,
    sK59: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_251,type,
    sK60: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_252,type,
    sK61: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_253,type,
    sK62: ( produc367475239e_name > $o ) > name ).

thf(func_def_254,type,
    sK63: ( produc367475239e_name > $o ) > name ).

thf(func_def_255,type,
    sK64: ( produc367475239e_name > $o ) > name ).

thf(func_def_256,type,
    sK65: ( produc367475239e_name > $o ) > name ).

thf(func_def_257,type,
    sK66: ( late_freeRes > $o ) > name ).

thf(func_def_258,type,
    sK67: ( late_freeRes > $o ) > name ).

thf(func_def_259,type,
    sK68: ( late_residual > $o ) > late_freeRes ).

thf(func_def_260,type,
    sK69: ( late_residual > $o ) > pi ).

thf(func_def_261,type,
    sK70: ( late_residual > $o ) > late_subject ).

thf(func_def_262,type,
    sK71: ( late_residual > $o ) > name ).

thf(func_def_263,type,
    sK72: ( late_residual > $o ) > pi ).

thf(func_def_264,type,
    sK73: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_265,type,
    sK74: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_266,type,
    sK75: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_267,type,
    sK76: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_268,type,
    sK77: ( list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_269,type,
    sK78: ( list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_270,type,
    sK79: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_271,type,
    sK80: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_272,type,
    sK81: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_273,type,
    sK82: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_274,type,
    sK83: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_275,type,
    sK84: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_276,type,
    sK85: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_277,type,
    sK86: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_278,type,
    sK87: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_279,type,
    sK88: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_280,type,
    sK89: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_281,type,
    sK90: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_282,type,
    sK91: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_283,type,
    sK92: ( ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o ) > produc367475239e_name > produc367475239e_name > $o ).

thf(func_def_284,type,
    sK93: set_Pr1834926343_pi_pi > pi ).

thf(func_def_285,type,
    sK94: set_Pr1834926343_pi_pi > pi ).

thf(func_def_286,type,
    sK95: set_Pr1834926343_pi_pi > name ).

thf(func_def_287,type,
    sK96: set_Pr1834926343_pi_pi > pi ).

thf(func_def_288,type,
    sK97: set_Pr1834926343_pi_pi > pi ).

thf(func_def_289,type,
    sK98: pi > pi > set_Pr1834926343_pi_pi > late_subject ).

thf(func_def_290,type,
    sK99: pi > pi > set_Pr1834926343_pi_pi > name ).

thf(func_def_291,type,
    sK100: pi > pi > set_Pr1834926343_pi_pi > pi ).

thf(func_def_292,type,
    sK101: set_Pr1834926343_pi_pi > pi > pi > late_freeRes ).

thf(func_def_293,type,
    sK102: set_Pr1834926343_pi_pi > pi > pi > pi ).

thf(func_def_294,type,
    sK103: ( late_freeRes > late_residual > $o ) > late_freeRes ).

thf(func_def_295,type,
    sK104: ( late_freeRes > late_residual > $o ) > pi ).

thf(func_def_296,type,
    sK105: ( late_freeRes > late_residual > $o ) > late_freeRes ).

thf(func_def_297,type,
    sK106: ( late_freeRes > late_residual > $o ) > late_subject ).

thf(func_def_298,type,
    sK107: ( late_freeRes > late_residual > $o ) > name ).

thf(func_def_299,type,
    sK108: ( late_freeRes > late_residual > $o ) > pi ).

thf(func_def_300,type,
    sK109: ( late_freeRes > late_residual > $o ) > late_freeRes ).

thf(func_def_301,type,
    sK110: ( late_freeRes > late_residual > $o ) > late_freeRes ).

thf(func_def_302,type,
    sK111: ( late_freeRes > late_residual > $o ) > pi ).

thf(func_def_303,type,
    sK112: ( late_freeRes > late_residual > $o ) > late_freeRes ).

thf(func_def_304,type,
    sK113: ( late_freeRes > late_residual > $o ) > late_subject ).

thf(func_def_305,type,
    sK114: ( late_freeRes > late_residual > $o ) > name ).

thf(func_def_306,type,
    sK115: ( late_freeRes > late_residual > $o ) > pi ).

thf(func_def_307,type,
    sK116: ( late_freeRes > late_residual > $o ) > late_freeRes ).

thf(func_def_308,type,
    sK117: ( late_subject > late_residual > $o ) > late_freeRes ).

thf(func_def_309,type,
    sK118: ( late_subject > late_residual > $o ) > pi ).

thf(func_def_310,type,
    sK119: ( late_subject > late_residual > $o ) > late_subject ).

thf(func_def_311,type,
    sK120: ( late_subject > late_residual > $o ) > late_subject ).

thf(func_def_312,type,
    sK121: ( late_subject > late_residual > $o ) > name ).

thf(func_def_313,type,
    sK122: ( late_subject > late_residual > $o ) > pi ).

thf(func_def_314,type,
    sK123: ( late_subject > late_residual > $o ) > late_subject ).

thf(func_def_315,type,
    sK124: ( late_subject > late_residual > $o ) > late_freeRes ).

thf(func_def_316,type,
    sK125: ( late_subject > late_residual > $o ) > pi ).

thf(func_def_317,type,
    sK126: ( late_subject > late_residual > $o ) > late_subject ).

thf(func_def_318,type,
    sK127: ( late_subject > late_residual > $o ) > late_subject ).

thf(func_def_319,type,
    sK128: ( late_subject > late_residual > $o ) > name ).

thf(func_def_320,type,
    sK129: ( late_subject > late_residual > $o ) > pi ).

thf(func_def_321,type,
    sK130: ( late_subject > late_residual > $o ) > late_subject ).

thf(func_def_322,type,
    sK131: ( name > late_residual > $o ) > late_freeRes ).

thf(func_def_323,type,
    sK132: ( name > late_residual > $o ) > pi ).

thf(func_def_324,type,
    sK133: ( name > late_residual > $o ) > name ).

thf(func_def_325,type,
    sK134: ( name > late_residual > $o ) > late_subject ).

thf(func_def_326,type,
    sK135: ( name > late_residual > $o ) > name ).

thf(func_def_327,type,
    sK136: ( name > late_residual > $o ) > pi ).

thf(func_def_328,type,
    sK137: ( name > late_residual > $o ) > name ).

thf(func_def_329,type,
    sK138: ( name > late_residual > $o ) > late_freeRes ).

thf(func_def_330,type,
    sK139: ( name > late_residual > $o ) > pi ).

thf(func_def_331,type,
    sK140: ( name > late_residual > $o ) > name ).

thf(func_def_332,type,
    sK141: ( name > late_residual > $o ) > late_subject ).

thf(func_def_333,type,
    sK142: ( name > late_residual > $o ) > name ).

thf(func_def_334,type,
    sK143: ( name > late_residual > $o ) > pi ).

thf(func_def_335,type,
    sK144: ( name > late_residual > $o ) > name ).

thf(func_def_336,type,
    sK145: ( pi > late_residual > $o ) > late_freeRes ).

thf(func_def_337,type,
    sK146: ( pi > late_residual > $o ) > pi ).

thf(func_def_338,type,
    sK147: ( pi > late_residual > $o ) > pi ).

thf(func_def_339,type,
    sK148: ( pi > late_residual > $o ) > late_subject ).

thf(func_def_340,type,
    sK149: ( pi > late_residual > $o ) > name ).

thf(func_def_341,type,
    sK150: ( pi > late_residual > $o ) > pi ).

thf(func_def_342,type,
    sK151: ( pi > late_residual > $o ) > pi ).

thf(func_def_343,type,
    sK152: ( pi > late_residual > $o ) > late_freeRes ).

thf(func_def_344,type,
    sK153: ( pi > late_residual > $o ) > pi ).

thf(func_def_345,type,
    sK154: ( pi > late_residual > $o ) > pi ).

thf(func_def_346,type,
    sK155: ( pi > late_residual > $o ) > late_subject ).

thf(func_def_347,type,
    sK156: ( pi > late_residual > $o ) > name ).

thf(func_def_348,type,
    sK157: ( pi > late_residual > $o ) > pi ).

thf(func_def_349,type,
    sK158: ( pi > late_residual > $o ) > pi ).

thf(func_def_350,type,
    sK159: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_351,type,
    sK160: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_352,type,
    sK161: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_353,type,
    sK162: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_354,type,
    sK163: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_355,type,
    sK164: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_356,type,
    sK165: ( list_P227219501e_name > list_P227219501e_name > $o ) > produc367475239e_name ).

thf(func_def_357,type,
    sK166: ( list_P227219501e_name > list_P227219501e_name > $o ) > list_P227219501e_name ).

thf(func_def_358,type,
    sK167: name > pi > late_residual > pi ).

thf(func_def_359,type,
    sK168: name > pi > late_residual > name ).

thf(func_def_360,type,
    sK169: name > pi > late_residual > name ).

thf(func_def_361,type,
    sK170: name > pi > late_residual > pi ).

thf(func_def_362,type,
    sK171: name > pi > late_residual > pi ).

thf(func_def_363,type,
    sK172: name > pi > late_residual > late_subject ).

thf(func_def_364,type,
    sK173: name > pi > late_residual > name ).

thf(func_def_365,type,
    sK174: name > pi > late_residual > pi ).

thf(func_def_366,type,
    sK175: name > pi > late_residual > name ).

thf(func_def_367,type,
    sK176: late_residual > pi > name > pi ).

thf(func_def_368,type,
    sK177: late_residual > pi > name > late_freeRes ).

thf(func_def_369,type,
    sK178: late_residual > pi > name > pi ).

thf(func_def_370,type,
    sK179: late_residual > pi > name > name ).

thf(func_def_371,type,
    sK180: set_Pr1834926343_pi_pi > pi ).

thf(func_def_372,type,
    sK181: set_Pr1834926343_pi_pi > pi ).

thf(func_def_373,type,
    sK182: set_Pr1834926343_pi_pi > name ).

thf(func_def_374,type,
    sK183: set_Pr1834926343_pi_pi > pi ).

thf(func_def_375,type,
    sK184: set_Pr1834926343_pi_pi > pi ).

thf(func_def_376,type,
    sK185: set_Pr1834926343_pi_pi > pi ).

thf(func_def_377,type,
    sK186: set_Pr1834926343_pi_pi > name ).

thf(func_def_378,type,
    sK187: set_Pr1834926343_pi_pi > pi ).

thf(func_def_379,type,
    sK188: set_Pr1834926343_pi_pi > pi ).

thf(func_def_380,type,
    sK189: set_Pr1834926343_pi_pi > pi ).

thf(func_def_381,type,
    sK190: set_Pr1834926343_pi_pi > name ).

thf(func_def_382,type,
    sK191: set_Pr1834926343_pi_pi > pi ).

thf(func_def_383,type,
    sK192: set_Pr1834926343_pi_pi > pi ).

thf(func_def_384,type,
    sK193: set_Pr1834926343_pi_pi > pi ).

thf(func_def_385,type,
    sK194: pi > late_freeRes > pi > name > pi ).

thf(func_def_386,type,
    sK195: pi > late_freeRes > pi > name > late_freeRes ).

thf(func_def_387,type,
    sK196: pi > late_freeRes > pi > name > pi ).

thf(func_def_388,type,
    sK197: pi > late_freeRes > pi > name > name ).

thf(func_def_389,type,
    sK198: pi > late_freeRes > set_Pr1834926343_pi_pi > pi > pi ).

thf(func_def_390,type,
    sK199: ( pi > $o ) > late_freeRes > pi > name > pi ).

thf(func_def_391,type,
    sK200: name > pi > late_subject > name > pi > pi ).

thf(func_def_392,type,
    sK201: name > pi > late_subject > name > pi > late_subject ).

thf(func_def_393,type,
    sK202: name > pi > late_subject > name > pi > name ).

thf(func_def_394,type,
    sK203: name > pi > late_subject > name > pi > pi ).

thf(func_def_395,type,
    sK204: name > pi > late_subject > name > pi > name ).

thf(func_def_396,type,
    sK205: pi > name > late_subject > pi > name > pi ).

thf(func_def_397,type,
    sK206: pi > name > late_subject > pi > name > name ).

thf(func_def_398,type,
    sK207: pi > name > late_subject > pi > name > name ).

thf(func_def_399,type,
    sK208: pi > name > late_subject > pi > name > pi ).

thf(func_def_400,type,
    sK209: pi > pi > late_subject > name > pi > pi ).

thf(func_def_401,type,
    sK210: pi > pi > late_subject > name > pi > late_subject ).

thf(func_def_402,type,
    sK211: pi > pi > late_subject > name > pi > name ).

thf(func_def_403,type,
    sK212: pi > pi > late_subject > name > pi > pi ).

thf(func_def_404,type,
    sK213: pi > pi > late_subject > name > pi > pi ).

thf(func_def_405,type,
    sK214: pi > pi > late_subject > name > pi > pi ).

thf(func_def_406,type,
    sK215: pi > pi > late_subject > name > pi > late_subject ).

thf(func_def_407,type,
    sK216: pi > pi > late_subject > name > pi > name ).

thf(func_def_408,type,
    sK217: pi > pi > late_subject > name > pi > pi ).

thf(func_def_409,type,
    sK218: pi > pi > late_subject > name > pi > pi ).

thf(func_def_410,type,
    sK219: pi > name > late_subject > set_Pr1834926343_pi_pi > pi > pi ).

thf(func_def_411,type,
    sK220: pi > late_subject > ( late_subject > pi > $o ) > name > name > name ).

thf(func_def_412,type,
    sK221: pi > late_subject > ( late_subject > pi > $o ) > name > name > pi ).

thf(func_def_413,type,
    sK222: ( late_subject > pi > $o ) > name > late_subject > pi > name > pi ).

thf(func_def_414,type,
    sK223: ( pi > $o ) > name > late_subject > pi > pi > pi ).

thf(func_def_415,type,
    sK224: ( pi > $o ) > name > late_subject > pi > pi > pi ).

thf(func_def_417,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_418,type,
    vOR: $o > $o > $o ).

thf(func_def_419,type,
    sK226: list_P227219501e_name > list_P227219501e_name ).

thf(f11938,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2264,f2269,f2274,f2279,f2284,f2289,f2294,f2298,f2331,f2335,f2339,f2343,f2347,f2351,f2355,f2359,f2363,f2367,f2371,f2375,f2379,f2383,f2387,f2392,f2397,f2402,f2407,f2412,f2417,f2421,f2425,f2429,f2433,f2445,f2449,f2453,f2457,f2461,f2465,f2469,f2473,f2477,f2481,f2485,f2489,f2493,f2497,f2501,f2505,f2509,f2513,f2532,f2536,f2541,f2545,f2550,f2555,f2559,f2567,f2573,f2577,f2584,f2590,f2594,f2608,f2618,f2623,f2627,f2631,f2635,f2639,f2648,f2652,f2656,f2660,f2665,f2672,f2676,f2680,f2697,f2701,f2731,f2735,f2739,f2743,f2748,f2752,f2756,f2800,f2804,f2810,f2814,f2830,f2834,f2838,f2856,f2860,f2864,f2869,f2910,f2914,f2918,f2922,f2926,f2930,f2990,f2998,f3004,f3018,f3046,f3050,f3054,f3058,f3062,f3099,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3254,f3258,f3262,f3314,f3364,f3384,f3390,f3394,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3428,f3432,f3436,f3440,f3444,f3448,f3452,f3470,f3474,f3478,f3482,f3486,f3490,f3494,f3498,f3502,f3506,f3510,f3514,f3518,f3522,f3526,f3530,f3534,f3538,f3583,f3691,f3834,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4081,f4227,f4231,f4235,f4243,f4255,f4259,f4263,f4267,f4279,f4311,f4315,f4319,f4331,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4386,f4390,f4394,f4398,f4600,f4739,f4767,f4771,f4788,f4792,f4796,f4800,f4804,f4870,f4875,f4880,f4884,f4888,f4895,f4899,f4933,f4954,f4959,f4965,f4969,f4973,f4977,f5021,f5051,f5055,f5073,f5077,f5081,f5085,f5089,f5331,f5335,f5343,f5351,f5367,f5371,f5375,f5379,f5489,f5493,f5507,f5511,f5515,f5519,f5523,f5531,f5535,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5569,f5600,f5604,f5616,f5622,f5626,f5636,f5640,f5644,f5668,f5672,f5708,f5721,f5727,f5731,f5735,f5753,f5763,f5769,f5775,f5785,f5789,f5802,f5808,f5819,f5823,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5876,f5894,f5898,f5902,f5906,f5921,f5925,f5931,f5940,f5949,f5969,f5973,f5988,f5992,f5996,f6000,f6004,f6008,f6012,f6016,f6020,f6024,f6036,f6050,f6064,f6074,f6081,f6099,f6103,f6107,f6128,f6135,f6139,f6149,f6159,f6163,f6189,f6201,f6205,f6209,f6232,f6244,f6256,f6260,f6264,f6281,f6285,f6299,f6303,f6307,f6334,f6343,f6364,f6368,f6372,f6382,f6394,f6399,f6403,f6407,f6417,f6429,f6433,f6446,f6498,f6504,f6510,f6518,f6522,f6530,f6536,f6542,f6546,f6554,f6558,f6564,f6568,f6572,f6576,f6580,f6584,f6588,f6592,f6636,f6644,f6648,f6652,f6656,f6660,f6664,f6668,f6672,f6676,f6680,f6684,f6690,f6694,f6698,f6785,f6846,f6850,f6854,f6918,f6948,f6952,f6956,f6960,f6964,f6968,f6972,f6976,f7009,f7013,f7017,f7021,f7025,f7029,f7033,f7037,f7041,f7045,f7049,f7072,f7113,f7117,f7121,f7125,f7129,f7133,f7155,f7159,f7169,f7173,f7177,f7181,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7632,f7762,f7766,f7770,f7774,f7807,f7811,f7815,f7819,f7823,f7827,f7831,f7835,f8066,f8070,f8074,f8078,f8082,f8086,f8090,f8094,f8098,f8102,f8110,f8114,f8118,f8130,f8708,f8712,f8842,f8851,f8855,f8859,f8863,f8867,f8917,f8932,f8946,f8950,f8954,f8958,f8962,f8966,f8982,f8986,f8990,f8994,f8998,f9002,f9006,f9010,f9014,f9018,f9025,f9029,f9033,f9037,f9041,f9045,f9049,f9053,f9066,f9489,f9526,f9530,f9534,f9538,f9542,f9546,f9621,f9625,f9629,f9633,f9637,f9641,f9645,f9649,f9653,f9657,f9661,f9665,f9669,f9673,f9677,f9681,f9685,f9777,f9781,f9785,f9789,f9793,f9827,f10109,f10113,f10117,f10121,f10132,f10765,f11085,f11105,f11135,f11177,f11299,f11304,f11308,f11313,f11317,f11321,f11325,f11329,f11333,f11337,f11341,f11345,f11349,f11353,f11358,f11362,f11366,f11370,f11374,f11378,f11382,f11635,f11854,f11901,f11905,f11909,f11913,f11917,f11921,f11934,f11937]) ).

thf(f11937,plain,
    ( ~ spl225_76
    | ~ spl225_579 ),
    inference(avatar_contradiction_clause,[],[f11936]) ).

thf(f11936,plain,
    ( $false
    | ~ spl225_76
    | ~ spl225_579 ),
    inference(trivial_inequality_removal,[],[f11922]) ).

thf(f11922,plain,
    ( ( $true = $false )
    | ~ spl225_76
    | ~ spl225_579 ),
    inference(superposition,[],[f11853,f2664]) ).

thf(f2664,plain,
    ( ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $true )
    | ~ spl225_76 ),
    inference(avatar_component_clause,[],[f2662]) ).

thf(f2662,plain,
    ( spl225_76
  <=> ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_76])]) ).

thf(f11853,plain,
    ( ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $false )
    | ~ spl225_579 ),
    inference(avatar_component_clause,[],[f11851]) ).

thf(f11851,plain,
    ( spl225_579
  <=> ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_579])]) ).

thf(f11934,plain,
    ( ~ spl225_76
    | ~ spl225_579 ),
    inference(avatar_contradiction_clause,[],[f11933]) ).

thf(f11933,plain,
    ( $false
    | ~ spl225_76
    | ~ spl225_579 ),
    inference(trivial_inequality_removal,[],[f11924]) ).

thf(f11924,plain,
    ( ( $true = $false )
    | ~ spl225_76
    | ~ spl225_579 ),
    inference(superposition,[],[f2664,f11853]) ).

thf(f11921,plain,
    spl225_585,
    inference(avatar_split_clause,[],[f2049,f11919]) ).

thf(f11919,plain,
    ( spl225_585
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
        | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_585])]) ).

thf(f2049,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2046]) ).

thf(f2046,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
      | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1552]) ).

thf(f1552,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ),
    inference(cnf_transformation,[],[f488]) ).

thf(f488,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: late_subject] : ( vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ),
    inference(fool_elimination,[],[f487]) ).

thf(f487,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: late_subject] :
      ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1 = X2)
      = ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) ) ),
    inference(rectify,[],[f152]) ).

thf(f152,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: late_subject] :
      ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X2 = X22)
      = ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_eq__eqvt) ).

thf(f11917,plain,
    spl225_584,
    inference(avatar_split_clause,[],[f2048,f11915]) ).

thf(f11915,plain,
    ( spl225_584
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) != vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_584])]) ).

thf(f2048,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) != vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2047]) ).

thf(f2047,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1552]) ).

thf(f11913,plain,
    spl225_583,
    inference(avatar_split_clause,[],[f2045,f11911]) ).

thf(f11911,plain,
    ( spl225_583
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name] :
        ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) )
        | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) != vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_583])]) ).

thf(f2045,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) )
      | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) != vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2042]) ).

thf(f2042,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1862]) ).

thf(f1862,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1553,f1358,f1358]) ).

thf(f1358,plain,
    perm_name_name = name_prm_name,
    inference(cnf_transformation,[],[f344]) ).

thf(f344,axiom,
    perm_name_name = name_prm_name,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_Agent_Oname__prm__name__def) ).

thf(f1553,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) ),
    inference(cnf_transformation,[],[f490]) ).

thf(f490,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) ),
    inference(fool_elimination,[],[f489]) ).

thf(f489,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: name] :
      ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1 = X2)
      = ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) ) ),
    inference(rectify,[],[f155]) ).

thf(f155,axiom,
    ! [X5: list_P227219501e_name,X2: name,X22: name] :
      ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X2 = X22)
      = ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_eq__eqvt) ).

thf(f11909,plain,
    spl225_582,
    inference(avatar_split_clause,[],[f2044,f11907]) ).

thf(f11907,plain,
    ( spl225_582
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name] :
        ( ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) )
        | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_582])]) ).

thf(f2044,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) )
      | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2043]) ).

thf(f2043,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2)) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1862]) ).

thf(f11905,plain,
    spl225_581,
    inference(avatar_split_clause,[],[f2041,f11903]) ).

thf(f11903,plain,
    ( spl225_581
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
        | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_581])]) ).

thf(f2041,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2038]) ).

thf(f2038,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
      | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1554]) ).

thf(f1554,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ),
    inference(cnf_transformation,[],[f492]) ).

thf(f492,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: pi] : ( vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ),
    inference(fool_elimination,[],[f491]) ).

thf(f491,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: pi] :
      ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1 = X2)
      = ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) ) ),
    inference(rectify,[],[f156]) ).

thf(f156,axiom,
    ! [X5: list_P227219501e_name,X2: pi,X22: pi] :
      ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X2 = X22)
      = ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_eq__eqvt) ).

thf(f11901,plain,
    spl225_580,
    inference(avatar_split_clause,[],[f2040,f11899]) ).

thf(f11899,plain,
    ( spl225_580
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_580])]) ).

thf(f2040,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2039]) ).

thf(f2039,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1554]) ).

thf(f11854,plain,
    ( spl225_579
    | ~ spl225_356
    | ~ spl225_568 ),
    inference(avatar_split_clause,[],[f11820,f11343,f6396,f11851]) ).

thf(f6396,plain,
    ( spl225_356
  <=> ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_356])]) ).

thf(f11343,plain,
    ( spl225_568
  <=> ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_568])]) ).

thf(f11820,plain,
    ( ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $false )
    | ~ spl225_356
    | ~ spl225_568 ),
    inference(trivial_inequality_removal,[],[f11811]) ).

thf(f11811,plain,
    ( ( $true = $false )
    | ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $false )
    | ~ spl225_356
    | ~ spl225_568 ),
    inference(superposition,[],[f11344,f6398]) ).

thf(f6398,plain,
    ( ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))) )
    | ~ spl225_356 ),
    inference(avatar_component_clause,[],[f6396]) ).

thf(f11344,plain,
    ( ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) )
    | ~ spl225_568 ),
    inference(avatar_component_clause,[],[f11343]) ).

thf(f11635,plain,
    ( spl225_578
    | ~ spl225_57
    | ~ spl225_493 ),
    inference(avatar_split_clause,[],[f8940,f8930,f2552,f11632]) ).

thf(f11632,plain,
    ( spl225_578
  <=> ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,z),vAPP(name,late_subject,late_BoundOutputS,b)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_578])]) ).

thf(f2552,plain,
    ( spl225_57
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_57])]) ).

thf(f8930,plain,
    ( spl225_493
  <=> ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_BoundOutputS,b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_493])]) ).

thf(f8940,plain,
    ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,z),vAPP(name,late_subject,late_BoundOutputS,b)) )
    | ~ spl225_57
    | ~ spl225_493 ),
    inference(trivial_inequality_removal,[],[f8935]) ).

thf(f8935,plain,
    ( ( $true != $true )
    | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,z),vAPP(name,late_subject,late_BoundOutputS,b)) )
    | ~ spl225_57
    | ~ spl225_493 ),
    inference(superposition,[],[f8931,f2554]) ).

thf(f2554,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true )
    | ~ spl225_57 ),
    inference(avatar_component_clause,[],[f2552]) ).

thf(f8931,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_BoundOutputS,b)) ) )
    | ~ spl225_493 ),
    inference(avatar_component_clause,[],[f8930]) ).

thf(f11382,plain,
    ( spl225_577
    | ~ spl225_54
    | ~ spl225_248 ),
    inference(avatar_split_clause,[],[f5501,f5491,f2539,f11380]) ).

thf(f11380,plain,
    ( spl225_577
  <=> ! [X0: name,X3: pi,X2: pi,X1: late_freeRes] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X3) = $true )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_577])]) ).

thf(f2539,plain,
    ( spl225_54
  <=> ! [X0: name,X1: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_54])]) ).

thf(f5491,plain,
    ( spl225_248
  <=> ! [X2: late_freeRes,X4: pi > $o,X0: name,X3: pi,X1: pi] :
        ( ( $true = vAPP(pi,$o,X4,X3) )
        | ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_248])]) ).

thf(f5501,plain,
    ( ! [X2: pi,X3: pi,X0: name,X1: late_freeRes] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X3) = $true )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X3)) ) )
    | ~ spl225_54
    | ~ spl225_248 ),
    inference(trivial_inequality_removal,[],[f5498]) ).

thf(f5498,plain,
    ( ! [X2: pi,X3: pi,X0: name,X1: late_freeRes] :
        ( ( $true != $true )
        | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X3) = $true )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X3)) ) )
    | ~ spl225_54
    | ~ spl225_248 ),
    inference(superposition,[],[f5492,f2540]) ).

thf(f2540,plain,
    ( ! [X0: name,X1: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)) )
    | ~ spl225_54 ),
    inference(avatar_component_clause,[],[f2539]) ).

thf(f5492,plain,
    ( ! [X2: late_freeRes,X3: pi,X0: name,X1: pi,X4: pi > $o] :
        ( ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
        | ( $true = vAPP(pi,$o,X4,X3) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) )
    | ~ spl225_248 ),
    inference(avatar_component_clause,[],[f5491]) ).

thf(f11378,plain,
    ( spl225_576
    | ~ spl225_29
    | ~ spl225_187 ),
    inference(avatar_split_clause,[],[f4305,f4265,f2414,f11376]) ).

thf(f11376,plain,
    ( spl225_576
  <=> ! [X0: name] :
        ( ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),x)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_576])]) ).

thf(f2414,plain,
    ( spl225_29
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_29])]) ).

thf(f4265,plain,
    ( spl225_187
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_187])]) ).

thf(f4305,plain,
    ( ! [X0: name] :
        ( ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),x)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) )
    | ~ spl225_29
    | ~ spl225_187 ),
    inference(trivial_inequality_removal,[],[f4286]) ).

thf(f4286,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),x)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) )
    | ~ spl225_29
    | ~ spl225_187 ),
    inference(superposition,[],[f4266,f2416]) ).

thf(f2416,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p) = $true )
    | ~ spl225_29 ),
    inference(avatar_component_clause,[],[f2414]) ).

thf(f4266,plain,
    ( ! [X2: name,X0: name,X1: pi] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1) )
        | ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) )
    | ~ spl225_187 ),
    inference(avatar_component_clause,[],[f4265]) ).

thf(f11374,plain,
    ( spl225_575
    | ~ spl225_24
    | ~ spl225_187 ),
    inference(avatar_split_clause,[],[f4304,f4265,f2389,f11372]) ).

thf(f11372,plain,
    ( spl225_575
  <=> ! [X0: name] :
        ( ( q2 = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),y)),nil_Pr743626285e_name)),q2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_575])]) ).

thf(f2389,plain,
    ( spl225_24
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),q2) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_24])]) ).

thf(f4304,plain,
    ( ! [X0: name] :
        ( ( q2 = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),y)),nil_Pr743626285e_name)),q2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) )
    | ~ spl225_24
    | ~ spl225_187 ),
    inference(trivial_inequality_removal,[],[f4287]) ).

thf(f4287,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( q2 = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),y)),nil_Pr743626285e_name)),q2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) )
    | ~ spl225_24
    | ~ spl225_187 ),
    inference(superposition,[],[f4266,f2391]) ).

thf(f2391,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),q2) = $true )
    | ~ spl225_24 ),
    inference(avatar_component_clause,[],[f2389]) ).

thf(f11370,plain,
    ( spl225_574
    | ~ spl225_25
    | ~ spl225_187 ),
    inference(avatar_split_clause,[],[f4303,f4265,f2394,f11368]) ).

thf(f11368,plain,
    ( spl225_574
  <=> ! [X0: name] :
        ( ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),y)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_574])]) ).

thf(f2394,plain,
    ( spl225_25
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),p) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_25])]) ).

thf(f4303,plain,
    ( ! [X0: name] :
        ( ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),y)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) )
    | ~ spl225_25
    | ~ spl225_187 ),
    inference(trivial_inequality_removal,[],[f4288]) ).

thf(f4288,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),y)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) )
    | ~ spl225_25
    | ~ spl225_187 ),
    inference(superposition,[],[f4266,f2396]) ).

thf(f2396,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),p) = $true )
    | ~ spl225_25 ),
    inference(avatar_component_clause,[],[f2394]) ).

thf(f11366,plain,
    ( spl225_573
    | ~ spl225_27
    | ~ spl225_187 ),
    inference(avatar_split_clause,[],[f4301,f4265,f2404,f11364]) ).

thf(f11364,plain,
    ( spl225_573
  <=> ! [X0: name] :
        ( ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_573])]) ).

thf(f2404,plain,
    ( spl225_27
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_27])]) ).

thf(f4301,plain,
    ( ! [X0: name] :
        ( ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) )
    | ~ spl225_27
    | ~ spl225_187 ),
    inference(trivial_inequality_removal,[],[f4290]) ).

thf(f4290,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),p) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) ) )
    | ~ spl225_27
    | ~ spl225_187 ),
    inference(superposition,[],[f4266,f2406]) ).

thf(f2406,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p) = $true )
    | ~ spl225_27 ),
    inference(avatar_component_clause,[],[f2404]) ).

thf(f11362,plain,
    ( spl225_572
    | ~ spl225_26
    | ~ spl225_187 ),
    inference(avatar_split_clause,[],[f4300,f4265,f2399,f11360]) ).

thf(f11360,plain,
    ( spl225_572
  <=> ! [X0: name] :
        ( ( p2 = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),p2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_572])]) ).

thf(f2399,plain,
    ( spl225_26
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p2) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_26])]) ).

thf(f4300,plain,
    ( ! [X0: name] :
        ( ( p2 = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),p2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) )
    | ~ spl225_26
    | ~ spl225_187 ),
    inference(trivial_inequality_removal,[],[f4291]) ).

thf(f4291,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p2 = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),p2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) )
    | ~ spl225_26
    | ~ spl225_187 ),
    inference(superposition,[],[f4266,f2401]) ).

thf(f2401,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p2) = $true )
    | ~ spl225_26 ),
    inference(avatar_component_clause,[],[f2399]) ).

thf(f11358,plain,
    ( spl225_571
    | ~ spl225_29
    | ~ spl225_427 ),
    inference(avatar_split_clause,[],[f7151,f7131,f2414,f11355]) ).

thf(f11355,plain,
    ( spl225_571
  <=> ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,x),vAPP(name,late_subject,late_InputS,b)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_571])]) ).

thf(f7131,plain,
    ( spl225_427
  <=> ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_427])]) ).

thf(f7151,plain,
    ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,x),vAPP(name,late_subject,late_InputS,b)) )
    | ~ spl225_29
    | ~ spl225_427 ),
    inference(trivial_inequality_removal,[],[f7142]) ).

thf(f7142,plain,
    ( ( $true != $true )
    | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,x),vAPP(name,late_subject,late_InputS,b)) )
    | ~ spl225_29
    | ~ spl225_427 ),
    inference(superposition,[],[f7132,f2416]) ).

thf(f7132,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,b)) ) )
    | ~ spl225_427 ),
    inference(avatar_component_clause,[],[f7131]) ).

thf(f11353,plain,
    ( spl225_570
    | ~ spl225_28
    | ~ spl225_187 ),
    inference(avatar_split_clause,[],[f4299,f4265,f2409,f11351]) ).

thf(f11351,plain,
    ( spl225_570
  <=> ! [X0: name] :
        ( ( q = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),q) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_570])]) ).

thf(f2409,plain,
    ( spl225_28
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_28])]) ).

thf(f4299,plain,
    ( ! [X0: name] :
        ( ( q = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),q) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) ) )
    | ~ spl225_28
    | ~ spl225_187 ),
    inference(trivial_inequality_removal,[],[f4292]) ).

thf(f4292,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( q = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),z)),nil_Pr743626285e_name)),q) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) ) )
    | ~ spl225_28
    | ~ spl225_187 ),
    inference(superposition,[],[f4266,f2411]) ).

thf(f2411,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q) = $true )
    | ~ spl225_28 ),
    inference(avatar_component_clause,[],[f2409]) ).

thf(f11349,plain,
    ( spl225_569
    | ~ spl225_99
    | ~ spl225_124 ),
    inference(avatar_split_clause,[],[f3339,f3252,f2866,f11347]) ).

thf(f11347,plain,
    ( spl225_569
  <=> ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),pxQ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_569])]) ).

thf(f2866,plain,
    ( spl225_99
  <=> ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),pxQ)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_99])]) ).

thf(f3252,plain,
    ( spl225_124
  <=> ! [X0: pi,X3: name,X2: pi,X1: late_freeRes] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_124])]) ).

thf(f3339,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),pxQ) ) )
    | ~ spl225_99
    | ~ spl225_124 ),
    inference(trivial_inequality_removal,[],[f3336]) ).

thf(f3336,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),pxQ) ) )
    | ~ spl225_99
    | ~ spl225_124 ),
    inference(superposition,[],[f3253,f2868]) ).

thf(f2868,plain,
    ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),pxQ)) )
    | ~ spl225_99 ),
    inference(avatar_component_clause,[],[f2866]) ).

thf(f3253,plain,
    ( ! [X2: pi,X3: name,X0: pi,X1: late_freeRes] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) ) )
    | ~ spl225_124 ),
    inference(avatar_component_clause,[],[f3252]) ).

thf(f11345,plain,
    ( spl225_568
    | ~ spl225_8
    | ~ spl225_109 ),
    inference(avatar_split_clause,[],[f3010,f3002,f2296,f11343]) ).

thf(f2296,plain,
    ( spl225_8
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_8])]) ).

thf(f3002,plain,
    ( spl225_109
  <=> ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_109])]) ).

thf(f3010,plain,
    ( ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) )
    | ~ spl225_8
    | ~ spl225_109 ),
    inference(trivial_inequality_removal,[],[f3009]) ).

thf(f3009,plain,
    ( ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
        ( ( $true != $true )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) )
    | ~ spl225_8
    | ~ spl225_109 ),
    inference(superposition,[],[f3003,f2297]) ).

thf(f2297,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl225_8 ),
    inference(avatar_component_clause,[],[f2296]) ).

thf(f3003,plain,
    ( ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) ) )
    | ~ spl225_109 ),
    inference(avatar_component_clause,[],[f3002]) ).

thf(f11341,plain,
    ( spl225_567
    | ~ spl225_76
    | ~ spl225_91 ),
    inference(avatar_split_clause,[],[f2820,f2808,f2662,f11339]) ).

thf(f11339,plain,
    ( spl225_567
  <=> ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_567])]) ).

thf(f2808,plain,
    ( spl225_91
  <=> ! [X2: name,X0: pi,X1: late_residual] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_91])]) ).

thf(f2820,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) ) )
    | ~ spl225_76
    | ~ spl225_91 ),
    inference(trivial_inequality_removal,[],[f2815]) ).

thf(f2815,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) ) )
    | ~ spl225_76
    | ~ spl225_91 ),
    inference(superposition,[],[f2809,f2664]) ).

thf(f2809,plain,
    ( ! [X2: name,X0: pi,X1: late_residual] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) ) )
    | ~ spl225_91 ),
    inference(avatar_component_clause,[],[f2808]) ).

thf(f11337,plain,
    spl225_566,
    inference(avatar_split_clause,[],[f2221,f11335]) ).

thf(f11335,plain,
    ( spl225_566
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = $false )
        | ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_566])]) ).

thf(f2221,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = $false )
      | ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1827]) ).

thf(f1827,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: name] : ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(definition_unfolding,[],[f1441,f1358]) ).

thf(f1441,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: name] : ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f811]) ).

thf(f811,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: pi_Rep] : ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(rectify,[],[f95]) ).

thf(f95,axiom,
    ! [X5: list_P227219501e_name,X0: name,X2: pi_Rep] : ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X0)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_fresh__bij) ).

thf(f11333,plain,
    spl225_565,
    inference(avatar_split_clause,[],[f2220,f11331]) ).

thf(f11331,plain,
    ( spl225_565
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = $true )
        | ( $false = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_565])]) ).

thf(f2220,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = $true )
      | ( $false = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1827]) ).

thf(f11329,plain,
    spl225_564,
    inference(avatar_split_clause,[],[f2219,f11327]) ).

thf(f11327,plain,
    ( spl225_564
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = $false )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_564])]) ).

thf(f2219,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = $false )
      | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1828]) ).

thf(f1828,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: name] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(definition_unfolding,[],[f1442,f1358]) ).

thf(f1442,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: name] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f812]) ).

thf(f812,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: late_freeRes] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(rectify,[],[f97]) ).

thf(f97,axiom,
    ! [X5: list_P227219501e_name,X0: name,X2: late_freeRes] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X0)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fresh__bij) ).

thf(f11325,plain,
    spl225_563,
    inference(avatar_split_clause,[],[f2218,f11323]) ).

thf(f11323,plain,
    ( spl225_563
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = $true )
        | ( $false = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_563])]) ).

thf(f2218,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = $true )
      | ( $false = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1828]) ).

thf(f11321,plain,
    spl225_562,
    inference(avatar_split_clause,[],[f2217,f11319]) ).

thf(f11319,plain,
    ( spl225_562
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = $false )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_562])]) ).

thf(f2217,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = $false )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1829]) ).

thf(f1829,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(definition_unfolding,[],[f1443,f1358]) ).

thf(f1443,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f813]) ).

thf(f813,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: late_subject] : ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(rectify,[],[f96]) ).

thf(f96,axiom,
    ! [X5: list_P227219501e_name,X0: name,X2: late_subject] : ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X0)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_fresh__bij) ).

thf(f11317,plain,
    spl225_561,
    inference(avatar_split_clause,[],[f2216,f11315]) ).

thf(f11315,plain,
    ( spl225_561
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = $true )
        | ( $false = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_561])]) ).

thf(f2216,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = $true )
      | ( $false = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1829]) ).

thf(f11313,plain,
    ( spl225_560
    | ~ spl225_25
    | ~ spl225_427 ),
    inference(avatar_split_clause,[],[f7150,f7131,f2394,f11310]) ).

thf(f11310,plain,
    ( spl225_560
  <=> ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,y),vAPP(name,late_subject,late_InputS,b)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_560])]) ).

thf(f7150,plain,
    ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,y),vAPP(name,late_subject,late_InputS,b)) )
    | ~ spl225_25
    | ~ spl225_427 ),
    inference(trivial_inequality_removal,[],[f7143]) ).

thf(f7143,plain,
    ( ( $true != $true )
    | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,y),vAPP(name,late_subject,late_InputS,b)) )
    | ~ spl225_25
    | ~ spl225_427 ),
    inference(superposition,[],[f7132,f2396]) ).

thf(f11308,plain,
    spl225_559,
    inference(avatar_split_clause,[],[f2213,f11306]) ).

thf(f11306,plain,
    ( spl225_559
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = $false )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_559])]) ).

thf(f2213,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = $false )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1831]) ).

thf(f1831,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(definition_unfolding,[],[f1445,f1358]) ).

thf(f1445,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f815]) ).

thf(f815,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: pi] : ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f99]) ).

thf(f99,axiom,
    ! [X5: list_P227219501e_name,X0: name,X2: pi] : ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_fresh__bij) ).

thf(f11304,plain,
    spl225_558,
    inference(avatar_split_clause,[],[f2212,f11302]) ).

thf(f11302,plain,
    ( spl225_558
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = $true )
        | ( $false = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_558])]) ).

thf(f2212,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: name] :
      ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = $true )
      | ( $false = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1831]) ).

thf(f11299,plain,
    ( spl225_557
    | ~ spl225_97 ),
    inference(avatar_split_clause,[],[f2887,f2858,f11297]) ).

thf(f11297,plain,
    ( spl225_557
  <=> ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) != X0 )
        | ( X0 = X1 )
        | ( nil_Pr743626285e_name != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_557])]) ).

thf(f2858,plain,
    ( spl225_97
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_97])]) ).

thf(f2887,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) != X0 )
        | ( X0 = X1 )
        | ( nil_Pr743626285e_name != X0 ) )
    | ~ spl225_97 ),
    inference(equality_proxy_clausification,[],[f2886]) ).

thf(f2886,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) != X0 )
        | ( X0 = X1 )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),nil_Pr743626285e_name) ) )
    | ~ spl225_97 ),
    inference(equality_proxy_clausification,[],[f2885]) ).

thf(f2885,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) != X0 )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),nil_Pr743626285e_name) ) )
    | ~ spl225_97 ),
    inference(equality_proxy_clausification,[],[f2882]) ).

thf(f2882,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),nil_Pr743626285e_name) ) )
    | ~ spl225_97 ),
    inference(primitive_instantiation,[],[f2859]) ).

thf(f2859,plain,
    ( ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) )
    | ~ spl225_97 ),
    inference(avatar_component_clause,[],[f2858]) ).

thf(f11177,plain,
    ( spl225_556
    | ~ spl225_54
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3042,f3016,f2539,f11175]) ).

thf(f11175,plain,
    ( spl225_556
  <=> ! [X0: name,X3: name,X2: name,X1: pi] :
        ( ( X0 = X2 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X3),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_556])]) ).

thf(f3016,plain,
    ( spl225_110
  <=> ! [X0: name,X3: name,X2: name,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) )
        | ( X0 = X2 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_110])]) ).

thf(f3042,plain,
    ( ! [X2: name,X3: name,X0: name,X1: pi] :
        ( ( X0 = X2 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X3),X2)) ) )
    | ~ spl225_54
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3019]) ).

thf(f3019,plain,
    ( ! [X2: name,X3: name,X0: name,X1: pi] :
        ( ( $true != $true )
        | ( X0 = X2 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X3),X2)) ) )
    | ~ spl225_54
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2540]) ).

thf(f3017,plain,
    ( ! [X2: name,X3: name,X0: name,X1: pi] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( X0 = X2 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) ) )
    | ~ spl225_110 ),
    inference(avatar_component_clause,[],[f3016]) ).

thf(f11135,plain,
    ( spl225_555
    | ~ spl225_27
    | ~ spl225_427 ),
    inference(avatar_split_clause,[],[f7149,f7131,f2404,f11132]) ).

thf(f11132,plain,
    ( spl225_555
  <=> ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,z),vAPP(name,late_subject,late_InputS,b)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_555])]) ).

thf(f7149,plain,
    ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,z),vAPP(name,late_subject,late_InputS,b)) )
    | ~ spl225_27
    | ~ spl225_427 ),
    inference(trivial_inequality_removal,[],[f7144]) ).

thf(f7144,plain,
    ( ( $true != $true )
    | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,z),vAPP(name,late_subject,late_InputS,b)) )
    | ~ spl225_27
    | ~ spl225_427 ),
    inference(superposition,[],[f7132,f2406]) ).

thf(f11105,plain,
    ( spl225_554
    | ~ spl225_32
    | ~ spl225_396 ),
    inference(avatar_split_clause,[],[f6841,f6696,f2427,f11102]) ).

thf(f11102,plain,
    ( spl225_554
  <=> ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,q)),q_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_554])]) ).

thf(f2427,plain,
    ( spl225_32
  <=> ! [X0: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_32])]) ).

thf(f6696,plain,
    ( spl225_396
  <=> ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q_a) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_396])]) ).

thf(f6841,plain,
    ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,q)),q_a) )
    | ~ spl225_32
    | ~ spl225_396 ),
    inference(trivial_inequality_removal,[],[f6838]) ).

thf(f6838,plain,
    ( ( $true != $true )
    | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,q)),q_a) )
    | ~ spl225_32
    | ~ spl225_396 ),
    inference(superposition,[],[f6697,f2428]) ).

thf(f2428,plain,
    ( ! [X0: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),X0) )
    | ~ spl225_32 ),
    inference(avatar_component_clause,[],[f2427]) ).

thf(f6697,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q_a) ) )
    | ~ spl225_396 ),
    inference(avatar_component_clause,[],[f6696]) ).

thf(f11085,plain,
    ( spl225_553
    | ~ spl225_34
    | ~ spl225_195
    | ~ spl225_200 ),
    inference(avatar_split_clause,[],[f4591,f4365,f4345,f2443,f11083]) ).

thf(f11083,plain,
    ( spl225_553
  <=> ! [X0: produc367475239e_name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_553])]) ).

thf(f2443,plain,
    ( spl225_34
  <=> ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_34])]) ).

thf(f4345,plain,
    ( spl225_195
  <=> ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_195])]) ).

thf(f4365,plain,
    ( spl225_200
  <=> ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_200])]) ).

thf(f4591,plain,
    ( ! [X0: produc367475239e_name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1)) = X1 )
    | ~ spl225_34
    | ~ spl225_195
    | ~ spl225_200 ),
    inference(forward_demodulation,[],[f4590,f2444]) ).

thf(f2444,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0)) = X0 )
    | ~ spl225_34 ),
    inference(avatar_component_clause,[],[f2443]) ).

thf(f4590,plain,
    ( ! [X0: produc367475239e_name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0))),nil_Pr743626285e_name)),X1)) = X1 )
    | ~ spl225_34
    | ~ spl225_195
    | ~ spl225_200 ),
    inference(forward_demodulation,[],[f4562,f4346]) ).

thf(f4346,plain,
    ( ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) )
    | ~ spl225_195 ),
    inference(avatar_component_clause,[],[f4345]) ).

thf(f4562,plain,
    ( ! [X0: produc367475239e_name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK49,X0)),vAPP(produc367475239e_name,name,sK48,X0))),nil_Pr743626285e_name)),X1)) = X1 )
    | ~ spl225_34
    | ~ spl225_200 ),
    inference(superposition,[],[f4366,f2444]) ).

thf(f4366,plain,
    ( ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 )
    | ~ spl225_200 ),
    inference(avatar_component_clause,[],[f4365]) ).

thf(f10765,plain,
    ( spl225_552
    | ~ spl225_8
    | spl225_492 ),
    inference(avatar_split_clause,[],[f9019,f8914,f2296,f10763]) ).

thf(f10763,plain,
    ( spl225_552
  <=> ! [X0: $o] :
        ( ( $false != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_552])]) ).

thf(f8914,plain,
    ( spl225_492
  <=> ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_492])]) ).

thf(f9019,plain,
    ( ! [X0: $o] :
        ( ( $false != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) )
        | ( $false = X0 ) )
    | ~ spl225_8
    | spl225_492 ),
    inference(superposition,[],[f8915,f2297]) ).

thf(f8915,plain,
    ( ( $false != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) )
    | spl225_492 ),
    inference(avatar_component_clause,[],[f8914]) ).

thf(f10132,plain,
    ( ~ spl225_477
    | ~ spl225_492 ),
    inference(avatar_contradiction_clause,[],[f10131]) ).

thf(f10131,plain,
    ( $false
    | ~ spl225_477
    | ~ spl225_492 ),
    inference(trivial_inequality_removal,[],[f10130]) ).

thf(f10130,plain,
    ( ( $true = $false )
    | ~ spl225_477
    | ~ spl225_492 ),
    inference(forward_demodulation,[],[f8106,f8916]) ).

thf(f8916,plain,
    ( ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) )
    | ~ spl225_492 ),
    inference(avatar_component_clause,[],[f8914]) ).

thf(f8106,plain,
    ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) )
    | ~ spl225_477 ),
    inference(avatar_component_clause,[],[f8104]) ).

thf(f8104,plain,
    ( spl225_477
  <=> ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_477])]) ).

thf(f10121,plain,
    ~ spl225_548,
    inference(avatar_contradiction_clause,[],[f10120]) ).

thf(f10120,plain,
    ( $false
    | ~ spl225_548 ),
    inference(equality_resolution,[],[f9826]) ).

thf(f9826,plain,
    ( ! [X2: late_freeRes] : ( late_TauR != X2 )
    | ~ spl225_548 ),
    inference(avatar_component_clause,[],[f9825]) ).

thf(f9825,plain,
    ( spl225_548
  <=> ! [X2: late_freeRes] : ( late_TauR != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_548])]) ).

thf(f10117,plain,
    ( spl225_551
    | ~ spl225_56
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3037,f3016,f2547,f10115]) ).

thf(f10115,plain,
    ( spl225_551
  <=> ! [X0: name,X1: name] :
        ( ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_551])]) ).

thf(f2547,plain,
    ( spl225_56
  <=> ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_56])]) ).

thf(f3037,plain,
    ( ! [X0: name,X1: name] :
        ( ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),X1),X0)) ) )
    | ~ spl225_56
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3024]) ).

thf(f3024,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),X1),X0)) ) )
    | ~ spl225_56
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2549]) ).

thf(f2549,plain,
    ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true )
    | ~ spl225_56 ),
    inference(avatar_component_clause,[],[f2547]) ).

thf(f10113,plain,
    ( spl225_550
    | ~ spl225_57
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3033,f3016,f2552,f10111]) ).

thf(f10111,plain,
    ( spl225_550
  <=> ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_550])]) ).

thf(f3033,plain,
    ( ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),X1),X0)) ) )
    | ~ spl225_57
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3028]) ).

thf(f3028,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),X1),X0)) ) )
    | ~ spl225_57
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2554]) ).

thf(f10109,plain,
    ( spl225_549
    | ~ spl225_60
    | ~ spl225_98 ),
    inference(avatar_split_clause,[],[f2888,f2862,f2571,f10107]) ).

thf(f10107,plain,
    ( spl225_549
  <=> ! [X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)),X1)) )
        | ( nil_Pr743626285e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_549])]) ).

thf(f2571,plain,
    ( spl225_60
  <=> ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)) = X0 )
        | ( nil_Pr743626285e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_60])]) ).

thf(f2862,plain,
    ( spl225_98
  <=> ! [X2: name,X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_98])]) ).

thf(f2888,plain,
    ( ! [X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)),X1)) )
        | ( nil_Pr743626285e_name = X0 ) )
    | ~ spl225_60
    | ~ spl225_98 ),
    inference(superposition,[],[f2863,f2572]) ).

thf(f2572,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)) = X0 )
        | ( nil_Pr743626285e_name = X0 ) )
    | ~ spl225_60 ),
    inference(avatar_component_clause,[],[f2571]) ).

thf(f2863,plain,
    ( ! [X2: name,X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) )
    | ~ spl225_98 ),
    inference(avatar_component_clause,[],[f2862]) ).

thf(f9827,plain,
    ( spl225_548
    | ~ spl225_21
    | ~ spl225_532 ),
    inference(avatar_split_clause,[],[f9691,f9643,f2377,f9825]) ).

thf(f2377,plain,
    ( spl225_21
  <=> ! [X0: name,X1: name] : ( late_TauR != vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_21])]) ).

thf(f9643,plain,
    ( spl225_532
  <=> ! [X0: late_freeRes,X1: late_freeRes] : ( X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_532])]) ).

thf(f9691,plain,
    ( ! [X2: late_freeRes] : ( late_TauR != X2 )
    | ~ spl225_21
    | ~ spl225_532 ),
    inference(superposition,[],[f2378,f9644]) ).

thf(f9644,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes] : ( X0 = X1 )
    | ~ spl225_532 ),
    inference(avatar_component_clause,[],[f9643]) ).

thf(f2378,plain,
    ( ! [X0: name,X1: name] : ( late_TauR != vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) )
    | ~ spl225_21 ),
    inference(avatar_component_clause,[],[f2377]) ).

thf(f9793,plain,
    ( spl225_547
    | ~ spl225_34
    | ~ spl225_204 ),
    inference(avatar_split_clause,[],[f4669,f4384,f2443,f9791]) ).

thf(f9791,plain,
    ( spl225_547
  <=> ! [X0: produc367475239e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_547])]) ).

thf(f4384,plain,
    ( spl225_204
  <=> ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_204])]) ).

thf(f4669,plain,
    ( ! [X0: produc367475239e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1)) = X1 )
    | ~ spl225_34
    | ~ spl225_204 ),
    inference(superposition,[],[f4385,f2444]) ).

thf(f4385,plain,
    ( ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 )
    | ~ spl225_204 ),
    inference(avatar_component_clause,[],[f4384]) ).

thf(f9789,plain,
    ( spl225_546
    | ~ spl225_34
    | ~ spl225_202 ),
    inference(avatar_split_clause,[],[f4601,f4373,f2443,f9787]) ).

thf(f9787,plain,
    ( spl225_546
  <=> ! [X0: produc367475239e_name,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_546])]) ).

thf(f4373,plain,
    ( spl225_202
  <=> ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_202])]) ).

thf(f4601,plain,
    ( ! [X0: produc367475239e_name,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1)) = X1 )
    | ~ spl225_34
    | ~ spl225_202 ),
    inference(superposition,[],[f4374,f2444]) ).

thf(f4374,plain,
    ( ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 )
    | ~ spl225_202 ),
    inference(avatar_component_clause,[],[f4373]) ).

thf(f9785,plain,
    ( spl225_545
    | ~ spl225_18
    | ~ spl225_98
    | ~ spl225_162 ),
    inference(avatar_split_clause,[],[f3979,f3532,f2862,f2365,f9783]) ).

thf(f9783,plain,
    ( spl225_545
  <=> ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_545])]) ).

thf(f2365,plain,
    ( spl225_18
  <=> ! [X0: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_18])]) ).

thf(f3532,plain,
    ( spl225_162
  <=> ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_162])]) ).

thf(f3979,plain,
    ( ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2)) = X2 )
    | ~ spl225_18
    | ~ spl225_98
    | ~ spl225_162 ),
    inference(forward_demodulation,[],[f3961,f2366]) ).

thf(f2366,plain,
    ( ! [X0: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X0) = X0 )
    | ~ spl225_18 ),
    inference(avatar_component_clause,[],[f2365]) ).

thf(f3961,plain,
    ( ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2))) = X2 )
    | ~ spl225_98
    | ~ spl225_162 ),
    inference(superposition,[],[f3533,f2863]) ).

thf(f3533,plain,
    ( ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2)) = X2 )
    | ~ spl225_162 ),
    inference(avatar_component_clause,[],[f3532]) ).

thf(f9781,plain,
    ( spl225_544
    | ~ spl225_18
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(avatar_split_clause,[],[f3945,f3528,f2862,f2365,f9779]) ).

thf(f9779,plain,
    ( spl225_544
  <=> ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_544])]) ).

thf(f3528,plain,
    ( spl225_161
  <=> ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_161])]) ).

thf(f3945,plain,
    ( ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X2) )
    | ~ spl225_18
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(forward_demodulation,[],[f3924,f2366]) ).

thf(f3924,plain,
    ( ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X2)) )
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(superposition,[],[f3529,f2863]) ).

thf(f3529,plain,
    ( ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2) )
    | ~ spl225_161 ),
    inference(avatar_component_clause,[],[f3528]) ).

thf(f9777,plain,
    ( spl225_543
    | ~ spl225_54
    | ~ spl225_160 ),
    inference(avatar_split_clause,[],[f3910,f3524,f2539,f9775]) ).

thf(f9775,plain,
    ( spl225_543
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_543])]) ).

thf(f3524,plain,
    ( spl225_160
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_160])]) ).

thf(f3910,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2))) )
    | ~ spl225_54
    | ~ spl225_160 ),
    inference(superposition,[],[f2540,f3525]) ).

thf(f3525,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_160 ),
    inference(avatar_component_clause,[],[f3524]) ).

thf(f9685,plain,
    ( spl225_542
    | ~ spl225_18
    | ~ spl225_157 ),
    inference(avatar_split_clause,[],[f3835,f3512,f2365,f9683]) ).

thf(f9683,plain,
    ( spl225_542
  <=> ! [X0: name,X1: list_name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,nil_Pr743626285e_name),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X0),X1)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X0),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,nil_Pr743626285e_name),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_542])]) ).

thf(f3512,plain,
    ( spl225_157
  <=> ! [X2: list_name,X0: list_P227219501e_name,X1: name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X1),X2)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_157])]) ).

thf(f3835,plain,
    ( ! [X0: name,X1: list_name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,nil_Pr743626285e_name),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X0),X1)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X0),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,nil_Pr743626285e_name),X1)) )
    | ~ spl225_18
    | ~ spl225_157 ),
    inference(superposition,[],[f3513,f2366]) ).

thf(f3513,plain,
    ( ! [X2: list_name,X0: list_P227219501e_name,X1: name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X1),X2)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),X2)) )
    | ~ spl225_157 ),
    inference(avatar_component_clause,[],[f3512]) ).

thf(f9681,plain,
    ( spl225_541
    | ~ spl225_11
    | ~ spl225_154 ),
    inference(avatar_split_clause,[],[f3793,f3500,f2337,f9679]) ).

thf(f9679,plain,
    ( spl225_541
  <=> ! [X0: list_P227219501e_name,X1: name] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,late_TauR),X1)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,late_TauR),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_541])]) ).

thf(f2337,plain,
    ( spl225_11
  <=> ! [X0: list_P227219501e_name] : ( late_TauR = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),late_TauR) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_11])]) ).

thf(f3500,plain,
    ( spl225_154
  <=> ! [X2: name,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X1),X2)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_154])]) ).

thf(f3793,plain,
    ( ! [X0: list_P227219501e_name,X1: name] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,late_TauR),X1)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,late_TauR),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_154 ),
    inference(superposition,[],[f3501,f2338]) ).

thf(f2338,plain,
    ( ! [X0: list_P227219501e_name] : ( late_TauR = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),late_TauR) )
    | ~ spl225_11 ),
    inference(avatar_component_clause,[],[f2337]) ).

thf(f3501,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X1),X2)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) )
    | ~ spl225_154 ),
    inference(avatar_component_clause,[],[f3500]) ).

thf(f9677,plain,
    ( spl225_540
    | ~ spl225_11
    | ~ spl225_147 ),
    inference(avatar_split_clause,[],[f3712,f3472,f2337,f9675]) ).

thf(f9675,plain,
    ( spl225_540
  <=> ! [X0: list_P227219501e_name,X1: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X1)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_540])]) ).

thf(f3472,plain,
    ( spl225_147
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_147])]) ).

thf(f3712,plain,
    ( ! [X0: list_P227219501e_name,X1: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X1)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_147 ),
    inference(superposition,[],[f3473,f2338]) ).

thf(f3473,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_147 ),
    inference(avatar_component_clause,[],[f3472]) ).

thf(f9673,plain,
    ( spl225_539
    | ~ spl225_19
    | ~ spl225_144 ),
    inference(avatar_split_clause,[],[f3673,f3446,f2369,f9671]) ).

thf(f9671,plain,
    ( spl225_539
  <=> ! [X0: pi,X1: list_pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,nil_Pr743626285e_name),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X0),X1)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X0),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,nil_Pr743626285e_name),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_539])]) ).

thf(f2369,plain,
    ( spl225_19
  <=> ! [X0: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_19])]) ).

thf(f3446,plain,
    ( spl225_144
  <=> ! [X2: list_pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X1),X2)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_144])]) ).

thf(f3673,plain,
    ( ! [X0: pi,X1: list_pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,nil_Pr743626285e_name),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X0),X1)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X0),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,nil_Pr743626285e_name),X1)) )
    | ~ spl225_19
    | ~ spl225_144 ),
    inference(superposition,[],[f3447,f2370]) ).

thf(f2370,plain,
    ( ! [X0: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X0) = X0 )
    | ~ spl225_19 ),
    inference(avatar_component_clause,[],[f2369]) ).

thf(f3447,plain,
    ( ! [X2: list_pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X1),X2)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),X2)) )
    | ~ spl225_144 ),
    inference(avatar_component_clause,[],[f3446]) ).

thf(f9669,plain,
    ( spl225_538
    | ~ spl225_17
    | ~ spl225_143 ),
    inference(avatar_split_clause,[],[f3669,f3442,f2361,f9667]) ).

thf(f9667,plain,
    ( spl225_538
  <=> ! [X0: late_subject,X1: list_Late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,nil_Pr743626285e_name),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X0),X1)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X0),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,nil_Pr743626285e_name),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_538])]) ).

thf(f2361,plain,
    ( spl225_17
  <=> ! [X0: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_17])]) ).

thf(f3442,plain,
    ( spl225_143
  <=> ! [X2: list_Late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X1),X2)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_143])]) ).

thf(f3669,plain,
    ( ! [X0: late_subject,X1: list_Late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,nil_Pr743626285e_name),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X0),X1)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X0),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,nil_Pr743626285e_name),X1)) )
    | ~ spl225_17
    | ~ spl225_143 ),
    inference(superposition,[],[f3443,f2362]) ).

thf(f2362,plain,
    ( ! [X0: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X0) = X0 )
    | ~ spl225_17 ),
    inference(avatar_component_clause,[],[f2361]) ).

thf(f3443,plain,
    ( ! [X2: list_Late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X1),X2)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),X2)) )
    | ~ spl225_143 ),
    inference(avatar_component_clause,[],[f3442]) ).

thf(f9665,plain,
    ( spl225_537
    | ~ spl225_16
    | ~ spl225_142 ),
    inference(avatar_split_clause,[],[f3663,f3438,f2357,f9663]) ).

thf(f9663,plain,
    ( spl225_537
  <=> ! [X0: late_freeRes,X1: list_Late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,nil_Pr743626285e_name),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X0),X1)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,nil_Pr743626285e_name),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_537])]) ).

thf(f2357,plain,
    ( spl225_16
  <=> ! [X0: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_16])]) ).

thf(f3438,plain,
    ( spl225_142
  <=> ! [X2: list_Late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X1),X2)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_142])]) ).

thf(f3663,plain,
    ( ! [X0: late_freeRes,X1: list_Late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,nil_Pr743626285e_name),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X0),X1)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_142 ),
    inference(superposition,[],[f3439,f2358]) ).

thf(f2358,plain,
    ( ! [X0: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X0) = X0 )
    | ~ spl225_16 ),
    inference(avatar_component_clause,[],[f2357]) ).

thf(f3439,plain,
    ( ! [X2: list_Late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X1),X2)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),X2)) )
    | ~ spl225_142 ),
    inference(avatar_component_clause,[],[f3438]) ).

thf(f9661,plain,
    ( spl225_536
    | ~ spl225_11
    | ~ spl225_142 ),
    inference(avatar_split_clause,[],[f3662,f3438,f2337,f9659]) ).

thf(f9659,plain,
    ( spl225_536
  <=> ! [X0: list_P227219501e_name,X1: list_Late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,late_TauR),X1)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,late_TauR),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_536])]) ).

thf(f3662,plain,
    ( ! [X0: list_P227219501e_name,X1: list_Late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,late_TauR),X1)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,late_TauR),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_142 ),
    inference(superposition,[],[f3439,f2338]) ).

thf(f9657,plain,
    ( spl225_535
    | ~ spl225_11
    | ~ spl225_139 ),
    inference(avatar_split_clause,[],[f3631,f3426,f2337,f9655]) ).

thf(f9655,plain,
    ( spl225_535
  <=> ! [X0: list_P227219501e_name,X1: pi] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X0),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,late_TauR),X1)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,late_TauR),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_535])]) ).

thf(f3426,plain,
    ( spl225_139
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X0),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X1),X2)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_139])]) ).

thf(f3631,plain,
    ( ! [X0: list_P227219501e_name,X1: pi] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X0),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,late_TauR),X1)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,late_TauR),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_139 ),
    inference(superposition,[],[f3427,f2338]) ).

thf(f3427,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X0),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X1),X2)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_139 ),
    inference(avatar_component_clause,[],[f3426]) ).

thf(f9653,plain,
    ( spl225_534
    | ~ spl225_11
    | ~ spl225_137 ),
    inference(avatar_split_clause,[],[f3600,f3418,f2337,f9651]) ).

thf(f9651,plain,
    ( spl225_534
  <=> ! [X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X0),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,late_TauR),X1)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,late_TauR),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_534])]) ).

thf(f3418,plain,
    ( spl225_137
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X0),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X1),X2)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_137])]) ).

thf(f3600,plain,
    ( ! [X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X0),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,late_TauR),X1)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,late_TauR),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_137 ),
    inference(superposition,[],[f3419,f2338]) ).

thf(f3419,plain,
    ( ! [X2: late_subject,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X0),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X1),X2)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
    | ~ spl225_137 ),
    inference(avatar_component_clause,[],[f3418]) ).

thf(f9649,plain,
    ( spl225_533
    | ~ spl225_11
    | ~ spl225_136 ),
    inference(avatar_split_clause,[],[f3590,f3414,f2337,f9647]) ).

thf(f9647,plain,
    ( spl225_533
  <=> ! [X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X0),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X1),late_TauR)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),late_TauR) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_533])]) ).

thf(f3414,plain,
    ( spl225_136
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X0),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X1),X2)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_136])]) ).

thf(f3590,plain,
    ( ! [X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X0),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X1),late_TauR)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),late_TauR) )
    | ~ spl225_11
    | ~ spl225_136 ),
    inference(superposition,[],[f3415,f2338]) ).

thf(f3415,plain,
    ( ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X0),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X1),X2)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
    | ~ spl225_136 ),
    inference(avatar_component_clause,[],[f3414]) ).

thf(f9645,plain,
    ( spl225_477
    | spl225_532
    | ~ spl225_43
    | ~ spl225_463 ),
    inference(avatar_split_clause,[],[f8041,f7821,f2479,f9643,f8104]) ).

thf(f2479,plain,
    ( spl225_43
  <=> ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$true),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_43])]) ).

thf(f7821,plain,
    ( spl225_463
  <=> ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_463])]) ).

thf(f8041,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes] :
        ( ( X0 = X1 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) ) )
    | ~ spl225_43
    | ~ spl225_463 ),
    inference(superposition,[],[f7822,f2480]) ).

thf(f2480,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$true),X0),X1) = X0 )
    | ~ spl225_43 ),
    inference(avatar_component_clause,[],[f2479]) ).

thf(f7822,plain,
    ( ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_463 ),
    inference(avatar_component_clause,[],[f7821]) ).

thf(f9641,plain,
    ( spl225_531
    | ~ spl225_11
    | ~ spl225_134 ),
    inference(avatar_split_clause,[],[f3571,f3406,f2337,f9639]) ).

thf(f9639,plain,
    ( spl225_531
  <=> ! [X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X1),late_TauR)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),late_TauR) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_531])]) ).

thf(f3406,plain,
    ( spl225_134
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X1),X2)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_134])]) ).

thf(f3571,plain,
    ( ! [X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X1),late_TauR)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),late_TauR) )
    | ~ spl225_11
    | ~ spl225_134 ),
    inference(superposition,[],[f3407,f2338]) ).

thf(f3407,plain,
    ( ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X1),X2)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
    | ~ spl225_134 ),
    inference(avatar_component_clause,[],[f3406]) ).

thf(f9637,plain,
    ( spl225_530
    | ~ spl225_11
    | ~ spl225_134 ),
    inference(avatar_split_clause,[],[f3567,f3406,f2337,f9635]) ).

thf(f9635,plain,
    ( spl225_530
  <=> ! [X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,late_TauR),X1)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,late_TauR),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_530])]) ).

thf(f3567,plain,
    ( ! [X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,late_TauR),X1)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,late_TauR),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_134 ),
    inference(superposition,[],[f3407,f2338]) ).

thf(f9633,plain,
    ( spl225_529
    | ~ spl225_11
    | ~ spl225_132 ),
    inference(avatar_split_clause,[],[f3540,f3398,f2337,f9631]) ).

thf(f9631,plain,
    ( spl225_529
  <=> ! [X0: list_P227219501e_name,X1: pi_Rep] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X0),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,late_TauR),X1)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,late_TauR),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_529])]) ).

thf(f3398,plain,
    ( spl225_132
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X0),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X1),X2)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_132])]) ).

thf(f3540,plain,
    ( ! [X0: list_P227219501e_name,X1: pi_Rep] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X0),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,late_TauR),X1)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,late_TauR),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)) )
    | ~ spl225_11
    | ~ spl225_132 ),
    inference(superposition,[],[f3399,f2338]) ).

thf(f3399,plain,
    ( ! [X2: pi_Rep,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X0),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X1),X2)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
    | ~ spl225_132 ),
    inference(avatar_component_clause,[],[f3398]) ).

thf(f9629,plain,
    ( spl225_528
    | ~ spl225_8
    | ~ spl225_97 ),
    inference(avatar_split_clause,[],[f2884,f2858,f2296,f9627]) ).

thf(f9627,plain,
    ( spl225_528
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_528])]) ).

thf(f2884,plain,
    ( ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) ) )
    | ~ spl225_8
    | ~ spl225_97 ),
    inference(trivial_inequality_removal,[],[f2883]) ).

thf(f2883,plain,
    ( ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true != $true )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) ) )
    | ~ spl225_8
    | ~ spl225_97 ),
    inference(superposition,[],[f2859,f2297]) ).

thf(f9625,plain,
    ( spl225_527
    | ~ spl225_8
    | ~ spl225_96 ),
    inference(avatar_split_clause,[],[f2875,f2854,f2296,f9623]) ).

thf(f9623,plain,
    ( spl225_527
  <=> ! [X0: late_freeRes > $o,X1: late_freeRes] :
        ( ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
        | ( $true = vAPP(late_freeRes,$o,X0,X1) )
        | ( $false = vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_527])]) ).

thf(f2854,plain,
    ( spl225_96
  <=> ! [X0: late_freeRes > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_freeRes,$o,X0,X1) )
        | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
        | ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_96])]) ).

thf(f2875,plain,
    ( ! [X0: late_freeRes > $o,X1: late_freeRes] :
        ( ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
        | ( $true = vAPP(late_freeRes,$o,X0,X1) )
        | ( $false = vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) )
    | ~ spl225_8
    | ~ spl225_96 ),
    inference(trivial_inequality_removal,[],[f2874]) ).

thf(f2874,plain,
    ( ! [X0: late_freeRes > $o,X1: late_freeRes] :
        ( ( $true != $true )
        | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
        | ( $true = vAPP(late_freeRes,$o,X0,X1) )
        | ( $false = vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) )
    | ~ spl225_8
    | ~ spl225_96 ),
    inference(superposition,[],[f2855,f2297]) ).

thf(f2855,plain,
    ( ! [X0: late_freeRes > $o,X1: late_freeRes] :
        ( ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) )
        | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
        | ( $true = vAPP(late_freeRes,$o,X0,X1) ) )
    | ~ spl225_96 ),
    inference(avatar_component_clause,[],[f2854]) ).

thf(f9621,plain,
    ( spl225_526
    | ~ spl225_93 ),
    inference(avatar_split_clause,[],[f2847,f2828,f9619]) ).

thf(f9619,plain,
    ( spl225_526
  <=> ! [X0: late_subject,X1: late_subject] :
        ( ( vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_526])]) ).

thf(f2828,plain,
    ( spl225_93
  <=> ! [X0: late_subject > $o,X1: late_subject] :
        ( ( $true = vAPP(late_subject,$o,X0,X1) )
        | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
        | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_93])]) ).

thf(f2847,plain,
    ( ! [X0: late_subject,X1: late_subject] :
        ( ( vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_93 ),
    inference(equality_proxy_clausification,[],[f2846]) ).

thf(f2846,plain,
    ( ! [X0: late_subject,X1: late_subject] :
        ( ( vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0),X1) ) )
    | ~ spl225_93 ),
    inference(equality_proxy_clausification,[],[f2845]) ).

thf(f2845,plain,
    ( ! [X0: late_subject,X1: late_subject] :
        ( ( vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0))) != X0 )
        | ( $true != vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0),vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0)))) )
        | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0),X1) ) )
    | ~ spl225_93 ),
    inference(equality_proxy_clausification,[],[f2842]) ).

thf(f2842,plain,
    ( ! [X0: late_subject,X1: late_subject] :
        ( ( $true != vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0),vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0)))) )
        | ( $true != vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0),vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0)))) )
        | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X0),X1) ) )
    | ~ spl225_93 ),
    inference(primitive_instantiation,[],[f2829]) ).

thf(f2829,plain,
    ( ! [X0: late_subject > $o,X1: late_subject] :
        ( ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) )
        | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
        | ( $true = vAPP(late_subject,$o,X0,X1) ) )
    | ~ spl225_93 ),
    inference(avatar_component_clause,[],[f2828]) ).

thf(f9546,plain,
    ( spl225_525
    | ~ spl225_32
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3032,f3016,f2427,f9544]) ).

thf(f9544,plain,
    ( spl225_525
  <=> ! [X2: name,X0: pi,X1: name] :
        ( ( vAPP(pi,name,sK47,X0) = X1 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_525])]) ).

thf(f3032,plain,
    ( ! [X2: name,X0: pi,X1: name] :
        ( ( vAPP(pi,name,sK47,X0) = X1 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X1)) ) )
    | ~ spl225_32
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3029]) ).

thf(f3029,plain,
    ( ! [X2: name,X0: pi,X1: name] :
        ( ( $true != $true )
        | ( vAPP(pi,name,sK47,X0) = X1 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X1)) ) )
    | ~ spl225_32
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2428]) ).

thf(f9542,plain,
    ( spl225_524
    | ~ spl225_86 ),
    inference(avatar_split_clause,[],[f2788,f2746,f9540]) ).

thf(f9540,plain,
    ( spl225_524
  <=> ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK65,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_524])]) ).

thf(f2746,plain,
    ( spl225_86
  <=> ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_86])]) ).

thf(f2788,plain,
    ( ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK65,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_86 ),
    inference(equality_proxy_clausification,[],[f2787]) ).

thf(f2787,plain,
    ( ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK65,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))) != X0 )
        | ( $true = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X1) ) )
    | ~ spl225_86 ),
    inference(equality_proxy_clausification,[],[f2784]) ).

thf(f2784,plain,
    ( ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( $true != vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK65,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0)))) )
        | ( $true = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X1) ) )
    | ~ spl225_86 ),
    inference(primitive_instantiation,[],[f2747]) ).

thf(f2747,plain,
    ( ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) )
        | ( $true = vAPP(produc367475239e_name,$o,X0,X1) ) )
    | ~ spl225_86 ),
    inference(avatar_component_clause,[],[f2746]) ).

thf(f9538,plain,
    ( spl225_523
    | ~ spl225_85 ),
    inference(avatar_split_clause,[],[f2780,f2741,f9536]) ).

thf(f9536,plain,
    ( spl225_523
  <=> ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK63,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_523])]) ).

thf(f2741,plain,
    ( spl225_85
  <=> ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_85])]) ).

thf(f2780,plain,
    ( ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK63,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_85 ),
    inference(equality_proxy_clausification,[],[f2779]) ).

thf(f2779,plain,
    ( ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK63,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))) != X0 )
        | ( $true = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X1) ) )
    | ~ spl225_85 ),
    inference(equality_proxy_clausification,[],[f2776]) ).

thf(f2776,plain,
    ( ! [X0: produc367475239e_name,X1: produc367475239e_name] :
        ( ( $true != vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0))),vAPP(sTfun(produc367475239e_name,$o),name,sK63,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0)))) )
        | ( $true = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X1) ) )
    | ~ spl225_85 ),
    inference(primitive_instantiation,[],[f2742]) ).

thf(f2742,plain,
    ( ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) )
        | ( $true = vAPP(produc367475239e_name,$o,X0,X1) ) )
    | ~ spl225_85 ),
    inference(avatar_component_clause,[],[f2741]) ).

thf(f9534,plain,
    ( spl225_522
    | ~ spl225_84 ),
    inference(avatar_split_clause,[],[f2772,f2737,f9532]) ).

thf(f9532,plain,
    ( spl225_522
  <=> ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_522])]) ).

thf(f2737,plain,
    ( spl225_84
  <=> ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_84])]) ).

thf(f2772,plain,
    ( ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_84 ),
    inference(equality_proxy_clausification,[],[f2771]) ).

thf(f2771,plain,
    ( ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))) != X0 )
        | ( $true = vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0),X1) ) )
    | ~ spl225_84 ),
    inference(equality_proxy_clausification,[],[f2768]) ).

thf(f2768,plain,
    ( ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0)))) )
        | ( $true = vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0),X1) ) )
    | ~ spl225_84 ),
    inference(primitive_instantiation,[],[f2738]) ).

thf(f2738,plain,
    ( ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) )
        | ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) ) )
    | ~ spl225_84 ),
    inference(avatar_component_clause,[],[f2737]) ).

thf(f9530,plain,
    ( spl225_521
    | ~ spl225_83 ),
    inference(avatar_split_clause,[],[f2764,f2733,f9528]) ).

thf(f9528,plain,
    ( spl225_521
  <=> ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_521])]) ).

thf(f2733,plain,
    ( spl225_83
  <=> ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_83])]) ).

thf(f2764,plain,
    ( ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_83 ),
    inference(equality_proxy_clausification,[],[f2763]) ).

thf(f2763,plain,
    ( ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))) != X0 )
        | ( $true = vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0),X1) ) )
    | ~ spl225_83 ),
    inference(equality_proxy_clausification,[],[f2760]) ).

thf(f2760,plain,
    ( ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0))),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0)))) )
        | ( $true = vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),X0),X1) ) )
    | ~ spl225_83 ),
    inference(primitive_instantiation,[],[f2734]) ).

thf(f2734,plain,
    ( ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) )
        | ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) ) )
    | ~ spl225_83 ),
    inference(avatar_component_clause,[],[f2733]) ).

thf(f9526,plain,
    ( spl225_520
    | ~ spl225_52
    | ~ spl225_71 ),
    inference(avatar_split_clause,[],[f2642,f2637,f2530,f9524]) ).

thf(f9524,plain,
    ( spl225_520
  <=> ! [X0: late_subject,X1: list_P227219501e_name] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),vAPP(late_subject,name,sK18,X0))) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X0) )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_520])]) ).

thf(f2530,plain,
    ( spl225_52
  <=> ! [X0: late_subject] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(late_subject,name,sK18,X0)) = X0 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_52])]) ).

thf(f2637,plain,
    ( spl225_71
  <=> ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_BoundOutputS,X1)) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_71])]) ).

thf(f2642,plain,
    ( ! [X0: late_subject,X1: list_P227219501e_name] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),vAPP(late_subject,name,sK18,X0))) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X0) )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) )
    | ~ spl225_52
    | ~ spl225_71 ),
    inference(superposition,[],[f2638,f2531]) ).

thf(f2531,plain,
    ( ! [X0: late_subject] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(late_subject,name,sK18,X0)) = X0 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) )
    | ~ spl225_52 ),
    inference(avatar_component_clause,[],[f2530]) ).

thf(f2638,plain,
    ( ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_BoundOutputS,X1)) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) )
    | ~ spl225_71 ),
    inference(avatar_component_clause,[],[f2637]) ).

thf(f9489,plain,
    ( spl225_519
    | ~ spl225_8
    | ~ spl225_477 ),
    inference(avatar_split_clause,[],[f8978,f8104,f2296,f9487]) ).

thf(f9487,plain,
    ( spl225_519
  <=> ! [X0: $o] :
        ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_519])]) ).

thf(f8978,plain,
    ( ! [X0: $o] :
        ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_477 ),
    inference(duplicate_literal_removal,[],[f8976]) ).

thf(f8976,plain,
    ( ! [X0: $o] :
        ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) )
        | ( $false = X0 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_477 ),
    inference(binary_proxy_clausification,[],[f8967]) ).

thf(f8967,plain,
    ( ! [X0: $o] :
        ( ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) = X0 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_477 ),
    inference(superposition,[],[f8106,f2297]) ).

thf(f9066,plain,
    ( spl225_518
    | spl225_5
    | ~ spl225_54
    | ~ spl225_491 ),
    inference(avatar_split_clause,[],[f8928,f8865,f2539,f2281,f9063]) ).

thf(f9063,plain,
    ( spl225_518
  <=> ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),q2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_518])]) ).

thf(f2281,plain,
    ( spl225_5
  <=> ( x = z ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_5])]) ).

thf(f8865,plain,
    ( spl225_491
  <=> ! [X0: name] :
        ( ( z = X0 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_491])]) ).

thf(f8928,plain,
    ( ( x = z )
    | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),q2) )
    | ~ spl225_54
    | ~ spl225_491 ),
    inference(trivial_inequality_removal,[],[f8920]) ).

thf(f8920,plain,
    ( ( $true != $true )
    | ( x = z )
    | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),q2) )
    | ~ spl225_54
    | ~ spl225_491 ),
    inference(superposition,[],[f8866,f2540]) ).

thf(f8866,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) )
    | ~ spl225_491 ),
    inference(avatar_component_clause,[],[f8865]) ).

thf(f9053,plain,
    ( spl225_517
    | ~ spl225_69
    | ~ spl225_238 ),
    inference(avatar_split_clause,[],[f5278,f5087,f2629,f9051]) ).

thf(f9051,plain,
    ( spl225_517
  <=> ! [X5: pi,X4: pi,X0: list_P227219501e_name,X3: pi,X2: name,X1: name] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_517])]) ).

thf(f2629,plain,
    ( spl225_69
  <=> ! [X4: pi,X0: name,X3: pi,X2: pi,X1: name] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_69])]) ).

thf(f5087,plain,
    ( spl225_238
  <=> ! [X0: list_P227219501e_name,X3: pi,X2: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_238])]) ).

thf(f5278,plain,
    ( ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: name,X4: pi,X5: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) )
    | ~ spl225_69
    | ~ spl225_238 ),
    inference(superposition,[],[f2630,f5088]) ).

thf(f5088,plain,
    ( ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) )
    | ~ spl225_238 ),
    inference(avatar_component_clause,[],[f5087]) ).

thf(f2630,plain,
    ( ! [X2: pi,X3: pi,X0: name,X1: name,X4: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) )
    | ~ spl225_69 ),
    inference(avatar_component_clause,[],[f2629]) ).

thf(f9049,plain,
    ( spl225_516
    | ~ spl225_68
    | ~ spl225_238 ),
    inference(avatar_split_clause,[],[f5277,f5087,f2625,f9047]) ).

thf(f9047,plain,
    ( spl225_516
  <=> ! [X3: pi,X4: name,X0: list_P227219501e_name,X5: pi,X2: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_516])]) ).

thf(f2625,plain,
    ( spl225_68
  <=> ! [X4: pi,X0: name,X3: name,X2: pi,X1: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_68])]) ).

thf(f5277,plain,
    ( ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: name,X4: name,X5: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X5) )
    | ~ spl225_68
    | ~ spl225_238 ),
    inference(superposition,[],[f2626,f5088]) ).

thf(f2626,plain,
    ( ! [X2: pi,X3: name,X0: name,X1: name,X4: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) )
    | ~ spl225_68 ),
    inference(avatar_component_clause,[],[f2625]) ).

thf(f9045,plain,
    ( spl225_515
    | ~ spl225_67
    | ~ spl225_236 ),
    inference(avatar_split_clause,[],[f5144,f5079,f2621,f9043]) ).

thf(f9043,plain,
    ( spl225_515
  <=> ! [X5: pi,X4: late_freeRes,X0: list_P227219501e_name,X3: pi,X2: name,X1: late_subject] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5) != vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_515])]) ).

thf(f2621,plain,
    ( spl225_67
  <=> ! [X4: pi,X0: late_subject,X3: late_freeRes,X2: pi,X1: name] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4) != vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_67])]) ).

thf(f5079,plain,
    ( spl225_236
  <=> ! [X0: list_P227219501e_name,X3: pi,X2: name,X1: late_subject] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_236])]) ).

thf(f5144,plain,
    ( ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: late_subject,X4: late_freeRes,X5: pi] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5) != vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
    | ~ spl225_67
    | ~ spl225_236 ),
    inference(superposition,[],[f2622,f5080]) ).

thf(f5080,plain,
    ( ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) )
    | ~ spl225_236 ),
    inference(avatar_component_clause,[],[f5079]) ).

thf(f2622,plain,
    ( ! [X2: pi,X3: late_freeRes,X0: late_subject,X1: name,X4: pi] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4) != vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X1),X2) )
    | ~ spl225_67 ),
    inference(avatar_component_clause,[],[f2621]) ).

thf(f9041,plain,
    ( spl225_514
    | ~ spl225_55
    | ~ spl225_233 ),
    inference(avatar_split_clause,[],[f5067,f5053,f2543,f9039]) ).

thf(f9039,plain,
    ( spl225_514
  <=> ! [X3: pi,X4: name,X0: pi,X5: pi,X2: name,X1: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),X1),X2) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_514])]) ).

thf(f2543,plain,
    ( spl225_55
  <=> ! [X2: name,X0: pi,X1: pi,X3: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_55])]) ).

thf(f5053,plain,
    ( spl225_233
  <=> ! [X0: pi,X3: name,X2: name,X1: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),X2),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X3)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_233])]) ).

thf(f5067,plain,
    ( ! [X2: name,X3: pi,X0: pi,X1: name,X4: name,X5: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),X1),X2) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X5) )
    | ~ spl225_55
    | ~ spl225_233 ),
    inference(superposition,[],[f2544,f5054]) ).

thf(f5054,plain,
    ( ! [X2: name,X3: name,X0: pi,X1: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),X2),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X3)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) )
    | ~ spl225_233 ),
    inference(avatar_component_clause,[],[f5053]) ).

thf(f2544,plain,
    ( ! [X2: name,X3: pi,X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X3) )
    | ~ spl225_55 ),
    inference(avatar_component_clause,[],[f2543]) ).

thf(f9037,plain,
    ( spl225_513
    | ~ spl225_54
    | ~ spl225_224 ),
    inference(avatar_split_clause,[],[f4950,f4931,f2539,f9035]) ).

thf(f9035,plain,
    ( spl225_513
  <=> ! [X2: pi,X0: name,X1: name] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_513])]) ).

thf(f4931,plain,
    ( spl225_224
  <=> ! [X2: name,X0: name,X1: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2),X0) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_224])]) ).

thf(f4950,plain,
    ( ! [X2: pi,X0: name,X1: name] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)),X0),X1)) )
    | ~ spl225_54
    | ~ spl225_224 ),
    inference(superposition,[],[f2540,f4932]) ).

thf(f4932,plain,
    ( ! [X2: name,X0: name,X1: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2),X0) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) )
    | ~ spl225_224 ),
    inference(avatar_component_clause,[],[f4931]) ).

thf(f9033,plain,
    ( spl225_512
    | ~ spl225_55
    | ~ spl225_224 ),
    inference(avatar_split_clause,[],[f4949,f4931,f2543,f9031]) ).

thf(f9031,plain,
    ( spl225_512
  <=> ! [X4: pi,X0: name,X3: pi,X2: pi,X1: name] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_512])]) ).

thf(f4949,plain,
    ( ! [X2: pi,X3: pi,X0: name,X1: name,X4: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)),X0),X1) )
    | ~ spl225_55
    | ~ spl225_224 ),
    inference(superposition,[],[f2544,f4932]) ).

thf(f9029,plain,
    ( spl225_511
    | ~ spl225_23
    | ~ spl225_181 ),
    inference(avatar_split_clause,[],[f4238,f4229,f2385,f9027]) ).

thf(f9027,plain,
    ( spl225_511
  <=> ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0)) != X0 )
        | ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 )
        | ( nil_Pr743626285e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_511])]) ).

thf(f2385,plain,
    ( spl225_23
  <=> ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_23])]) ).

thf(f4229,plain,
    ( spl225_181
  <=> ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK12,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0))) = X0 )
        | ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 )
        | ( nil_Pr743626285e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_181])]) ).

thf(f4238,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0)) != X0 )
        | ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 )
        | ( nil_Pr743626285e_name = X0 ) )
    | ~ spl225_23
    | ~ spl225_181 ),
    inference(superposition,[],[f2386,f4230]) ).

thf(f4230,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK12,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0))) = X0 )
        | ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 )
        | ( nil_Pr743626285e_name = X0 ) )
    | ~ spl225_181 ),
    inference(avatar_component_clause,[],[f4229]) ).

thf(f2386,plain,
    ( ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) != X1 )
    | ~ spl225_23 ),
    inference(avatar_component_clause,[],[f2385]) ).

thf(f9025,plain,
    ( spl225_510
    | ~ spl225_29
    | ~ spl225_167 ),
    inference(avatar_split_clause,[],[f4052,f3984,f2414,f9023]) ).

thf(f9023,plain,
    ( spl225_510
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_510])]) ).

thf(f3984,plain,
    ( spl225_167
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_167])]) ).

thf(f4052,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),x)) )
    | ~ spl225_29
    | ~ spl225_167 ),
    inference(trivial_inequality_removal,[],[f4033]) ).

thf(f4033,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),x)) ) )
    | ~ spl225_29
    | ~ spl225_167 ),
    inference(superposition,[],[f3985,f2416]) ).

thf(f3985,plain,
    ( ! [X2: name,X0: name,X1: pi] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) ) )
    | ~ spl225_167 ),
    inference(avatar_component_clause,[],[f3984]) ).

thf(f9018,plain,
    ( spl225_509
    | ~ spl225_24
    | ~ spl225_167 ),
    inference(avatar_split_clause,[],[f4051,f3984,f2389,f9016]) ).

thf(f9016,plain,
    ( spl225_509
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),q2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),X0),y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_509])]) ).

thf(f4051,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),q2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),X0),y)) )
    | ~ spl225_24
    | ~ spl225_167 ),
    inference(trivial_inequality_removal,[],[f4034]) ).

thf(f4034,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),q2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),X0),y)) ) )
    | ~ spl225_24
    | ~ spl225_167 ),
    inference(superposition,[],[f3985,f2391]) ).

thf(f9014,plain,
    ( spl225_508
    | ~ spl225_25
    | ~ spl225_167 ),
    inference(avatar_split_clause,[],[f4050,f3984,f2394,f9012]) ).

thf(f9012,plain,
    ( spl225_508
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_508])]) ).

thf(f4050,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),y)) )
    | ~ spl225_25
    | ~ spl225_167 ),
    inference(trivial_inequality_removal,[],[f4035]) ).

thf(f4035,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),y)) ) )
    | ~ spl225_25
    | ~ spl225_167 ),
    inference(superposition,[],[f3985,f2396]) ).

thf(f9010,plain,
    ( spl225_507
    | ~ spl225_27
    | ~ spl225_167 ),
    inference(avatar_split_clause,[],[f4048,f3984,f2404,f9008]) ).

thf(f9008,plain,
    ( spl225_507
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),z)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_507])]) ).

thf(f4048,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),z)) )
    | ~ spl225_27
    | ~ spl225_167 ),
    inference(trivial_inequality_removal,[],[f4037]) ).

thf(f4037,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X0),z)) ) )
    | ~ spl225_27
    | ~ spl225_167 ),
    inference(superposition,[],[f3985,f2406]) ).

thf(f9006,plain,
    ( spl225_506
    | ~ spl225_26
    | ~ spl225_167 ),
    inference(avatar_split_clause,[],[f4047,f3984,f2399,f9004]) ).

thf(f9004,plain,
    ( spl225_506
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),X0),z)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_506])]) ).

thf(f4047,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),X0),z)) )
    | ~ spl225_26
    | ~ spl225_167 ),
    inference(trivial_inequality_removal,[],[f4038]) ).

thf(f4038,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),p2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),X0),z)) ) )
    | ~ spl225_26
    | ~ spl225_167 ),
    inference(superposition,[],[f3985,f2401]) ).

thf(f9002,plain,
    ( spl225_505
    | ~ spl225_28
    | ~ spl225_167 ),
    inference(avatar_split_clause,[],[f4046,f3984,f2409,f9000]) ).

thf(f9000,plain,
    ( spl225_505
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),q) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),X0),z)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_505])]) ).

thf(f4046,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),q) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),X0),z)) )
    | ~ spl225_28
    | ~ spl225_167 ),
    inference(trivial_inequality_removal,[],[f4039]) ).

thf(f4039,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),q) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),X0),z)) ) )
    | ~ spl225_28
    | ~ spl225_167 ),
    inference(superposition,[],[f3985,f2411]) ).

thf(f8998,plain,
    ( spl225_504
    | ~ spl225_18
    | ~ spl225_37
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(avatar_split_clause,[],[f3944,f3528,f2862,f2455,f2365,f8996]) ).

thf(f8996,plain,
    ( spl225_504
  <=> ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK53,X0)),vAPP(produc367475239e_name,name,sK52,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_504])]) ).

thf(f2455,plain,
    ( spl225_37
  <=> ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK52,X0)),vAPP(produc367475239e_name,name,sK53,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_37])]) ).

thf(f3944,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK53,X0)),vAPP(produc367475239e_name,name,sK52,X0))),X1) )
    | ~ spl225_18
    | ~ spl225_37
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(forward_demodulation,[],[f3943,f2366]) ).

thf(f3943,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1)) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK53,X0)),vAPP(produc367475239e_name,name,sK52,X0))),X1) )
    | ~ spl225_37
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(forward_demodulation,[],[f3919,f2863]) ).

thf(f3919,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK53,X0)),vAPP(produc367475239e_name,name,sK52,X0))),X1) )
    | ~ spl225_37
    | ~ spl225_161 ),
    inference(superposition,[],[f3529,f2456]) ).

thf(f2456,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK52,X0)),vAPP(produc367475239e_name,name,sK53,X0)) = X0 )
    | ~ spl225_37 ),
    inference(avatar_component_clause,[],[f2455]) ).

thf(f8994,plain,
    ( spl225_503
    | ~ spl225_18
    | ~ spl225_34
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(avatar_split_clause,[],[f3942,f3528,f2862,f2443,f2365,f8992]) ).

thf(f8992,plain,
    ( spl225_503
  <=> ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK49,X0)),vAPP(produc367475239e_name,name,sK48,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_503])]) ).

thf(f3942,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK49,X0)),vAPP(produc367475239e_name,name,sK48,X0))),X1) )
    | ~ spl225_18
    | ~ spl225_34
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(forward_demodulation,[],[f3941,f2366]) ).

thf(f3941,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1)) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK49,X0)),vAPP(produc367475239e_name,name,sK48,X0))),X1) )
    | ~ spl225_34
    | ~ spl225_98
    | ~ spl225_161 ),
    inference(forward_demodulation,[],[f3918,f2863]) ).

thf(f3918,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK49,X0)),vAPP(produc367475239e_name,name,sK48,X0))),X1) )
    | ~ spl225_34
    | ~ spl225_161 ),
    inference(superposition,[],[f3529,f2444]) ).

thf(f8990,plain,
    ( spl225_502
    | ~ spl225_68
    | ~ spl225_160 ),
    inference(avatar_split_clause,[],[f3908,f3524,f2625,f8988]) ).

thf(f8988,plain,
    ( spl225_502
  <=> ! [X3: name,X4: name,X0: list_P227219501e_name,X5: pi,X2: pi,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X3),X4),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_502])]) ).

thf(f3908,plain,
    ( ! [X2: pi,X3: name,X0: list_P227219501e_name,X1: name,X4: name,X5: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X3),X4),X5) )
    | ~ spl225_68
    | ~ spl225_160 ),
    inference(superposition,[],[f2626,f3525]) ).

thf(f8986,plain,
    ( spl225_501
    | ~ spl225_69
    | ~ spl225_150 ),
    inference(avatar_split_clause,[],[f3773,f3484,f2629,f8984]) ).

thf(f8984,plain,
    ( spl225_501
  <=> ! [X3: name,X4: name,X0: list_P227219501e_name,X5: pi,X2: pi,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X3),X4),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_501])]) ).

thf(f3484,plain,
    ( spl225_150
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_150])]) ).

thf(f3773,plain,
    ( ! [X2: pi,X3: name,X0: list_P227219501e_name,X1: pi,X4: name,X5: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X3),X4),X5) )
    | ~ spl225_69
    | ~ spl225_150 ),
    inference(superposition,[],[f2630,f3485]) ).

thf(f3485,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_150 ),
    inference(avatar_component_clause,[],[f3484]) ).

thf(f8982,plain,
    ( spl225_500
    | ~ spl225_67
    | ~ spl225_147 ),
    inference(avatar_split_clause,[],[f3723,f3472,f2621,f8980]) ).

thf(f8980,plain,
    ( spl225_500
  <=> ! [X3: late_subject,X4: name,X0: list_P227219501e_name,X5: pi,X2: pi,X1: late_freeRes] : ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5) != vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_500])]) ).

thf(f3723,plain,
    ( ! [X2: pi,X3: late_subject,X0: list_P227219501e_name,X1: late_freeRes,X4: name,X5: pi] : ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5) != vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
    | ~ spl225_67
    | ~ spl225_147 ),
    inference(superposition,[],[f2622,f3473]) ).

thf(f8966,plain,
    ( spl225_499
    | ~ spl225_8
    | ~ spl225_95 ),
    inference(avatar_split_clause,[],[f2852,f2836,f2296,f8964]) ).

thf(f8964,plain,
    ( spl225_499
  <=> ! [X4: pi,X0: name,X3: late_freeRes,X2: pi,X1: name] : ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_499])]) ).

thf(f2836,plain,
    ( spl225_95
  <=> ! [X4: pi,X0: name,X3: late_freeRes,X2: pi,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_95])]) ).

thf(f2852,plain,
    ( ! [X2: pi,X3: late_freeRes,X0: name,X1: name,X4: pi] : ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
    | ~ spl225_8
    | ~ spl225_95 ),
    inference(trivial_inequality_removal,[],[f2851]) ).

thf(f2851,plain,
    ( ! [X2: pi,X3: late_freeRes,X0: name,X1: name,X4: pi] :
        ( ( $true != $true )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ) )
    | ~ spl225_8
    | ~ spl225_95 ),
    inference(superposition,[],[f2837,f2297]) ).

thf(f2837,plain,
    ( ! [X2: pi,X3: late_freeRes,X0: name,X1: name,X4: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
    | ~ spl225_95 ),
    inference(avatar_component_clause,[],[f2836]) ).

thf(f8962,plain,
    ( spl225_498
    | ~ spl225_8
    | ~ spl225_94 ),
    inference(avatar_split_clause,[],[f2849,f2832,f2296,f8960]) ).

thf(f8960,plain,
    ( spl225_498
  <=> ! [X0: name,X3: late_residual,X2: pi,X1: name] : ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_498])]) ).

thf(f2832,plain,
    ( spl225_94
  <=> ! [X0: name,X3: late_residual,X2: pi,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_94])]) ).

thf(f2849,plain,
    ( ! [X2: pi,X3: late_residual,X0: name,X1: name] : ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) )
    | ~ spl225_8
    | ~ spl225_94 ),
    inference(trivial_inequality_removal,[],[f2848]) ).

thf(f2848,plain,
    ( ! [X2: pi,X3: late_residual,X0: name,X1: name] :
        ( ( $true != $true )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) ) )
    | ~ spl225_8
    | ~ spl225_94 ),
    inference(superposition,[],[f2833,f2297]) ).

thf(f2833,plain,
    ( ! [X2: pi,X3: late_residual,X0: name,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) )
    | ~ spl225_94 ),
    inference(avatar_component_clause,[],[f2832]) ).

thf(f8958,plain,
    ( spl225_497
    | ~ spl225_8
    | ~ spl225_93 ),
    inference(avatar_split_clause,[],[f2844,f2828,f2296,f8956]) ).

thf(f8956,plain,
    ( spl225_497
  <=> ! [X0: late_subject > $o,X1: late_subject] :
        ( ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
        | ( $true = vAPP(late_subject,$o,X0,X1) )
        | ( $false = vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_497])]) ).

thf(f2844,plain,
    ( ! [X0: late_subject > $o,X1: late_subject] :
        ( ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
        | ( $true = vAPP(late_subject,$o,X0,X1) )
        | ( $false = vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) )
    | ~ spl225_8
    | ~ spl225_93 ),
    inference(trivial_inequality_removal,[],[f2843]) ).

thf(f2843,plain,
    ( ! [X0: late_subject > $o,X1: late_subject] :
        ( ( $true != $true )
        | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
        | ( $true = vAPP(late_subject,$o,X0,X1) )
        | ( $false = vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) )
    | ~ spl225_8
    | ~ spl225_93 ),
    inference(superposition,[],[f2829,f2297]) ).

thf(f8954,plain,
    ( spl225_496
    | ~ spl225_54
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2726,f2699,f2539,f8952]) ).

thf(f8952,plain,
    ( spl225_496
  <=> ! [X2: name,X0: name,X1: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_496])]) ).

thf(f2699,plain,
    ( spl225_81
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_81])]) ).

thf(f2726,plain,
    ( ! [X2: name,X0: name,X1: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X0),X2) )
    | ~ spl225_54
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2703]) ).

thf(f2703,plain,
    ( ! [X2: name,X0: name,X1: pi] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X0),X2) ) )
    | ~ spl225_54
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2540]) ).

thf(f2700,plain,
    ( ! [X2: name,X0: name,X1: pi] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 ) )
    | ~ spl225_81 ),
    inference(avatar_component_clause,[],[f2699]) ).

thf(f8950,plain,
    ( spl225_495
    | ~ spl225_56
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2721,f2699,f2547,f8948]) ).

thf(f8948,plain,
    ( spl225_495
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),y),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_495])]) ).

thf(f2721,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),y),X0) )
    | ~ spl225_56
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2708]) ).

thf(f2708,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),y),X0) ) )
    | ~ spl225_56
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2549]) ).

thf(f8946,plain,
    ( spl225_494
    | ~ spl225_57
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2717,f2699,f2552,f8944]) ).

thf(f8944,plain,
    ( spl225_494
  <=> ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),z),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_494])]) ).

thf(f2717,plain,
    ( ! [X0: name] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),z),X0) )
    | ~ spl225_57
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2712]) ).

thf(f2712,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),z),X0) ) )
    | ~ spl225_57
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2554]) ).

thf(f8932,plain,
    ( spl225_493
    | ~ spl225_106
    | ~ spl225_183 ),
    inference(avatar_split_clause,[],[f4250,f4241,f2987,f8930]) ).

thf(f2987,plain,
    ( spl225_106
  <=> ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,b)),z),q2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_106])]) ).

thf(f4241,plain,
    ( spl225_183
  <=> ! [X2: name,X4: name,X0: pi,X3: pi,X1: late_subject] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_183])]) ).

thf(f4250,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_BoundOutputS,b)) ) )
    | ~ spl225_106
    | ~ spl225_183 ),
    inference(trivial_inequality_removal,[],[f4245]) ).

thf(f4245,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_BoundOutputS,b)) ) )
    | ~ spl225_106
    | ~ spl225_183 ),
    inference(superposition,[],[f4242,f2989]) ).

thf(f2989,plain,
    ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,b)),z),q2)) )
    | ~ spl225_106 ),
    inference(avatar_component_clause,[],[f2987]) ).

thf(f4242,plain,
    ( ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: name] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) ) )
    | ~ spl225_183 ),
    inference(avatar_component_clause,[],[f4241]) ).

thf(f8917,plain,
    ( spl225_492
    | ~ spl225_8
    | spl225_477 ),
    inference(avatar_split_clause,[],[f8835,f8104,f2296,f8914]) ).

thf(f8835,plain,
    ( ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) )
    | ~ spl225_8
    | spl225_477 ),
    inference(trivial_inequality_removal,[],[f8834]) ).

thf(f8834,plain,
    ( ( $true != $true )
    | ( $false = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) )
    | ~ spl225_8
    | spl225_477 ),
    inference(superposition,[],[f8105,f2297]) ).

thf(f8105,plain,
    ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) )
    | spl225_477 ),
    inference(avatar_component_clause,[],[f8104]) ).

thf(f8867,plain,
    ( spl225_491
    | ~ spl225_106
    | ~ spl225_191 ),
    inference(avatar_split_clause,[],[f4326,f4317,f2987,f8865]) ).

thf(f4317,plain,
    ( spl225_191
  <=> ! [X4: name,X0: pi,X3: pi,X2: name,X1: late_subject] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) )
        | ( X2 = X4 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_191])]) ).

thf(f4326,plain,
    ( ! [X0: name] :
        ( ( z = X0 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) )
    | ~ spl225_106
    | ~ spl225_191 ),
    inference(trivial_inequality_removal,[],[f4321]) ).

thf(f4321,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( z = X0 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q2) ) )
    | ~ spl225_106
    | ~ spl225_191 ),
    inference(superposition,[],[f4318,f2989]) ).

thf(f4318,plain,
    ( ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: name] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
        | ( X2 = X4 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) ) )
    | ~ spl225_191 ),
    inference(avatar_component_clause,[],[f4317]) ).

thf(f8863,plain,
    ( spl225_490
    | ~ spl225_11
    | ~ spl225_116 ),
    inference(avatar_split_clause,[],[f3297,f3220,f2337,f8861]) ).

thf(f8861,plain,
    ( spl225_490
  <=> ! [X0: list_P227219501e_name,X1: late_freeRes > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_freeRes,late_subject,X1,late_TauR)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X0),X1),late_TauR) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_490])]) ).

thf(f3220,plain,
    ( spl225_116
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_freeRes,late_subject,X1,X2)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_116])]) ).

thf(f3297,plain,
    ( ! [X0: list_P227219501e_name,X1: late_freeRes > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_freeRes,late_subject,X1,late_TauR)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X0),X1),late_TauR) )
    | ~ spl225_11
    | ~ spl225_116 ),
    inference(superposition,[],[f3221,f2338]) ).

thf(f3221,plain,
    ( ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_freeRes,late_subject,X1,X2)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
    | ~ spl225_116 ),
    inference(avatar_component_clause,[],[f3220]) ).

thf(f8859,plain,
    ( spl225_489
    | ~ spl225_11
    | ~ spl225_112 ),
    inference(avatar_split_clause,[],[f3270,f3048,f2337,f8857]) ).

thf(f8857,plain,
    ( spl225_489
  <=> ! [X0: list_P227219501e_name,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,X1,late_TauR)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X0),X1),late_TauR) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_489])]) ).

thf(f3048,plain,
    ( spl225_112
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,X1,X2)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_112])]) ).

thf(f3270,plain,
    ( ! [X0: list_P227219501e_name,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,X1,late_TauR)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X0),X1),late_TauR) )
    | ~ spl225_11
    | ~ spl225_112 ),
    inference(superposition,[],[f3049,f2338]) ).

thf(f3049,plain,
    ( ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,X1,X2)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
    | ~ spl225_112 ),
    inference(avatar_component_clause,[],[f3048]) ).

thf(f8855,plain,
    ( spl225_488
    | ~ spl225_8
    | ~ spl225_91 ),
    inference(avatar_split_clause,[],[f2818,f2808,f2296,f8853]) ).

thf(f8853,plain,
    ( spl225_488
  <=> ! [X2: name,X0: pi,X1: late_residual] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_488])]) ).

thf(f2818,plain,
    ( ! [X2: name,X0: pi,X1: late_residual] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) )
    | ~ spl225_8
    | ~ spl225_91 ),
    inference(trivial_inequality_removal,[],[f2817]) ).

thf(f2817,plain,
    ( ! [X2: name,X0: pi,X1: late_residual] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
        | ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
        | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) )
    | ~ spl225_8
    | ~ spl225_91 ),
    inference(superposition,[],[f2809,f2297]) ).

thf(f8851,plain,
    ( spl225_487
    | ~ spl225_33 ),
    inference(avatar_split_clause,[],[f2434,f2431,f8848]) ).

thf(f8848,plain,
    ( spl225_487
  <=> ( nil_Pr743626285e_name = vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,vAPP(sTfun(list_P227219501e_name,$o),sTfun(list_P227219501e_name,$o),vAPP(sTfun($o,$o),sTfun(sTfun(list_P227219501e_name,$o),sTfun(list_P227219501e_name,$o)),bCOMB,vNOT),vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_487])]) ).

thf(f2431,plain,
    ( spl225_33
  <=> ! [X0: list_P227219501e_name > $o] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_33])]) ).

thf(f2434,plain,
    ( ( nil_Pr743626285e_name = vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,vAPP(sTfun(list_P227219501e_name,$o),sTfun(list_P227219501e_name,$o),vAPP(sTfun($o,$o),sTfun(sTfun(list_P227219501e_name,$o),sTfun(list_P227219501e_name,$o)),bCOMB,vNOT),vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name))) )
    | ~ spl225_33 ),
    inference(leibniz_equality_elimination,[],[f2432]) ).

thf(f2432,plain,
    ( ! [X0: list_P227219501e_name > $o] :
        ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) )
    | ~ spl225_33 ),
    inference(avatar_component_clause,[],[f2431]) ).

thf(f8842,plain,
    ( spl225_486
    | ~ spl225_8
    | ~ spl225_89 ),
    inference(avatar_split_clause,[],[f2806,f2798,f2296,f8840]) ).

thf(f8840,plain,
    ( spl225_486
  <=> ! [X0: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) )
        | ( $false = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_486])]) ).

thf(f2798,plain,
    ( spl225_89
  <=> ! [X0: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_89])]) ).

thf(f2806,plain,
    ( ! [X0: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) )
        | ( $false = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) )
    | ~ spl225_8
    | ~ spl225_89 ),
    inference(trivial_inequality_removal,[],[f2805]) ).

thf(f2805,plain,
    ( ! [X0: set_Pr1834926343_pi_pi] :
        ( ( $true != $true )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) )
        | ( $false = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) )
    | ~ spl225_8
    | ~ spl225_89 ),
    inference(superposition,[],[f2799,f2297]) ).

thf(f2799,plain,
    ( ! [X0: set_Pr1834926343_pi_pi] :
        ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) ) )
    | ~ spl225_89 ),
    inference(avatar_component_clause,[],[f2798]) ).

thf(f8712,plain,
    ( spl225_485
    | ~ spl225_37
    | ~ spl225_92 ),
    inference(avatar_split_clause,[],[f2822,f2812,f2455,f8710]) ).

thf(f8710,plain,
    ( spl225_485
  <=> ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK53,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK52,X0) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_485])]) ).

thf(f2812,plain,
    ( spl225_92
  <=> ! [X2: name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( X1 = X2 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_92])]) ).

thf(f2822,plain,
    ( ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK53,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK52,X0) = X1 ) )
    | ~ spl225_37
    | ~ spl225_92 ),
    inference(superposition,[],[f2813,f2456]) ).

thf(f2813,plain,
    ( ! [X2: name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( X1 = X2 )
        | ( X0 = X1 ) )
    | ~ spl225_92 ),
    inference(avatar_component_clause,[],[f2812]) ).

thf(f8708,plain,
    ( spl225_484
    | ~ spl225_34
    | ~ spl225_92 ),
    inference(avatar_split_clause,[],[f2821,f2812,f2443,f8706]) ).

thf(f8706,plain,
    ( spl225_484
  <=> ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK49,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK48,X0) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_484])]) ).

thf(f2821,plain,
    ( ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK49,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK48,X0) = X1 ) )
    | ~ spl225_34
    | ~ spl225_92 ),
    inference(superposition,[],[f2813,f2444]) ).

thf(f8130,plain,
    ( spl225_481
    | spl225_482
    | ~ spl225_483
    | ~ spl225_206 ),
    inference(avatar_split_clause,[],[f4732,f4392,f8127,f8123,f8120]) ).

thf(f8120,plain,
    ( spl225_481
  <=> ! [X0: list_P227219501e_name,X1: list_P227219501e_name] : ( X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_481])]) ).

thf(f8123,plain,
    ( spl225_482
  <=> ( vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,vEQ(list_P227219501e_name)) = vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,vEQ(list_P227219501e_name)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_482])]) ).

thf(f8127,plain,
    ( spl225_483
  <=> ( nil_Pr743626285e_name = vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,vEQ(list_P227219501e_name)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_483])]) ).

thf(f4392,plain,
    ( spl225_206
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_206])]) ).

thf(f4732,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,vEQ(list_P227219501e_name)) )
        | ( vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,vEQ(list_P227219501e_name)) = vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,vEQ(list_P227219501e_name)) )
        | ( X0 = X1 ) )
    | ~ spl225_206 ),
    inference(equality_proxy_clausification,[],[f4731]) ).

thf(f4731,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,vEQ(list_P227219501e_name)) )
        | ( vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,vEQ(list_P227219501e_name)) = vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,vEQ(list_P227219501e_name)) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) ) )
    | ~ spl225_206 ),
    inference(equality_proxy_clausification,[],[f4730]) ).

thf(f4730,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,vEQ(list_P227219501e_name)) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,vEQ(list_P227219501e_name))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,vEQ(list_P227219501e_name))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) ) )
    | ~ spl225_206 ),
    inference(equality_proxy_clausification,[],[f4727]) ).

thf(f4727,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,vEQ(list_P227219501e_name))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,vEQ(list_P227219501e_name))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,vEQ(list_P227219501e_name))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) ) )
    | ~ spl225_206 ),
    inference(primitive_instantiation,[],[f4393]) ).

thf(f4393,plain,
    ( ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) )
    | ~ spl225_206 ),
    inference(avatar_component_clause,[],[f4392]) ).

thf(f8118,plain,
    ( spl225_480
    | ~ spl225_48
    | ~ spl225_177 ),
    inference(avatar_split_clause,[],[f4181,f4024,f2499,f8116]) ).

thf(f8116,plain,
    ( spl225_480
  <=> ! [X2: list_P227219501e_name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X2),X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_480])]) ).

thf(f2499,plain,
    ( spl225_48
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$true),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_48])]) ).

thf(f4024,plain,
    ( spl225_177
  <=> ! [X0: list_P227219501e_name,X3: name,X2: name,X1: $o] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_177])]) ).

thf(f4181,plain,
    ( ! [X2: list_P227219501e_name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X2),X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) )
    | ~ spl225_48
    | ~ spl225_177 ),
    inference(superposition,[],[f4025,f2500]) ).

thf(f2500,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$true),X0),X1) = X0 )
    | ~ spl225_48 ),
    inference(avatar_component_clause,[],[f2499]) ).

thf(f4025,plain,
    ( ! [X2: name,X3: name,X0: list_P227219501e_name,X1: $o] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
    | ~ spl225_177 ),
    inference(avatar_component_clause,[],[f4024]) ).

thf(f8114,plain,
    ( spl225_479
    | ~ spl225_50
    | ~ spl225_176 ),
    inference(avatar_split_clause,[],[f4152,f4020,f2507,f8112]) ).

thf(f8112,plain,
    ( spl225_479
  <=> ! [X2: list_P227219501e_name,X0: pi,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_479])]) ).

thf(f2507,plain,
    ( spl225_50
  <=> ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$true),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_50])]) ).

thf(f4020,plain,
    ( spl225_176
  <=> ! [X0: list_P227219501e_name,X3: pi,X2: pi,X1: $o] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_176])]) ).

thf(f4152,plain,
    ( ! [X2: list_P227219501e_name,X0: pi,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) )
    | ~ spl225_50
    | ~ spl225_176 ),
    inference(superposition,[],[f4021,f2508]) ).

thf(f2508,plain,
    ( ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$true),X0),X1) = X0 )
    | ~ spl225_50 ),
    inference(avatar_component_clause,[],[f2507]) ).

thf(f4021,plain,
    ( ! [X2: pi,X3: pi,X0: list_P227219501e_name,X1: $o] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
    | ~ spl225_176 ),
    inference(avatar_component_clause,[],[f4020]) ).

thf(f8110,plain,
    ( spl225_477
    | spl225_478
    | ~ spl225_41
    | ~ spl225_462 ),
    inference(avatar_split_clause,[],[f8037,f7817,f2471,f8108,f8104]) ).

thf(f8108,plain,
    ( spl225_478
  <=> ! [X0: pi_Rep,X1: pi_Rep] : ( X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_478])]) ).

thf(f2471,plain,
    ( spl225_41
  <=> ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$true),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_41])]) ).

thf(f7817,plain,
    ( spl225_462
  <=> ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_462])]) ).

thf(f8037,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep] :
        ( ( X0 = X1 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),$true) ) )
    | ~ spl225_41
    | ~ spl225_462 ),
    inference(superposition,[],[f7818,f2472]) ).

thf(f2472,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$true),X0),X1) = X0 )
    | ~ spl225_41 ),
    inference(avatar_component_clause,[],[f2471]) ).

thf(f7818,plain,
    ( ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_462 ),
    inference(avatar_component_clause,[],[f7817]) ).

thf(f8102,plain,
    ( spl225_476
    | ~ spl225_45
    | ~ spl225_174 ),
    inference(avatar_split_clause,[],[f4119,f4012,f2487,f8100]) ).

thf(f8100,plain,
    ( spl225_476
  <=> ! [X2: list_P227219501e_name,X0: late_subject,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X2),X0) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_476])]) ).

thf(f2487,plain,
    ( spl225_45
  <=> ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$true),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_45])]) ).

thf(f4012,plain,
    ( spl225_174
  <=> ! [X0: list_P227219501e_name,X3: late_subject,X2: late_subject,X1: $o] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_174])]) ).

thf(f4119,plain,
    ( ! [X2: list_P227219501e_name,X0: late_subject,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X2),X0) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) )
    | ~ spl225_45
    | ~ spl225_174 ),
    inference(superposition,[],[f4013,f2488]) ).

thf(f2488,plain,
    ( ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$true),X0),X1) = X0 )
    | ~ spl225_45 ),
    inference(avatar_component_clause,[],[f2487]) ).

thf(f4013,plain,
    ( ! [X2: late_subject,X3: late_subject,X0: list_P227219501e_name,X1: $o] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
    | ~ spl225_174 ),
    inference(avatar_component_clause,[],[f4012]) ).

thf(f8098,plain,
    ( spl225_475
    | ~ spl225_43
    | ~ spl225_172 ),
    inference(avatar_split_clause,[],[f4084,f4004,f2479,f8096]) ).

thf(f8096,plain,
    ( spl225_475
  <=> ! [X2: list_P227219501e_name,X0: late_freeRes,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X2),X0) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_475])]) ).

thf(f4004,plain,
    ( spl225_172
  <=> ! [X0: list_P227219501e_name,X3: late_freeRes,X2: late_freeRes,X1: $o] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_172])]) ).

thf(f4084,plain,
    ( ! [X2: list_P227219501e_name,X0: late_freeRes,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X2),X0) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) )
    | ~ spl225_43
    | ~ spl225_172 ),
    inference(superposition,[],[f4005,f2480]) ).

thf(f4005,plain,
    ( ! [X2: late_freeRes,X3: late_freeRes,X0: list_P227219501e_name,X1: $o] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
    | ~ spl225_172 ),
    inference(avatar_component_clause,[],[f4004]) ).

thf(f8094,plain,
    ( spl225_474
    | ~ spl225_41
    | ~ spl225_169 ),
    inference(avatar_split_clause,[],[f4057,f3992,f2471,f8092]) ).

thf(f8092,plain,
    ( spl225_474
  <=> ! [X2: list_P227219501e_name,X0: pi_Rep,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X2),X0) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_474])]) ).

thf(f3992,plain,
    ( spl225_169
  <=> ! [X0: list_P227219501e_name,X3: pi_Rep,X2: pi_Rep,X1: $o] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_169])]) ).

thf(f4057,plain,
    ( ! [X2: list_P227219501e_name,X0: pi_Rep,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X2),X0) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X2),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X2),$true) ) )
    | ~ spl225_41
    | ~ spl225_169 ),
    inference(superposition,[],[f3993,f2472]) ).

thf(f3993,plain,
    ( ! [X2: pi_Rep,X3: pi_Rep,X0: list_P227219501e_name,X1: $o] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
    | ~ spl225_169 ),
    inference(avatar_component_clause,[],[f3992]) ).

thf(f8090,plain,
    ( spl225_473
    | ~ spl225_76
    | ~ spl225_123 ),
    inference(avatar_split_clause,[],[f3334,f3248,f2662,f8088]) ).

thf(f8088,plain,
    ( spl225_473
  <=> ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_473])]) ).

thf(f3248,plain,
    ( spl225_123
  <=> ! [X0: pi,X3: name,X2: pi,X1: late_freeRes] :
        ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_123])]) ).

thf(f3334,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)) ) )
    | ~ spl225_76
    | ~ spl225_123 ),
    inference(trivial_inequality_removal,[],[f3329]) ).

thf(f3329,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)) ) )
    | ~ spl225_76
    | ~ spl225_123 ),
    inference(superposition,[],[f3249,f2664]) ).

thf(f3249,plain,
    ( ! [X2: pi,X3: name,X0: pi,X1: late_freeRes] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) ) )
    | ~ spl225_123 ),
    inference(avatar_component_clause,[],[f3248]) ).

thf(f8086,plain,
    ( spl225_472
    | ~ spl225_8
    | ~ spl225_88 ),
    inference(avatar_split_clause,[],[f2796,f2754,f2296,f8084]) ).

thf(f8084,plain,
    ( spl225_472
  <=> ! [X2: pi,X0: name,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_472])]) ).

thf(f2754,plain,
    ( spl225_88
  <=> ! [X2: pi,X0: name,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_88])]) ).

thf(f2796,plain,
    ( ! [X2: pi,X0: name,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) )
    | ~ spl225_8
    | ~ spl225_88 ),
    inference(trivial_inequality_removal,[],[f2795]) ).

thf(f2795,plain,
    ( ! [X2: pi,X0: name,X1: pi] :
        ( ( $true != $true )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) )
    | ~ spl225_8
    | ~ spl225_88 ),
    inference(superposition,[],[f2755,f2297]) ).

thf(f2755,plain,
    ( ! [X2: pi,X0: name,X1: pi] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) )
    | ~ spl225_88 ),
    inference(avatar_component_clause,[],[f2754]) ).

thf(f8082,plain,
    ( spl225_471
    | ~ spl225_8
    | ~ spl225_87 ),
    inference(avatar_split_clause,[],[f2792,f2750,f2296,f8080]) ).

thf(f8080,plain,
    ( spl225_471
  <=> ! [X2: pi,X0: name,X1: pi] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
        | ( $false = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_471])]) ).

thf(f2750,plain,
    ( spl225_87
  <=> ! [X2: pi,X0: name,X1: pi] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
        | ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_87])]) ).

thf(f2792,plain,
    ( ! [X2: pi,X0: name,X1: pi] :
        ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
        | ( $false = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) )
    | ~ spl225_8
    | ~ spl225_87 ),
    inference(trivial_inequality_removal,[],[f2791]) ).

thf(f2791,plain,
    ( ! [X2: pi,X0: name,X1: pi] :
        ( ( $true != $true )
        | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
        | ( $false = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) )
    | ~ spl225_8
    | ~ spl225_87 ),
    inference(superposition,[],[f2751,f2297]) ).

thf(f2751,plain,
    ( ! [X2: pi,X0: name,X1: pi] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) )
        | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true ) )
    | ~ spl225_87 ),
    inference(avatar_component_clause,[],[f2750]) ).

thf(f8078,plain,
    ( spl225_470
    | ~ spl225_8
    | ~ spl225_86 ),
    inference(avatar_split_clause,[],[f2786,f2746,f2296,f8076]) ).

thf(f8076,plain,
    ( spl225_470
  <=> ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $false = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_470])]) ).

thf(f2786,plain,
    ( ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $false = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) )
    | ~ spl225_8
    | ~ spl225_86 ),
    inference(trivial_inequality_removal,[],[f2785]) ).

thf(f2785,plain,
    ( ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true != $true )
        | ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $false = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) )
    | ~ spl225_8
    | ~ spl225_86 ),
    inference(superposition,[],[f2747,f2297]) ).

thf(f8074,plain,
    ( spl225_469
    | ~ spl225_8
    | ~ spl225_85 ),
    inference(avatar_split_clause,[],[f2778,f2741,f2296,f8072]) ).

thf(f8072,plain,
    ( spl225_469
  <=> ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $false = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_469])]) ).

thf(f2778,plain,
    ( ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $false = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) )
    | ~ spl225_8
    | ~ spl225_85 ),
    inference(trivial_inequality_removal,[],[f2777]) ).

thf(f2777,plain,
    ( ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
        ( ( $true != $true )
        | ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
        | ( $false = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) )
    | ~ spl225_8
    | ~ spl225_85 ),
    inference(superposition,[],[f2742,f2297]) ).

thf(f8070,plain,
    ( spl225_468
    | ~ spl225_8
    | ~ spl225_84 ),
    inference(avatar_split_clause,[],[f2770,f2737,f2296,f8068]) ).

thf(f8068,plain,
    ( spl225_468
  <=> ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_468])]) ).

thf(f2770,plain,
    ( ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) )
    | ~ spl225_8
    | ~ spl225_84 ),
    inference(trivial_inequality_removal,[],[f2769]) ).

thf(f2769,plain,
    ( ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true != $true )
        | ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) )
    | ~ spl225_8
    | ~ spl225_84 ),
    inference(superposition,[],[f2738,f2297]) ).

thf(f8066,plain,
    ( spl225_467
    | ~ spl225_8
    | ~ spl225_83 ),
    inference(avatar_split_clause,[],[f2762,f2733,f2296,f8064]) ).

thf(f8064,plain,
    ( spl225_467
  <=> ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_467])]) ).

thf(f2762,plain,
    ( ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) )
    | ~ spl225_8
    | ~ spl225_83 ),
    inference(trivial_inequality_removal,[],[f2761]) ).

thf(f2761,plain,
    ( ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
        ( ( $true != $true )
        | ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) )
    | ~ spl225_8
    | ~ spl225_83 ),
    inference(superposition,[],[f2734,f2297]) ).

thf(f7835,plain,
    ( spl225_466
    | ~ spl225_18
    | ~ spl225_177 ),
    inference(avatar_split_clause,[],[f4205,f4024,f2365,f7833]) ).

thf(f7833,plain,
    ( spl225_466
  <=> ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_466])]) ).

thf(f4205,plain,
    ( ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_18
    | ~ spl225_177 ),
    inference(forward_demodulation,[],[f4182,f2366]) ).

thf(f4182,plain,
    ( ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X2) = vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_18
    | ~ spl225_177 ),
    inference(superposition,[],[f4025,f2366]) ).

thf(f7831,plain,
    ( spl225_465
    | ~ spl225_19
    | ~ spl225_176 ),
    inference(avatar_split_clause,[],[f4167,f4020,f2369,f7829]) ).

thf(f7829,plain,
    ( spl225_465
  <=> ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_465])]) ).

thf(f4167,plain,
    ( ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_19
    | ~ spl225_176 ),
    inference(forward_demodulation,[],[f4153,f2370]) ).

thf(f4153,plain,
    ( ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X2) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_19
    | ~ spl225_176 ),
    inference(superposition,[],[f4021,f2370]) ).

thf(f7827,plain,
    ( spl225_464
    | ~ spl225_17
    | ~ spl225_174 ),
    inference(avatar_split_clause,[],[f4135,f4012,f2361,f7825]) ).

thf(f7825,plain,
    ( spl225_464
  <=> ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_464])]) ).

thf(f4135,plain,
    ( ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_17
    | ~ spl225_174 ),
    inference(forward_demodulation,[],[f4120,f2362]) ).

thf(f4120,plain,
    ( ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X2) = vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_17
    | ~ spl225_174 ),
    inference(superposition,[],[f4013,f2362]) ).

thf(f7823,plain,
    ( spl225_463
    | ~ spl225_16
    | ~ spl225_172 ),
    inference(avatar_split_clause,[],[f4101,f4004,f2357,f7821]) ).

thf(f4101,plain,
    ( ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_16
    | ~ spl225_172 ),
    inference(forward_demodulation,[],[f4085,f2358]) ).

thf(f4085,plain,
    ( ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X2) = vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_16
    | ~ spl225_172 ),
    inference(superposition,[],[f4005,f2358]) ).

thf(f7819,plain,
    ( spl225_462
    | ~ spl225_15
    | ~ spl225_169 ),
    inference(avatar_split_clause,[],[f4068,f3992,f2353,f7817]) ).

thf(f2353,plain,
    ( spl225_15
  <=> ! [X0: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_15])]) ).

thf(f4068,plain,
    ( ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X2 )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_15
    | ~ spl225_169 ),
    inference(forward_demodulation,[],[f4058,f2354]) ).

thf(f2354,plain,
    ( ! [X0: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X0) = X0 )
    | ~ spl225_15 ),
    inference(avatar_component_clause,[],[f2353]) ).

thf(f4058,plain,
    ( ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X2) = vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,nil_Pr743626285e_name),X0) ) )
    | ~ spl225_15
    | ~ spl225_169 ),
    inference(superposition,[],[f3993,f2354]) ).

thf(f7815,plain,
    ( spl225_461
    | ~ spl225_29
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3040,f3016,f2414,f7813]) ).

thf(f7813,plain,
    ( spl225_461
  <=> ! [X0: name,X1: name] :
        ( ( x = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_461])]) ).

thf(f3040,plain,
    ( ! [X0: name,X1: name] :
        ( ( x = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) )
    | ~ spl225_29
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3021]) ).

thf(f3021,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( x = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) )
    | ~ spl225_29
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2416]) ).

thf(f7811,plain,
    ( spl225_460
    | ~ spl225_24
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3039,f3016,f2389,f7809]) ).

thf(f7809,plain,
    ( spl225_460
  <=> ! [X0: name,X1: name] :
        ( ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_460])]) ).

thf(f3039,plain,
    ( ! [X0: name,X1: name] :
        ( ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),X1),X0)) ) )
    | ~ spl225_24
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3022]) ).

thf(f3022,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),X1),X0)) ) )
    | ~ spl225_24
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2391]) ).

thf(f7807,plain,
    ( spl225_459
    | ~ spl225_25
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3038,f3016,f2394,f7805]) ).

thf(f7805,plain,
    ( spl225_459
  <=> ! [X0: name,X1: name] :
        ( ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_459])]) ).

thf(f3038,plain,
    ( ! [X0: name,X1: name] :
        ( ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) )
    | ~ spl225_25
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3023]) ).

thf(f3023,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) )
    | ~ spl225_25
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2396]) ).

thf(f7774,plain,
    ( spl225_458
    | ~ spl225_27
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3036,f3016,f2404,f7772]) ).

thf(f7772,plain,
    ( spl225_458
  <=> ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_458])]) ).

thf(f3036,plain,
    ( ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) )
    | ~ spl225_27
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3025]) ).

thf(f3025,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),X1),X0)) ) )
    | ~ spl225_27
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2406]) ).

thf(f7770,plain,
    ( spl225_457
    | ~ spl225_26
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3035,f3016,f2399,f7768]) ).

thf(f7768,plain,
    ( spl225_457
  <=> ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_457])]) ).

thf(f3035,plain,
    ( ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),X1),X0)) ) )
    | ~ spl225_26
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3026]) ).

thf(f3026,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),X1),X0)) ) )
    | ~ spl225_26
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2401]) ).

thf(f7766,plain,
    ( spl225_456
    | ~ spl225_28
    | ~ spl225_110 ),
    inference(avatar_split_clause,[],[f3034,f3016,f2409,f7764]) ).

thf(f7764,plain,
    ( spl225_456
  <=> ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_456])]) ).

thf(f3034,plain,
    ( ! [X0: name,X1: name] :
        ( ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),X1),X0)) ) )
    | ~ spl225_28
    | ~ spl225_110 ),
    inference(trivial_inequality_removal,[],[f3027]) ).

thf(f3027,plain,
    ( ! [X0: name,X1: name] :
        ( ( $true != $true )
        | ( z = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),X1),X0)) ) )
    | ~ spl225_28
    | ~ spl225_110 ),
    inference(superposition,[],[f3017,f2411]) ).

thf(f7762,plain,
    ( spl225_455
    | ~ spl225_8
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2715,f2699,f2296,f7760]) ).

thf(f7760,plain,
    ( spl225_455
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 )
        | ( $false = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_455])]) ).

thf(f2715,plain,
    ( ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 )
        | ( $false = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) )
    | ~ spl225_8
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2714]) ).

thf(f2714,plain,
    ( ! [X2: name,X0: name,X1: pi] :
        ( ( $true != $true )
        | ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 )
        | ( $false = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) )
    | ~ spl225_8
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2297]) ).

thf(f7632,plain,
    ( spl225_454
    | spl225_4
    | ~ spl225_29
    | ~ spl225_419 ),
    inference(avatar_split_clause,[],[f7109,f7043,f2414,f2276,f7629]) ).

thf(f7629,plain,
    ( spl225_454
  <=> ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_454])]) ).

thf(f2276,plain,
    ( spl225_4
  <=> ( x = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_4])]) ).

thf(f7043,plain,
    ( spl225_419
  <=> ! [X0: name] :
        ( ( y = X0 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_419])]) ).

thf(f7109,plain,
    ( ( x = y )
    | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p2) )
    | ~ spl225_29
    | ~ spl225_419 ),
    inference(trivial_inequality_removal,[],[f7101]) ).

thf(f7101,plain,
    ( ( $true != $true )
    | ( x = y )
    | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p2) )
    | ~ spl225_29
    | ~ spl225_419 ),
    inference(superposition,[],[f7044,f2416]) ).

thf(f7044,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( y = X0 )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) )
    | ~ spl225_419 ),
    inference(avatar_component_clause,[],[f7043]) ).

thf(f7427,plain,
    ( spl225_453
    | ~ spl225_18
    | ~ spl225_34
    | ~ spl225_98
    | ~ spl225_161
    | ~ spl225_162 ),
    inference(avatar_split_clause,[],[f3976,f3532,f3528,f2862,f2443,f2365,f7425]) ).

thf(f7425,plain,
    ( spl225_453
  <=> ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_453])]) ).

thf(f3976,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1)) = X1 )
    | ~ spl225_18
    | ~ spl225_34
    | ~ spl225_98
    | ~ spl225_161
    | ~ spl225_162 ),
    inference(forward_demodulation,[],[f3975,f2444]) ).

thf(f3975,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0))),X1)) = X1 )
    | ~ spl225_18
    | ~ spl225_34
    | ~ spl225_98
    | ~ spl225_161
    | ~ spl225_162 ),
    inference(forward_demodulation,[],[f3952,f3945]) ).

thf(f3952,plain,
    ( ! [X0: produc367475239e_name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK49,X0)),vAPP(produc367475239e_name,name,sK48,X0))),X1)) = X1 )
    | ~ spl225_34
    | ~ spl225_162 ),
    inference(superposition,[],[f3533,f2444]) ).

thf(f7423,plain,
    ( spl225_452
    | ~ spl225_55
    | ~ spl225_160 ),
    inference(avatar_split_clause,[],[f3909,f3524,f2543,f7421]) ).

thf(f7421,plain,
    ( spl225_452
  <=> ! [X4: pi,X0: list_P227219501e_name,X3: pi,X2: pi,X1: name] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_452])]) ).

thf(f3909,plain,
    ( ! [X2: pi,X3: pi,X0: list_P227219501e_name,X1: name,X4: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) )
    | ~ spl225_55
    | ~ spl225_160 ),
    inference(superposition,[],[f2544,f3525]) ).

thf(f7419,plain,
    ( spl225_451
    | ~ spl225_18
    | ~ spl225_159 ),
    inference(avatar_split_clause,[],[f3889,f3520,f2365,f7417]) ).

thf(f7417,plain,
    ( spl225_451
  <=> ! [X0: name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_451])]) ).

thf(f3520,plain,
    ( spl225_159
  <=> ! [X2: name,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_159])]) ).

thf(f3889,plain,
    ( ! [X0: name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_18
    | ~ spl225_159 ),
    inference(forward_demodulation,[],[f3874,f2366]) ).

thf(f3874,plain,
    ( ! [X0: name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X0)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_18
    | ~ spl225_159 ),
    inference(superposition,[],[f3521,f2366]) ).

thf(f3521,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) )
    | ~ spl225_159 ),
    inference(avatar_component_clause,[],[f3520]) ).

thf(f7415,plain,
    ( spl225_450
    | ~ spl225_17
    | ~ spl225_18
    | ~ spl225_155 ),
    inference(avatar_split_clause,[],[f3825,f3504,f2365,f2361,f7413]) ).

thf(f7413,plain,
    ( spl225_450
  <=> ! [X0: late_subject,X1: name] : ( vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X0),X1) = vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,nil_Pr743626285e_name),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_450])]) ).

thf(f3504,plain,
    ( spl225_155
  <=> ! [X2: name,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,X0),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X1),X2)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_155])]) ).

thf(f3825,plain,
    ( ! [X0: late_subject,X1: name] : ( vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X0),X1) = vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,nil_Pr743626285e_name),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X0),X1)) )
    | ~ spl225_17
    | ~ spl225_18
    | ~ spl225_155 ),
    inference(forward_demodulation,[],[f3815,f2366]) ).

thf(f3815,plain,
    ( ! [X0: late_subject,X1: name] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,nil_Pr743626285e_name),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X0),X1)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1)) )
    | ~ spl225_17
    | ~ spl225_155 ),
    inference(superposition,[],[f3505,f2362]) ).

thf(f3505,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,X0),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X1),X2)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) )
    | ~ spl225_155 ),
    inference(avatar_component_clause,[],[f3504]) ).

thf(f7411,plain,
    ( spl225_449
    | ~ spl225_16
    | ~ spl225_18
    | ~ spl225_154 ),
    inference(avatar_split_clause,[],[f3805,f3500,f2365,f2357,f7409]) ).

thf(f7409,plain,
    ( spl225_449
  <=> ! [X0: late_freeRes,X1: name] : ( vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X0),X1) = vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,nil_Pr743626285e_name),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_449])]) ).

thf(f3805,plain,
    ( ! [X0: late_freeRes,X1: name] : ( vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X0),X1) = vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,nil_Pr743626285e_name),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X0),X1)) )
    | ~ spl225_16
    | ~ spl225_18
    | ~ spl225_154 ),
    inference(forward_demodulation,[],[f3794,f2366]) ).

thf(f3794,plain,
    ( ! [X0: late_freeRes,X1: name] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,nil_Pr743626285e_name),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X0),X1)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_154 ),
    inference(superposition,[],[f3501,f2358]) ).

thf(f7407,plain,
    ( spl225_448
    | ~ spl225_55
    | ~ spl225_150 ),
    inference(avatar_split_clause,[],[f3774,f3484,f2543,f7405]) ).

thf(f7405,plain,
    ( spl225_448
  <=> ! [X4: pi,X0: list_P227219501e_name,X3: name,X2: pi,X1: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_448])]) ).

thf(f3774,plain,
    ( ! [X2: pi,X3: name,X0: list_P227219501e_name,X1: pi,X4: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) )
    | ~ spl225_55
    | ~ spl225_150 ),
    inference(superposition,[],[f2544,f3485]) ).

thf(f7403,plain,
    ( spl225_447
    | ~ spl225_19
    | ~ spl225_149 ),
    inference(avatar_split_clause,[],[f3763,f3480,f2369,f7401]) ).

thf(f7401,plain,
    ( spl225_447
  <=> ! [X0: pi,X1: list_P227219501e_name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_447])]) ).

thf(f3480,plain,
    ( spl225_149
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_149])]) ).

thf(f3763,plain,
    ( ! [X0: pi,X1: list_P227219501e_name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_19
    | ~ spl225_149 ),
    inference(forward_demodulation,[],[f3753,f2370]) ).

thf(f3753,plain,
    ( ! [X0: pi,X1: list_P227219501e_name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X0)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_19
    | ~ spl225_149 ),
    inference(superposition,[],[f3481,f2370]) ).

thf(f3481,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_149 ),
    inference(avatar_component_clause,[],[f3480]) ).

thf(f7393,plain,
    ( spl225_446
    | ~ spl225_17
    | ~ spl225_148 ),
    inference(avatar_split_clause,[],[f3750,f3476,f2361,f7391]) ).

thf(f7391,plain,
    ( spl225_446
  <=> ! [X0: late_subject,X1: list_P227219501e_name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X0) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_446])]) ).

thf(f3476,plain,
    ( spl225_148
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_148])]) ).

thf(f3750,plain,
    ( ! [X0: late_subject,X1: list_P227219501e_name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X0) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_17
    | ~ spl225_148 ),
    inference(forward_demodulation,[],[f3734,f2362]) ).

thf(f3734,plain,
    ( ! [X0: late_subject,X1: list_P227219501e_name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X0)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_17
    | ~ spl225_148 ),
    inference(superposition,[],[f3477,f2362]) ).

thf(f3477,plain,
    ( ! [X2: late_subject,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
    | ~ spl225_148 ),
    inference(avatar_component_clause,[],[f3476]) ).

thf(f7389,plain,
    ( spl225_445
    | ~ spl225_16
    | ~ spl225_19
    | ~ spl225_147 ),
    inference(avatar_split_clause,[],[f3725,f3472,f2369,f2357,f7387]) ).

thf(f7387,plain,
    ( spl225_445
  <=> ! [X0: late_freeRes,X1: pi] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1) = vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,nil_Pr743626285e_name),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_445])]) ).

thf(f3725,plain,
    ( ! [X0: late_freeRes,X1: pi] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1) = vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,nil_Pr743626285e_name),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)) )
    | ~ spl225_16
    | ~ spl225_19
    | ~ spl225_147 ),
    inference(forward_demodulation,[],[f3713,f2370]) ).

thf(f3713,plain,
    ( ! [X0: late_freeRes,X1: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,nil_Pr743626285e_name),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_147 ),
    inference(superposition,[],[f3473,f2358]) ).

thf(f7385,plain,
    ( spl225_444
    | ~ spl225_16
    | ~ spl225_146 ),
    inference(avatar_split_clause,[],[f3709,f3468,f2357,f7383]) ).

thf(f7383,plain,
    ( spl225_444
  <=> ! [X0: late_freeRes,X1: list_P227219501e_name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X0) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_444])]) ).

thf(f3468,plain,
    ( spl225_146
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_146])]) ).

thf(f3709,plain,
    ( ! [X0: late_freeRes,X1: list_P227219501e_name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X0) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_16
    | ~ spl225_146 ),
    inference(forward_demodulation,[],[f3694,f2358]) ).

thf(f3694,plain,
    ( ! [X0: late_freeRes,X1: list_P227219501e_name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X0)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_16
    | ~ spl225_146 ),
    inference(superposition,[],[f3469,f2358]) ).

thf(f3469,plain,
    ( ! [X2: late_freeRes,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
    | ~ spl225_146 ),
    inference(avatar_component_clause,[],[f3468]) ).

thf(f7381,plain,
    ( spl225_443
    | ~ spl225_15
    | ~ spl225_145 ),
    inference(avatar_split_clause,[],[f3686,f3450,f2353,f7379]) ).

thf(f7379,plain,
    ( spl225_443
  <=> ! [X0: pi_Rep,X1: list_P227219501e_name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X0) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_443])]) ).

thf(f3450,plain,
    ( spl225_145
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_145])]) ).

thf(f3686,plain,
    ( ! [X0: pi_Rep,X1: list_P227219501e_name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X0) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_15
    | ~ spl225_145 ),
    inference(forward_demodulation,[],[f3677,f2354]) ).

thf(f3677,plain,
    ( ! [X0: pi_Rep,X1: list_P227219501e_name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X0)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,nil_Pr743626285e_name),X1)),X0) )
    | ~ spl225_15
    | ~ spl225_145 ),
    inference(superposition,[],[f3451,f2354]) ).

thf(f3451,plain,
    ( ! [X2: pi_Rep,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
    | ~ spl225_145 ),
    inference(avatar_component_clause,[],[f3450]) ).

thf(f7377,plain,
    ( spl225_442
    | ~ spl225_17
    | ~ spl225_19
    | ~ spl225_140 ),
    inference(avatar_split_clause,[],[f3652,f3430,f2369,f2361,f7375]) ).

thf(f7375,plain,
    ( spl225_442
  <=> ! [X0: late_subject,X1: pi] : ( vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X0),X1) = vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,nil_Pr743626285e_name),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_442])]) ).

thf(f3430,plain,
    ( spl225_140
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,X0),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X1),X2)) = vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_140])]) ).

thf(f3652,plain,
    ( ! [X0: late_subject,X1: pi] : ( vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X0),X1) = vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,nil_Pr743626285e_name),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X0),X1)) )
    | ~ spl225_17
    | ~ spl225_19
    | ~ spl225_140 ),
    inference(forward_demodulation,[],[f3646,f2370]) ).

thf(f3646,plain,
    ( ! [X0: late_subject,X1: pi] : ( vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,nil_Pr743626285e_name),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X0),X1)) = vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X1)) )
    | ~ spl225_17
    | ~ spl225_140 ),
    inference(superposition,[],[f3431,f2362]) ).

thf(f3431,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,X0),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X1),X2)) = vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_140 ),
    inference(avatar_component_clause,[],[f3430]) ).

thf(f7373,plain,
    ( spl225_441
    | ~ spl225_16
    | ~ spl225_19
    | ~ spl225_139 ),
    inference(avatar_split_clause,[],[f3638,f3426,f2369,f2357,f7371]) ).

thf(f7371,plain,
    ( spl225_441
  <=> ! [X0: late_freeRes,X1: pi] : ( vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X0),X1) = vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,nil_Pr743626285e_name),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_441])]) ).

thf(f3638,plain,
    ( ! [X0: late_freeRes,X1: pi] : ( vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X0),X1) = vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,nil_Pr743626285e_name),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X0),X1)) )
    | ~ spl225_16
    | ~ spl225_19
    | ~ spl225_139 ),
    inference(forward_demodulation,[],[f3632,f2370]) ).

thf(f3632,plain,
    ( ! [X0: late_freeRes,X1: pi] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,nil_Pr743626285e_name),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X0),X1)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_139 ),
    inference(superposition,[],[f3427,f2358]) ).

thf(f7369,plain,
    ( spl225_440
    | ~ spl225_17
    | ~ spl225_138 ),
    inference(avatar_split_clause,[],[f3625,f3422,f2361,f7367]) ).

thf(f7367,plain,
    ( spl225_440
  <=> ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X0),X1) = vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,nil_Pr743626285e_name),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_440])]) ).

thf(f3422,plain,
    ( spl225_138
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,X0),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X1),X2)) = vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_138])]) ).

thf(f3625,plain,
    ( ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X0),X1) = vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,nil_Pr743626285e_name),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X0),X1)) )
    | ~ spl225_17
    | ~ spl225_138 ),
    inference(forward_demodulation,[],[f3617,f2362]) ).

thf(f3617,plain,
    ( ! [X0: late_subject,X1: late_subject] : ( vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,nil_Pr743626285e_name),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X0),X1)) = vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X1)) )
    | ~ spl225_17
    | ~ spl225_138 ),
    inference(superposition,[],[f3423,f2362]) ).

thf(f3423,plain,
    ( ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,X0),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X1),X2)) = vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
    | ~ spl225_138 ),
    inference(avatar_component_clause,[],[f3422]) ).

thf(f7365,plain,
    ( spl225_439
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_137 ),
    inference(avatar_split_clause,[],[f3609,f3418,f2361,f2357,f7363]) ).

thf(f7363,plain,
    ( spl225_439
  <=> ! [X0: late_freeRes,X1: late_subject] : ( vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X0),X1) = vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,nil_Pr743626285e_name),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_439])]) ).

thf(f3609,plain,
    ( ! [X0: late_freeRes,X1: late_subject] : ( vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X0),X1) = vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,nil_Pr743626285e_name),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X0),X1)) )
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_137 ),
    inference(forward_demodulation,[],[f3601,f2362]) ).

thf(f3601,plain,
    ( ! [X0: late_freeRes,X1: late_subject] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,nil_Pr743626285e_name),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X0),X1)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_137 ),
    inference(superposition,[],[f3419,f2358]) ).

thf(f7361,plain,
    ( spl225_438
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_136 ),
    inference(avatar_split_clause,[],[f3594,f3414,f2361,f2357,f7359]) ).

thf(f7359,plain,
    ( spl225_438
  <=> ! [X0: late_subject,X1: late_freeRes] : ( vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X0),X1) = vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_438])]) ).

thf(f3594,plain,
    ( ! [X0: late_subject,X1: late_freeRes] : ( vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X0),X1) = vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X0),X1)) )
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_136 ),
    inference(forward_demodulation,[],[f3587,f2358]) ).

thf(f3587,plain,
    ( ! [X0: late_subject,X1: late_freeRes] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X0),X1)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X1)) )
    | ~ spl225_17
    | ~ spl225_136 ),
    inference(superposition,[],[f3415,f2362]) ).

thf(f7357,plain,
    ( spl225_437
    | ~ spl225_16
    | ~ spl225_134 ),
    inference(avatar_split_clause,[],[f3575,f3406,f2357,f7355]) ).

thf(f7355,plain,
    ( spl225_437
  <=> ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X0),X1) = vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_437])]) ).

thf(f3575,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X0),X1) = vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X0),X1)) )
    | ~ spl225_16
    | ~ spl225_134 ),
    inference(forward_demodulation,[],[f3568,f2358]) ).

thf(f3568,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X0),X1)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_134 ),
    inference(superposition,[],[f3407,f2358]) ).

thf(f7353,plain,
    ( spl225_436
    | ~ spl225_15
    | ~ spl225_392 ),
    inference(avatar_split_clause,[],[f6789,f6678,f2353,f7351]) ).

thf(f7351,plain,
    ( spl225_436
  <=> ! [X0: pi_Rep,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_436])]) ).

thf(f6678,plain,
    ( spl225_392
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) != vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_392])]) ).

thf(f6789,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_15
    | ~ spl225_392 ),
    inference(superposition,[],[f6679,f2354]) ).

thf(f6679,plain,
    ( ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) != vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
        | ( X1 = X2 ) )
    | ~ spl225_392 ),
    inference(avatar_component_clause,[],[f6678]) ).

thf(f7349,plain,
    ( spl225_435
    | ~ spl225_15
    | ~ spl225_17
    | ~ spl225_133 ),
    inference(avatar_split_clause,[],[f3561,f3402,f2361,f2353,f7347]) ).

thf(f7347,plain,
    ( spl225_435
  <=> ! [X0: late_subject,X1: pi_Rep] : ( vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X0),X1) = vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_435])]) ).

thf(f3402,plain,
    ( spl225_133
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,X0),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X1),X2)) = vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_133])]) ).

thf(f3561,plain,
    ( ! [X0: late_subject,X1: pi_Rep] : ( vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X0),X1) = vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X0),X1)) )
    | ~ spl225_15
    | ~ spl225_17
    | ~ spl225_133 ),
    inference(forward_demodulation,[],[f3555,f2354]) ).

thf(f3555,plain,
    ( ! [X0: late_subject,X1: pi_Rep] : ( vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X0),X1)) = vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X1)) )
    | ~ spl225_17
    | ~ spl225_133 ),
    inference(superposition,[],[f3403,f2362]) ).

thf(f3403,plain,
    ( ! [X2: pi_Rep,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,X0),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X1),X2)) = vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
    | ~ spl225_133 ),
    inference(avatar_component_clause,[],[f3402]) ).

thf(f7345,plain,
    ( spl225_434
    | ~ spl225_15
    | ~ spl225_16
    | ~ spl225_132 ),
    inference(avatar_split_clause,[],[f3547,f3398,f2357,f2353,f7343]) ).

thf(f7343,plain,
    ( spl225_434
  <=> ! [X0: late_freeRes,X1: pi_Rep] : ( vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X0),X1) = vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_434])]) ).

thf(f3547,plain,
    ( ! [X0: late_freeRes,X1: pi_Rep] : ( vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X0),X1) = vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X0),X1)) )
    | ~ spl225_15
    | ~ spl225_16
    | ~ spl225_132 ),
    inference(forward_demodulation,[],[f3541,f2354]) ).

thf(f3541,plain,
    ( ! [X0: late_freeRes,X1: pi_Rep] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,nil_Pr743626285e_name),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X0),X1)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X1)) )
    | ~ spl225_16
    | ~ spl225_132 ),
    inference(superposition,[],[f3399,f2358]) ).

thf(f7181,plain,
    ( spl225_433
    | ~ spl225_37
    | ~ spl225_78 ),
    inference(avatar_split_clause,[],[f2692,f2674,f2455,f7179]) ).

thf(f7179,plain,
    ( spl225_433
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK52,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK53,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_433])]) ).

thf(f2674,plain,
    ( spl225_78
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_78])]) ).

thf(f2692,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK52,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK53,X0)) )
    | ~ spl225_37
    | ~ spl225_78 ),
    inference(superposition,[],[f2675,f2456]) ).

thf(f2675,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X1) = X0 )
    | ~ spl225_78 ),
    inference(avatar_component_clause,[],[f2674]) ).

thf(f7177,plain,
    ( spl225_432
    | ~ spl225_34
    | ~ spl225_78 ),
    inference(avatar_split_clause,[],[f2691,f2674,f2443,f7175]) ).

thf(f7175,plain,
    ( spl225_432
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK48,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK49,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_432])]) ).

thf(f2691,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK48,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK49,X0)) )
    | ~ spl225_34
    | ~ spl225_78 ),
    inference(superposition,[],[f2675,f2444]) ).

thf(f7173,plain,
    ( spl225_431
    | ~ spl225_37
    | ~ spl225_77 ),
    inference(avatar_split_clause,[],[f2690,f2670,f2455,f7171]) ).

thf(f7171,plain,
    ( spl225_431
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK53,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK52,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_431])]) ).

thf(f2670,plain,
    ( spl225_77
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_77])]) ).

thf(f2690,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK53,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK52,X0)) )
    | ~ spl225_37
    | ~ spl225_77 ),
    inference(superposition,[],[f2671,f2456]) ).

thf(f2671,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X0) = X1 )
    | ~ spl225_77 ),
    inference(avatar_component_clause,[],[f2670]) ).

thf(f7169,plain,
    ( spl225_430
    | ~ spl225_34
    | ~ spl225_77 ),
    inference(avatar_split_clause,[],[f2689,f2670,f2443,f7167]) ).

thf(f7167,plain,
    ( spl225_430
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK49,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK48,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_430])]) ).

thf(f2689,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK49,X0) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),nil_Pr743626285e_name)),vAPP(produc367475239e_name,name,sK48,X0)) )
    | ~ spl225_34
    | ~ spl225_77 ),
    inference(superposition,[],[f2671,f2444]) ).

thf(f7159,plain,
    ( spl225_429
    | ~ spl225_71
    | ~ spl225_74 ),
    inference(avatar_split_clause,[],[f2686,f2654,f2637,f7157]) ).

thf(f7157,plain,
    ( spl225_429
  <=> ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_BoundOutputS,X1) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_429])]) ).

thf(f2654,plain,
    ( spl225_74
  <=> ! [X0: name,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_74])]) ).

thf(f2686,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_BoundOutputS,X1) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),X1)) )
    | ~ spl225_71
    | ~ spl225_74 ),
    inference(forward_demodulation,[],[f2682,f2255]) ).

thf(f2255,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2) ),
    inference(forward_demodulation,[],[f2254,f1370]) ).

thf(f1370,plain,
    ! [X0: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f342]) ).

thf(f342,axiom,
    ! [X0: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_name__prm__name_Osimps_I1_J) ).

thf(f2254,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X2)) ),
    inference(forward_demodulation,[],[f1849,f1446]) ).

thf(f1446,plain,
    ! [X2: name,X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) ),
    inference(cnf_transformation,[],[f816]) ).

thf(f816,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)),X2) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) ),
    inference(rectify,[],[f337]) ).

thf(f337,axiom,
    ! [X2: produc367475239e_name,X43: list_P227219501e_name,X0: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X43)),X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X43),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_name__prm__name_Osimps_I2_J) ).

thf(f1849,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    inference(definition_unfolding,[],[f1507,f1358,f1358]) ).

thf(f1507,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f24,axiom,
    ! [X0: name,X1: name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_name__swap) ).

thf(f2682,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_BoundOutputS,X1) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1)) )
    | ~ spl225_71
    | ~ spl225_74 ),
    inference(superposition,[],[f2655,f2638]) ).

thf(f2655,plain,
    ( ! [X0: name,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 )
    | ~ spl225_74 ),
    inference(avatar_component_clause,[],[f2654]) ).

thf(f7155,plain,
    ( spl225_428
    | ~ spl225_70
    | ~ spl225_74 ),
    inference(avatar_split_clause,[],[f2685,f2654,f2633,f7153]) ).

thf(f7153,plain,
    ( spl225_428
  <=> ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X1) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_428])]) ).

thf(f2633,plain,
    ( spl225_70
  <=> ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_InputS,X1)) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_70])]) ).

thf(f2685,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X1) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),X1)) )
    | ~ spl225_70
    | ~ spl225_74 ),
    inference(forward_demodulation,[],[f2681,f2255]) ).

thf(f2681,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X1) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1)) )
    | ~ spl225_70
    | ~ spl225_74 ),
    inference(superposition,[],[f2655,f2634]) ).

thf(f2634,plain,
    ( ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_InputS,X1)) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) )
    | ~ spl225_70 ),
    inference(avatar_component_clause,[],[f2633]) ).

thf(f7133,plain,
    ( spl225_427
    | ~ spl225_82
    | ~ spl225_183 ),
    inference(avatar_split_clause,[],[f4251,f4241,f2728,f7131]) ).

thf(f2728,plain,
    ( spl225_82
  <=> ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,b)),y),p2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_82])]) ).

thf(f4251,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,b)) ) )
    | ~ spl225_82
    | ~ spl225_183 ),
    inference(trivial_inequality_removal,[],[f4244]) ).

thf(f4244,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,b)) ) )
    | ~ spl225_82
    | ~ spl225_183 ),
    inference(superposition,[],[f4242,f2730]) ).

thf(f2730,plain,
    ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,b)),y),p2)) )
    | ~ spl225_82 ),
    inference(avatar_component_clause,[],[f2728]) ).

thf(f7129,plain,
    ( spl225_426
    | ~ spl225_38
    | ~ spl225_88 ),
    inference(avatar_split_clause,[],[f2794,f2754,f2459,f7127]) ).

thf(f7127,plain,
    ( spl225_426
  <=> ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK54,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_426])]) ).

thf(f2459,plain,
    ( spl225_38
  <=> ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK54,X0)),vAPP(product_prod_pi_pi,pi,sK55,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_38])]) ).

thf(f2794,plain,
    ( ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK54,X0)) ) )
    | ~ spl225_38
    | ~ spl225_88 ),
    inference(superposition,[],[f2755,f2460]) ).

thf(f2460,plain,
    ( ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK54,X0)),vAPP(product_prod_pi_pi,pi,sK55,X0)) = X0 )
    | ~ spl225_38 ),
    inference(avatar_component_clause,[],[f2459]) ).

thf(f7125,plain,
    ( spl225_425
    | ~ spl225_36
    | ~ spl225_88 ),
    inference(avatar_split_clause,[],[f2793,f2754,f2451,f7123]) ).

thf(f7123,plain,
    ( spl225_425
  <=> ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK50,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_425])]) ).

thf(f2451,plain,
    ( spl225_36
  <=> ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK50,X0)),vAPP(product_prod_pi_pi,pi,sK51,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_36])]) ).

thf(f2793,plain,
    ( ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK50,X0)) ) )
    | ~ spl225_36
    | ~ spl225_88 ),
    inference(superposition,[],[f2755,f2452]) ).

thf(f2452,plain,
    ( ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK50,X0)),vAPP(product_prod_pi_pi,pi,sK51,X0)) = X0 )
    | ~ spl225_36 ),
    inference(avatar_component_clause,[],[f2451]) ).

thf(f7121,plain,
    ( spl225_424
    | ~ spl225_16
    | ~ spl225_390 ),
    inference(avatar_split_clause,[],[f6766,f6670,f2357,f7119]) ).

thf(f7119,plain,
    ( spl225_424
  <=> ! [X0: late_freeRes,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_424])]) ).

thf(f6670,plain,
    ( spl225_390
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_390])]) ).

thf(f6766,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_16
    | ~ spl225_390 ),
    inference(superposition,[],[f6671,f2358]) ).

thf(f6671,plain,
    ( ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
        | ( X1 = X2 ) )
    | ~ spl225_390 ),
    inference(avatar_component_clause,[],[f6670]) ).

thf(f7117,plain,
    ( spl225_423
    | ~ spl225_38
    | ~ spl225_87 ),
    inference(avatar_split_clause,[],[f2790,f2750,f2459,f7115]) ).

thf(f7115,plain,
    ( spl225_423
  <=> ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK55,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_423])]) ).

thf(f2790,plain,
    ( ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK55,X0)) ) )
    | ~ spl225_38
    | ~ spl225_87 ),
    inference(superposition,[],[f2751,f2460]) ).

thf(f7113,plain,
    ( spl225_422
    | ~ spl225_36
    | ~ spl225_87 ),
    inference(avatar_split_clause,[],[f2789,f2750,f2451,f7111]) ).

thf(f7111,plain,
    ( spl225_422
  <=> ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK51,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_422])]) ).

thf(f2789,plain,
    ( ! [X0: product_prod_pi_pi,X1: name] :
        ( ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X1),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),vAPP(product_prod_pi_pi,pi,sK51,X0)) ) )
    | ~ spl225_36
    | ~ spl225_87 ),
    inference(superposition,[],[f2751,f2452]) ).

thf(f7072,plain,
    ( spl225_421
    | ~ spl225_17
    | ~ spl225_388 ),
    inference(avatar_split_clause,[],[f6741,f6662,f2361,f7070]) ).

thf(f7070,plain,
    ( spl225_421
  <=> ! [X0: late_subject,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_421])]) ).

thf(f6662,plain,
    ( spl225_388
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) != vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_388])]) ).

thf(f6741,plain,
    ( ! [X0: late_subject,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_17
    | ~ spl225_388 ),
    inference(superposition,[],[f6663,f2362]) ).

thf(f6663,plain,
    ( ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) != vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
        | ( X1 = X2 ) )
    | ~ spl225_388 ),
    inference(avatar_component_clause,[],[f6662]) ).

thf(f7049,plain,
    ( spl225_420
    | ~ spl225_18
    | ~ spl225_387 ),
    inference(avatar_split_clause,[],[f6718,f6658,f2365,f7047]) ).

thf(f7047,plain,
    ( spl225_420
  <=> ! [X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_420])]) ).

thf(f6658,plain,
    ( spl225_387
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name] :
        ( ( X1 = X2 )
        | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) != vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_387])]) ).

thf(f6718,plain,
    ( ! [X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_18
    | ~ spl225_387 ),
    inference(superposition,[],[f6659,f2366]) ).

thf(f6659,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) != vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) )
        | ( X1 = X2 ) )
    | ~ spl225_387 ),
    inference(avatar_component_clause,[],[f6658]) ).

thf(f7045,plain,
    ( spl225_419
    | ~ spl225_82
    | ~ spl225_191 ),
    inference(avatar_split_clause,[],[f4327,f4317,f2728,f7043]) ).

thf(f4327,plain,
    ( ! [X0: name] :
        ( ( y = X0 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) )
    | ~ spl225_82
    | ~ spl225_191 ),
    inference(trivial_inequality_removal,[],[f4320]) ).

thf(f4320,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( y = X0 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),p2) ) )
    | ~ spl225_82
    | ~ spl225_191 ),
    inference(superposition,[],[f4318,f2730]) ).

thf(f7041,plain,
    ( spl225_418
    | ~ spl225_17
    | ~ spl225_18
    | ~ spl225_126 ),
    inference(avatar_split_clause,[],[f3358,f3260,f2365,f2361,f7039]) ).

thf(f7039,plain,
    ( spl225_418
  <=> ! [X0: name,X1: name > late_subject] : ( vAPP(name,late_subject,X1,X0) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_418])]) ).

thf(f3260,plain,
    ( spl225_126
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,X1,X2)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_126])]) ).

thf(f3358,plain,
    ( ! [X0: name,X1: name > late_subject] : ( vAPP(name,late_subject,X1,X0) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_17
    | ~ spl225_18
    | ~ spl225_126 ),
    inference(forward_demodulation,[],[f3351,f2362]) ).

thf(f3351,plain,
    ( ! [X0: name,X1: name > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),vAPP(name,late_subject,X1,X0)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_18
    | ~ spl225_126 ),
    inference(superposition,[],[f3261,f2366]) ).

thf(f3261,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: name > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,X1,X2)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) )
    | ~ spl225_126 ),
    inference(avatar_component_clause,[],[f3260]) ).

thf(f7037,plain,
    ( spl225_417
    | ~ spl225_16
    | ~ spl225_18
    | ~ spl225_125 ),
    inference(avatar_split_clause,[],[f3348,f3256,f2365,f2357,f7035]) ).

thf(f7035,plain,
    ( spl225_417
  <=> ! [X0: name,X1: name > late_freeRes] : ( vAPP(name,late_freeRes,X1,X0) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_417])]) ).

thf(f3256,plain,
    ( spl225_125
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,X1,X2)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_125])]) ).

thf(f3348,plain,
    ( ! [X0: name,X1: name > late_freeRes] : ( vAPP(name,late_freeRes,X1,X0) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_18
    | ~ spl225_125 ),
    inference(forward_demodulation,[],[f3341,f2358]) ).

thf(f3341,plain,
    ( ! [X0: name,X1: name > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),vAPP(name,late_freeRes,X1,X0)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_18
    | ~ spl225_125 ),
    inference(superposition,[],[f3257,f2366]) ).

thf(f3257,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: name > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,X1,X2)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) )
    | ~ spl225_125 ),
    inference(avatar_component_clause,[],[f3256]) ).

thf(f7033,plain,
    ( spl225_416
    | ~ spl225_17
    | ~ spl225_19
    | ~ spl225_118 ),
    inference(avatar_split_clause,[],[f3319,f3228,f2369,f2361,f7031]) ).

thf(f7031,plain,
    ( spl225_416
  <=> ! [X0: pi,X1: pi > late_subject] : ( vAPP(pi,late_subject,X1,X0) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_416])]) ).

thf(f3228,plain,
    ( spl225_118
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi,late_subject,X1,X2)) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_118])]) ).

thf(f3319,plain,
    ( ! [X0: pi,X1: pi > late_subject] : ( vAPP(pi,late_subject,X1,X0) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_17
    | ~ spl225_19
    | ~ spl225_118 ),
    inference(forward_demodulation,[],[f3316,f2362]) ).

thf(f3316,plain,
    ( ! [X0: pi,X1: pi > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),vAPP(pi,late_subject,X1,X0)) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_19
    | ~ spl225_118 ),
    inference(superposition,[],[f3229,f2370]) ).

thf(f3229,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: pi > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi,late_subject,X1,X2)) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_118 ),
    inference(avatar_component_clause,[],[f3228]) ).

thf(f7029,plain,
    ( spl225_415
    | ~ spl225_17
    | ~ spl225_117 ),
    inference(avatar_split_clause,[],[f3309,f3224,f2361,f7027]) ).

thf(f7027,plain,
    ( spl225_415
  <=> ! [X0: late_subject,X1: late_subject > late_subject] : ( vAPP(late_subject,late_subject,X1,X0) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_415])]) ).

thf(f3224,plain,
    ( spl225_117
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,X1,X2)) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_117])]) ).

thf(f3309,plain,
    ( ! [X0: late_subject,X1: late_subject > late_subject] : ( vAPP(late_subject,late_subject,X1,X0) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_17
    | ~ spl225_117 ),
    inference(forward_demodulation,[],[f3306,f2362]) ).

thf(f3306,plain,
    ( ! [X0: late_subject,X1: late_subject > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),vAPP(late_subject,late_subject,X1,X0)) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_17
    | ~ spl225_117 ),
    inference(superposition,[],[f3225,f2362]) ).

thf(f3225,plain,
    ( ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,X1,X2)) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
    | ~ spl225_117 ),
    inference(avatar_component_clause,[],[f3224]) ).

thf(f7025,plain,
    ( spl225_414
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_116 ),
    inference(avatar_split_clause,[],[f3301,f3220,f2361,f2357,f7023]) ).

thf(f7023,plain,
    ( spl225_414
  <=> ! [X0: late_freeRes,X1: late_freeRes > late_subject] : ( vAPP(late_freeRes,late_subject,X1,X0) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_414])]) ).

thf(f3301,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes > late_subject] : ( vAPP(late_freeRes,late_subject,X1,X0) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_116 ),
    inference(forward_demodulation,[],[f3298,f2362]) ).

thf(f3298,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),vAPP(late_freeRes,late_subject,X1,X0)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_116 ),
    inference(superposition,[],[f3221,f2358]) ).

thf(f7021,plain,
    ( spl225_413
    | ~ spl225_15
    | ~ spl225_17
    | ~ spl225_115 ),
    inference(avatar_split_clause,[],[f3294,f3060,f2361,f2353,f7019]) ).

thf(f7019,plain,
    ( spl225_413
  <=> ! [X0: pi_Rep,X1: pi_Rep > late_subject] : ( vAPP(pi_Rep,late_subject,X1,X0) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_413])]) ).

thf(f3060,plain,
    ( spl225_115
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi_Rep,late_subject,X1,X2)) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_115])]) ).

thf(f3294,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep > late_subject] : ( vAPP(pi_Rep,late_subject,X1,X0) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_15
    | ~ spl225_17
    | ~ spl225_115 ),
    inference(forward_demodulation,[],[f3291,f2362]) ).

thf(f3291,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),vAPP(pi_Rep,late_subject,X1,X0)) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_15
    | ~ spl225_115 ),
    inference(superposition,[],[f3061,f2354]) ).

thf(f3061,plain,
    ( ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi_Rep,late_subject,X1,X2)) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
    | ~ spl225_115 ),
    inference(avatar_component_clause,[],[f3060]) ).

thf(f7017,plain,
    ( spl225_412
    | ~ spl225_16
    | ~ spl225_19
    | ~ spl225_114 ),
    inference(avatar_split_clause,[],[f3288,f3056,f2369,f2357,f7015]) ).

thf(f7015,plain,
    ( spl225_412
  <=> ! [X0: pi,X1: pi > late_freeRes] : ( vAPP(pi,late_freeRes,X1,X0) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_412])]) ).

thf(f3056,plain,
    ( spl225_114
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi,late_freeRes,X1,X2)) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_114])]) ).

thf(f3288,plain,
    ( ! [X0: pi,X1: pi > late_freeRes] : ( vAPP(pi,late_freeRes,X1,X0) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_19
    | ~ spl225_114 ),
    inference(forward_demodulation,[],[f3285,f2358]) ).

thf(f3285,plain,
    ( ! [X0: pi,X1: pi > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),vAPP(pi,late_freeRes,X1,X0)) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_19
    | ~ spl225_114 ),
    inference(superposition,[],[f3057,f2370]) ).

thf(f3057,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: pi > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi,late_freeRes,X1,X2)) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
    | ~ spl225_114 ),
    inference(avatar_component_clause,[],[f3056]) ).

thf(f7013,plain,
    ( spl225_411
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_113 ),
    inference(avatar_split_clause,[],[f3282,f3052,f2361,f2357,f7011]) ).

thf(f7011,plain,
    ( spl225_411
  <=> ! [X0: late_subject,X1: late_subject > late_freeRes] : ( vAPP(late_subject,late_freeRes,X1,X0) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_411])]) ).

thf(f3052,plain,
    ( spl225_113
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_subject,late_freeRes,X1,X2)) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_113])]) ).

thf(f3282,plain,
    ( ! [X0: late_subject,X1: late_subject > late_freeRes] : ( vAPP(late_subject,late_freeRes,X1,X0) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_17
    | ~ spl225_113 ),
    inference(forward_demodulation,[],[f3279,f2358]) ).

thf(f3279,plain,
    ( ! [X0: late_subject,X1: late_subject > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),vAPP(late_subject,late_freeRes,X1,X0)) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_17
    | ~ spl225_113 ),
    inference(superposition,[],[f3053,f2362]) ).

thf(f3053,plain,
    ( ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_subject,late_freeRes,X1,X2)) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
    | ~ spl225_113 ),
    inference(avatar_component_clause,[],[f3052]) ).

thf(f7009,plain,
    ( spl225_410
    | ~ spl225_16
    | ~ spl225_112 ),
    inference(avatar_split_clause,[],[f3274,f3048,f2357,f7007]) ).

thf(f7007,plain,
    ( spl225_410
  <=> ! [X0: late_freeRes,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,X1,X0) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_410])]) ).

thf(f3274,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,X1,X0) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_112 ),
    inference(forward_demodulation,[],[f3271,f2358]) ).

thf(f3271,plain,
    ( ! [X0: late_freeRes,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),vAPP(late_freeRes,late_freeRes,X1,X0)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_16
    | ~ spl225_112 ),
    inference(superposition,[],[f3049,f2358]) ).

thf(f6976,plain,
    ( spl225_409
    | ~ spl225_15
    | ~ spl225_16
    | ~ spl225_111 ),
    inference(avatar_split_clause,[],[f3267,f3044,f2357,f2353,f6974]) ).

thf(f6974,plain,
    ( spl225_409
  <=> ! [X0: pi_Rep,X1: pi_Rep > late_freeRes] : ( vAPP(pi_Rep,late_freeRes,X1,X0) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,nil_Pr743626285e_name),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_409])]) ).

thf(f3044,plain,
    ( spl225_111
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi_Rep,late_freeRes,X1,X2)) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_111])]) ).

thf(f3267,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep > late_freeRes] : ( vAPP(pi_Rep,late_freeRes,X1,X0) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_15
    | ~ spl225_16
    | ~ spl225_111 ),
    inference(forward_demodulation,[],[f3264,f2358]) ).

thf(f3264,plain,
    ( ! [X0: pi_Rep,X1: pi_Rep > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),vAPP(pi_Rep,late_freeRes,X1,X0)) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,nil_Pr743626285e_name),X1),X0) )
    | ~ spl225_15
    | ~ spl225_111 ),
    inference(superposition,[],[f3045,f2354]) ).

thf(f3045,plain,
    ( ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi_Rep,late_freeRes,X1,X2)) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
    | ~ spl225_111 ),
    inference(avatar_component_clause,[],[f3044]) ).

thf(f6972,plain,
    spl225_408,
    inference(avatar_split_clause,[],[f2037,f6970]) ).

thf(f6970,plain,
    ( spl225_408
  <=> ! [X0: produc367475239e_name,X3: list_P227219501e_name,X2: produc367475239e_name,X1: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
        | ( X1 != X3 )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_408])]) ).

thf(f2037,plain,
    ! [X2: produc367475239e_name,X3: list_P227219501e_name,X0: produc367475239e_name,X1: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
      | ( X1 != X3 )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2036]) ).

thf(f2036,plain,
    ! [X2: produc367475239e_name,X3: list_P227219501e_name,X0: produc367475239e_name,X1: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
      | ( X1 != X3 )
      | ( $false = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2035]) ).

thf(f2035,plain,
    ! [X2: produc367475239e_name,X3: list_P227219501e_name,X0: produc367475239e_name,X1: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
      | ( $false = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X1),X3) )
      | ( $false = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f2034]) ).

thf(f2034,plain,
    ! [X2: produc367475239e_name,X3: list_P227219501e_name,X0: produc367475239e_name,X1: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X2)),vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X1),X3)) ) ),
    inference(equality_proxy_clausification,[],[f2027]) ).

thf(f2027,plain,
    ! [X2: produc367475239e_name,X3: list_P227219501e_name,X0: produc367475239e_name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X2)),vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X1),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1662]) ).

thf(f1662,plain,
    ! [X2: produc367475239e_name,X3: list_P227219501e_name,X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X2)),vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X1),X3)) ),
    inference(cnf_transformation,[],[f590]) ).

thf(f590,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name,X2: produc367475239e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),X0),X2)),vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X1),X3)) ),
    inference(fool_elimination,[],[f589]) ).

thf(f589,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name,X2: produc367475239e_name,X3: list_P227219501e_name] :
      ( ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f168]) ).

thf(f168,axiom,
    ! [X37: produc367475239e_name,X38: list_P227219501e_name,X39: produc367475239e_name,X40: list_P227219501e_name] :
      ( ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X37),X38) = vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X39),X40) )
        = ( X38 = X40 ) )
      & ( X37 = X39 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_list_Oinject) ).

thf(f6968,plain,
    spl225_407,
    inference(avatar_split_clause,[],[f2026,f6966]) ).

thf(f6966,plain,
    ( spl225_407
  <=> ! [X0: name,X3: name,X2: name,X1: name] :
        ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3) )
        | ( X1 != X3 )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_407])]) ).

thf(f2026,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3) )
      | ( X1 != X3 )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2025]) ).

thf(f2025,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3) )
      | ( X1 != X3 )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2024]) ).

thf(f2024,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f2023]) ).

thf(f2023,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) ) ),
    inference(equality_proxy_clausification,[],[f2016]) ).

thf(f2016,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1663]) ).

thf(f1663,plain,
    ! [X2: name,X3: name,X0: name,X1: name] : ( vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) ),
    inference(cnf_transformation,[],[f592]) ).

thf(f592,plain,
    ! [X0: name,X1: name,X2: name,X3: name] : ( vAPP(produc367475239e_name,$o,vAPP(produc367475239e_name,sTfun(produc367475239e_name,$o),vEQ(produc367475239e_name),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) ),
    inference(fool_elimination,[],[f591]) ).

thf(f591,plain,
    ! [X0: name,X1: name,X2: name,X3: name] :
      ( ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f171]) ).

thf(f171,axiom,
    ! [X3: name,X4: name,X7: name,X6: name] :
      ( ( ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X4) = vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X7),X6) )
        = ( X4 = X6 ) )
      & ( X3 = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_prod_Oinject) ).

thf(f6964,plain,
    spl225_406,
    inference(avatar_split_clause,[],[f1998,f6962]) ).

thf(f6962,plain,
    ( spl225_406
  <=> ! [X0: name,X3: name,X2: name,X1: name] :
        ( ( X1 != X3 )
        | ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3) )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_406])]) ).

thf(f1998,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( X1 != X3 )
      | ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3) )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f1997]) ).

thf(f1997,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( X1 != X3 )
      | ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1996]) ).

thf(f1996,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( X1 != X3 )
      | ( $true = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1995]) ).

thf(f1995,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3) )
      | ( $true = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1994]) ).

thf(f1994,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) )
      | ( $true = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1665]) ).

thf(f1665,plain,
    ! [X2: name,X3: name,X0: name,X1: name] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) ),
    inference(cnf_transformation,[],[f596]) ).

thf(f596,plain,
    ! [X0: name,X1: name,X2: name,X3: name] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X2)),vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X3)) = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) ),
    inference(fool_elimination,[],[f595]) ).

thf(f595,plain,
    ! [X0: name,X1: name,X2: name,X3: name] :
      ( ( ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f44]) ).

thf(f44,axiom,
    ! [X4: name,X3: name,X6: name,X7: name] :
      ( ( ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X3) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7) )
        = ( X3 = X7 ) )
      & ( X4 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Late__Semantics_OfreeRes_Oinject) ).

thf(f6960,plain,
    spl225_405,
    inference(avatar_split_clause,[],[f1980,f6958]) ).

thf(f6958,plain,
    ( spl225_405
  <=> ! [X0: late_freeRes,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3) )
        | ( X1 != X3 )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_405])]) ).

thf(f1980,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3) )
      | ( X1 != X3 )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f1979]) ).

thf(f1979,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3) )
      | ( X1 != X3 )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1978]) ).

thf(f1978,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3) )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1977]) ).

thf(f1977,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ) ),
    inference(equality_proxy_clausification,[],[f1970]) ).

thf(f1970,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( $true = vAPP(late_residual_Rep,$o,vAPP(late_residual_Rep,sTfun(late_residual_Rep,$o),vEQ(late_residual_Rep),vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1)),vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1667]) ).

thf(f1667,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] : ( vAPP(late_residual_Rep,$o,vAPP(late_residual_Rep,sTfun(late_residual_Rep,$o),vEQ(late_residual_Rep),vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1)),vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ),
    inference(cnf_transformation,[],[f600]) ).

thf(f600,plain,
    ! [X0: late_freeRes,X1: pi,X2: late_freeRes,X3: pi] : ( vAPP(late_residual_Rep,$o,vAPP(late_residual_Rep,sTfun(late_residual_Rep,$o),vEQ(late_residual_Rep),vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1)),vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ),
    inference(fool_elimination,[],[f599]) ).

thf(f599,plain,
    ! [X0: late_freeRes,X1: pi,X2: late_freeRes,X3: pi] :
      ( ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X0),X1) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f279]) ).

thf(f279,axiom,
    ! [X37: late_freeRes,X38: pi,X39: late_freeRes,X40: pi] :
      ( ( ( vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X37),X38) = vAPP(pi,late_residual_Rep,vAPP(late_freeRes,sTfun(pi,late_residual_Rep),late_r347633188eR_Rep,X39),X40) )
        = ( X38 = X40 ) )
      & ( X37 = X39 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_residual__Rep_Oinject_I2_J) ).

thf(f6956,plain,
    spl225_404,
    inference(avatar_split_clause,[],[f1969,f6954]) ).

thf(f6954,plain,
    ( spl225_404
  <=> ! [X0: pi,X3: pi,X2: pi,X1: pi] :
        ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3) )
        | ( X1 != X3 )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_404])]) ).

thf(f1969,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3) )
      | ( X1 != X3 )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f1968]) ).

thf(f1968,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3) )
      | ( X1 != X3 )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1967]) ).

thf(f1967,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1966]) ).

thf(f1966,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ) ),
    inference(equality_proxy_clausification,[],[f1959]) ).

thf(f1959,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1)),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1668]) ).

thf(f1668,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] : ( vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1)),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ),
    inference(cnf_transformation,[],[f602]) ).

thf(f602,plain,
    ! [X0: pi,X1: pi,X2: pi,X3: pi] : ( vAPP(product_prod_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(product_prod_pi_pi,$o),vEQ(product_prod_pi_pi),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1)),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) ),
    inference(fool_elimination,[],[f601]) ).

thf(f601,plain,
    ! [X0: pi,X1: pi,X2: pi,X3: pi] :
      ( ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f170]) ).

thf(f170,axiom,
    ! [X0: pi,X1: pi,X41: pi,X42: pi] :
      ( ( ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X0),X1) = vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X41),X42) )
        = ( X1 = X42 ) )
      & ( X0 = X41 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_old_Oprod_Oinject) ).

thf(f6952,plain,
    spl225_403,
    inference(avatar_split_clause,[],[f1941,f6950]) ).

thf(f6950,plain,
    ( spl225_403
  <=> ! [X0: late_freeRes,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( X1 != X3 )
        | ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_403])]) ).

thf(f1941,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( X1 != X3 )
      | ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f1940]) ).

thf(f1940,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( X1 != X3 )
      | ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1939]) ).

thf(f1939,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( X1 != X3 )
      | ( $true = vAPP(late_residual,$o,vAPP(late_residual,sTfun(late_residual,$o),vEQ(late_residual),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1938]) ).

thf(f1938,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3) )
      | ( $true = vAPP(late_residual,$o,vAPP(late_residual,sTfun(late_residual,$o),vEQ(late_residual),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1937]) ).

thf(f1937,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) )
      | ( $true = vAPP(late_residual,$o,vAPP(late_residual,sTfun(late_residual,$o),vEQ(late_residual),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1670]) ).

thf(f1670,plain,
    ! [X2: late_freeRes,X3: pi,X0: late_freeRes,X1: pi] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) = vAPP(late_residual,$o,vAPP(late_residual,sTfun(late_residual,$o),vEQ(late_residual),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ),
    inference(cnf_transformation,[],[f606]) ).

thf(f606,plain,
    ! [X0: late_freeRes,X1: pi,X2: late_freeRes,X3: pi] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) = vAPP(late_residual,$o,vAPP(late_residual,sTfun(late_residual,$o),vEQ(late_residual),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ),
    inference(fool_elimination,[],[f605]) ).

thf(f605,plain,
    ! [X0: late_freeRes,X1: pi,X2: late_freeRes,X3: pi] :
      ( ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X0),X1) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f157]) ).

thf(f157,axiom,
    ! [X4: late_freeRes,X3: pi,X6: late_freeRes,X7: pi] :
      ( ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X6),X7) )
        = ( X3 = X7 ) )
      & ( X4 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_residual_Oinject_I2_J) ).

thf(f6948,plain,
    spl225_402,
    inference(avatar_split_clause,[],[f1929,f6946]) ).

thf(f6946,plain,
    ( spl225_402
  <=> ! [X0: pi,X3: pi,X2: pi,X1: pi] :
        ( ( X1 != X3 )
        | ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3) )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_402])]) ).

thf(f1929,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( X1 != X3 )
      | ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3) )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f1928]) ).

thf(f1928,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( X1 != X3 )
      | ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1927]) ).

thf(f1927,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( X1 != X3 )
      | ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3)) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f1926]) ).

thf(f1926,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3) )
      | ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3)) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1925]) ).

thf(f1925,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) )
      | ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1671]) ).

thf(f1671,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: pi] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3)) ),
    inference(cnf_transformation,[],[f608]) ).

thf(f608,plain,
    ! [X0: pi,X1: pi,X2: pi,X3: pi] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X0),X2)),vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X3)) = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3)) ),
    inference(fool_elimination,[],[f607]) ).

thf(f607,plain,
    ! [X0: pi,X1: pi,X2: pi,X3: pi] :
      ( ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f288]) ).

thf(f288,axiom,
    ! [X4: pi,X3: pi,X6: pi,X7: pi] :
      ( ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X7) )
        = ( X3 = X7 ) )
      & ( X4 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_pi_Oinject_I7_J) ).

thf(f6918,plain,
    ( spl225_401
    | ~ spl225_28
    | ~ spl225_396 ),
    inference(avatar_split_clause,[],[f6842,f6696,f2409,f6915]) ).

thf(f6915,plain,
    ( spl225_401
  <=> ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_401])]) ).

thf(f6842,plain,
    ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q_a) )
    | ~ spl225_28
    | ~ spl225_396 ),
    inference(trivial_inequality_removal,[],[f6837]) ).

thf(f6837,plain,
    ( ( $true != $true )
    | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q_a) )
    | ~ spl225_28
    | ~ spl225_396 ),
    inference(superposition,[],[f6697,f2411]) ).

thf(f6854,plain,
    ( spl225_400
    | ~ spl225_37
    | ~ spl225_65 ),
    inference(avatar_split_clause,[],[f2610,f2606,f2455,f6852]) ).

thf(f6852,plain,
    ( spl225_400
  <=> ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK53,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK52,X0) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_400])]) ).

thf(f2606,plain,
    ( spl225_65
  <=> ! [X2: name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X1 )
        | ( X1 = X2 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_65])]) ).

thf(f2610,plain,
    ( ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK53,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK52,X0) = X1 ) )
    | ~ spl225_37
    | ~ spl225_65 ),
    inference(superposition,[],[f2607,f2456]) ).

thf(f2607,plain,
    ( ! [X2: name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X1 )
        | ( X1 = X2 )
        | ( X0 = X1 ) )
    | ~ spl225_65 ),
    inference(avatar_component_clause,[],[f2606]) ).

thf(f6850,plain,
    ( spl225_399
    | ~ spl225_34
    | ~ spl225_65 ),
    inference(avatar_split_clause,[],[f2609,f2606,f2443,f6848]) ).

thf(f6848,plain,
    ( spl225_399
  <=> ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK49,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK48,X0) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_399])]) ).

thf(f2609,plain,
    ( ! [X0: produc367475239e_name,X1: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),X1) = X1 )
        | ( vAPP(produc367475239e_name,name,sK49,X0) = X1 )
        | ( vAPP(produc367475239e_name,name,sK48,X0) = X1 ) )
    | ~ spl225_34
    | ~ spl225_65 ),
    inference(superposition,[],[f2607,f2444]) ).

thf(f6846,plain,
    ( spl225_398
    | ~ spl225_8
    | ~ spl225_63 ),
    inference(avatar_split_clause,[],[f2600,f2588,f2296,f6844]) ).

thf(f6844,plain,
    ( spl225_398
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_398])]) ).

thf(f2588,plain,
    ( spl225_63
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_63])]) ).

thf(f2600,plain,
    ( ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) )
    | ~ spl225_8
    | ~ spl225_63 ),
    inference(trivial_inequality_removal,[],[f2599]) ).

thf(f2599,plain,
    ( ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true != $true )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) )
    | ~ spl225_8
    | ~ spl225_63 ),
    inference(superposition,[],[f2589,f2297]) ).

thf(f2589,plain,
    ( ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,X1) ) )
    | ~ spl225_63 ),
    inference(avatar_component_clause,[],[f2588]) ).

thf(f6785,plain,
    ( spl225_397
    | ~ spl225_19
    | ~ spl225_384 ),
    inference(avatar_split_clause,[],[f6701,f6646,f2369,f6783]) ).

thf(f6783,plain,
    ( spl225_397
  <=> ! [X0: pi,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_397])]) ).

thf(f6646,plain,
    ( spl225_384
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_384])]) ).

thf(f6701,plain,
    ( ! [X0: pi,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X1) != X0 )
        | ( X0 = X1 ) )
    | ~ spl225_19
    | ~ spl225_384 ),
    inference(superposition,[],[f6647,f2370]) ).

thf(f6647,plain,
    ( ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
        | ( X1 = X2 ) )
    | ~ spl225_384 ),
    inference(avatar_component_clause,[],[f6646]) ).

thf(f6698,plain,
    ( spl225_396
    | ~ spl225_76
    | ~ spl225_124 ),
    inference(avatar_split_clause,[],[f3340,f3252,f2662,f6696]) ).

thf(f3340,plain,
    ( ! [X0: name] :
        ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q_a) ) )
    | ~ spl225_76
    | ~ spl225_124 ),
    inference(trivial_inequality_removal,[],[f3335]) ).

thf(f3335,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),q_a) ) )
    | ~ spl225_76
    | ~ spl225_124 ),
    inference(superposition,[],[f3253,f2664]) ).

thf(f6694,plain,
    spl225_395,
    inference(avatar_split_clause,[],[f2245,f6692]) ).

thf(f6692,plain,
    ( spl225_395
  <=> ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi > $o] :
        ( ( $false = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X1)) )
        | ( $true = vAPP(product_prod_pi_pi,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_395])]) ).

thf(f2245,plain,
    ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi > $o] :
      ( ( $false = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X1)) )
      | ( $true = vAPP(product_prod_pi_pi,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1403]) ).

thf(f1403,plain,
    ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi > $o] : ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X1)) = vAPP(product_prod_pi_pi,$o,X1,X0) ),
    inference(cnf_transformation,[],[f801]) ).

thf(f801,plain,
    ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi > $o] : ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X1)) = vAPP(product_prod_pi_pi,$o,X1,X0) ),
    inference(rectify,[],[f93]) ).

thf(f93,axiom,
    ! [X0: product_prod_pi_pi,X19: product_prod_pi_pi > $o] : ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X19)) = vAPP(product_prod_pi_pi,$o,X19,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mem__Collect__eq) ).

thf(f6690,plain,
    spl225_394,
    inference(avatar_split_clause,[],[f2244,f6688]) ).

thf(f6688,plain,
    ( spl225_394
  <=> ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi > $o] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X1)) )
        | ( $false = vAPP(product_prod_pi_pi,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_394])]) ).

thf(f2244,plain,
    ! [X0: product_prod_pi_pi,X1: product_prod_pi_pi > $o] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X0),vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,X1)) )
      | ( $false = vAPP(product_prod_pi_pi,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1403]) ).

thf(f6684,plain,
    spl225_393,
    inference(avatar_split_clause,[],[f2183,f6682]) ).

thf(f6682,plain,
    ( spl225_393
  <=> ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
        | ( X1 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_393])]) ).

thf(f2183,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2182]) ).

thf(f2182,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
      | ( $false = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2178]) ).

thf(f2178,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
      | ( $false = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1526]) ).

thf(f1526,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] : ( vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),X1),X2) ),
    inference(cnf_transformation,[],[f436]) ).

thf(f436,plain,
    ! [X0: list_P227219501e_name,X1: pi_Rep,X2: pi_Rep] : ( vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),X1),X2) ),
    inference(fool_elimination,[],[f435]) ).

thf(f435,plain,
    ! [X0: list_P227219501e_name,X1: pi_Rep,X2: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f133]) ).

thf(f133,axiom,
    ! [X5: list_P227219501e_name,X2: pi_Rep,X22: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X22) )
      = ( X2 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_perm__bij) ).

thf(f6680,plain,
    spl225_392,
    inference(avatar_split_clause,[],[f2181,f6678]) ).

thf(f2181,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) != vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
      | ( X1 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2180]) ).

thf(f2180,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1) != vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) )
      | ( $true = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2179]) ).

thf(f2179,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] :
      ( ( $false = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) )
      | ( $true = vAPP(pi_Rep,$o,vAPP(pi_Rep,sTfun(pi_Rep,$o),vEQ(pi_Rep),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1526]) ).

thf(f6676,plain,
    spl225_391,
    inference(avatar_split_clause,[],[f2177,f6674]) ).

thf(f6674,plain,
    ( spl225_391
  <=> ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
        | ( X1 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_391])]) ).

thf(f2177,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2176]) ).

thf(f2176,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2172]) ).

thf(f2172,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
      | ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1527]) ).

thf(f1527,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X1),X2) ),
    inference(cnf_transformation,[],[f438]) ).

thf(f438,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: late_freeRes] : ( vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X1),X2) ),
    inference(fool_elimination,[],[f437]) ).

thf(f437,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f132]) ).

thf(f132,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X22: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X22) )
      = ( X2 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_perm__bij) ).

thf(f6672,plain,
    spl225_390,
    inference(avatar_split_clause,[],[f2175,f6670]) ).

thf(f2175,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
      | ( X1 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2174]) ).

thf(f2174,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1) != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) )
      | ( $true = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2173]) ).

thf(f2173,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] :
      ( ( $false = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) )
      | ( $true = vAPP(late_freeRes,$o,vAPP(late_freeRes,sTfun(late_freeRes,$o),vEQ(late_freeRes),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1527]) ).

thf(f6668,plain,
    spl225_389,
    inference(avatar_split_clause,[],[f2171,f6666]) ).

thf(f6666,plain,
    ( spl225_389
  <=> ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
        | ( X1 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_389])]) ).

thf(f2171,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2170]) ).

thf(f2170,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      | ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2166]) ).

thf(f2166,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
      | ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1528]) ).

thf(f1528,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2) ),
    inference(cnf_transformation,[],[f440]) ).

thf(f440,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: late_subject] : ( vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2) ),
    inference(fool_elimination,[],[f439]) ).

thf(f439,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f131]) ).

thf(f131,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X22) )
      = ( X2 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_perm__bij) ).

thf(f6664,plain,
    spl225_388,
    inference(avatar_split_clause,[],[f2169,f6662]) ).

thf(f2169,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) != vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      | ( X1 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2168]) ).

thf(f2168,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1) != vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) )
      | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2167]) ).

thf(f2167,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] :
      ( ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) )
      | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1528]) ).

thf(f6660,plain,
    spl225_387,
    inference(avatar_split_clause,[],[f2165,f6658]) ).

thf(f2165,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( X1 = X2 )
      | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) != vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2164]) ).

thf(f2164,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( X1 = X2 )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2160]) ).

thf(f2160,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2) )
      | ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1854]) ).

thf(f1854,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2) = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1529,f1358,f1358]) ).

thf(f1529,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2) ),
    inference(cnf_transformation,[],[f442]) ).

thf(f442,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2) ),
    inference(fool_elimination,[],[f441]) ).

thf(f441,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f134]) ).

thf(f134,axiom,
    ! [X5: list_P227219501e_name,X2: name,X22: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X22) )
      = ( X2 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_perm__bij) ).

thf(f6656,plain,
    spl225_386,
    inference(avatar_split_clause,[],[f2163,f6654]) ).

thf(f6654,plain,
    ( spl225_386
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name] :
        ( ( X1 != X2 )
        | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_386])]) ).

thf(f2163,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( X1 != X2 )
      | ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2162]) ).

thf(f2162,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( X1 != X2 )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2161]) ).

thf(f2161,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] :
      ( ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X1),X2) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1854]) ).

thf(f6652,plain,
    spl225_385,
    inference(avatar_split_clause,[],[f2153,f6650]) ).

thf(f6650,plain,
    ( spl225_385
  <=> ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
        | ( X1 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_385])]) ).

thf(f2153,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2152]) ).

thf(f2152,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2148]) ).

thf(f2148,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
      | ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1531]) ).

thf(f1531,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2) ),
    inference(cnf_transformation,[],[f446]) ).

thf(f446,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: pi] : ( vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2) ),
    inference(fool_elimination,[],[f445]) ).

thf(f445,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f135]) ).

thf(f135,axiom,
    ! [X5: list_P227219501e_name,X2: pi,X22: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X22) )
      = ( X2 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_perm__bij) ).

thf(f6648,plain,
    spl225_384,
    inference(avatar_split_clause,[],[f2151,f6646]) ).

thf(f2151,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      | ( X1 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2150]) ).

thf(f2150,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1) != vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) )
      | ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2149]) ).

thf(f2149,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] :
      ( ( $false = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) )
      | ( $true = vAPP(pi,$o,vAPP(pi,sTfun(pi,$o),vEQ(pi),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1531]) ).

thf(f6644,plain,
    ( spl225_383
    | ~ spl225_46
    | ~ spl225_52 ),
    inference(avatar_split_clause,[],[f2666,f2530,f2491,f6642]) ).

thf(f6642,plain,
    ( spl225_383
  <=> ! [X0: late_subject,X1: name] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,X1) != X0 )
        | ( vAPP(late_subject,name,sK18,X0) = X1 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_383])]) ).

thf(f2491,plain,
    ( spl225_46
  <=> ! [X0: name,X1: name] :
        ( ( X0 = X1 )
        | ( vAPP(name,late_subject,late_BoundOutputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_46])]) ).

thf(f2666,plain,
    ( ! [X0: late_subject,X1: name] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,X1) != X0 )
        | ( vAPP(late_subject,name,sK18,X0) = X1 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) )
    | ~ spl225_46
    | ~ spl225_52 ),
    inference(superposition,[],[f2492,f2531]) ).

thf(f2492,plain,
    ( ! [X0: name,X1: name] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) )
        | ( X0 = X1 ) )
    | ~ spl225_46 ),
    inference(avatar_component_clause,[],[f2491]) ).

thf(f6636,plain,
    ( spl225_382
    | ~ spl225_32
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2716,f2699,f2427,f6634]) ).

thf(f6634,plain,
    ( spl225_382
  <=> ! [X0: pi,X1: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),vAPP(pi,name,sK47,X0)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_382])]) ).

thf(f2716,plain,
    ( ! [X0: pi,X1: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),vAPP(pi,name,sK47,X0)),X1) = X0 )
    | ~ spl225_32
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2713]) ).

thf(f2713,plain,
    ( ! [X0: pi,X1: name] :
        ( ( $true != $true )
        | ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),vAPP(pi,name,sK47,X0)),X1) = X0 ) )
    | ~ spl225_32
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2428]) ).

thf(f6592,plain,
    ( spl225_381
    | ~ spl225_18
    | ~ spl225_105 ),
    inference(avatar_split_clause,[],[f2980,f2928,f2365,f6590]) ).

thf(f6590,plain,
    ( spl225_381
  <=> ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) = X2 )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_381])]) ).

thf(f2928,plain,
    ( spl225_105
  <=> ! [X0: $o,X3: name,X2: name,X1: list_P227219501e_name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_105])]) ).

thf(f2980,plain,
    ( ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) = X2 )
        | ( $true = X0 ) )
    | ~ spl225_18
    | ~ spl225_105 ),
    inference(forward_demodulation,[],[f2968,f2366]) ).

thf(f2968,plain,
    ( ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X2) = vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) )
        | ( $true = X0 ) )
    | ~ spl225_18
    | ~ spl225_105 ),
    inference(superposition,[],[f2929,f2366]) ).

thf(f2929,plain,
    ( ! [X2: name,X3: name,X0: $o,X1: list_P227219501e_name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) )
        | ( $true = X0 ) )
    | ~ spl225_105 ),
    inference(avatar_component_clause,[],[f2928]) ).

thf(f6588,plain,
    ( spl225_380
    | ~ spl225_19
    | ~ spl225_104 ),
    inference(avatar_split_clause,[],[f2963,f2924,f2369,f6586]) ).

thf(f6586,plain,
    ( spl225_380
  <=> ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) = X2 )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_380])]) ).

thf(f2924,plain,
    ( spl225_104
  <=> ! [X0: $o,X3: pi,X2: pi,X1: list_P227219501e_name] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_104])]) ).

thf(f2963,plain,
    ( ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) = X2 )
        | ( $true = X0 ) )
    | ~ spl225_19
    | ~ spl225_104 ),
    inference(forward_demodulation,[],[f2959,f2370]) ).

thf(f2959,plain,
    ( ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X2) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) )
        | ( $true = X0 ) )
    | ~ spl225_19
    | ~ spl225_104 ),
    inference(superposition,[],[f2925,f2370]) ).

thf(f2925,plain,
    ( ! [X2: pi,X3: pi,X0: $o,X1: list_P227219501e_name] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) )
        | ( $true = X0 ) )
    | ~ spl225_104 ),
    inference(avatar_component_clause,[],[f2924]) ).

thf(f6584,plain,
    ( spl225_379
    | ~ spl225_17
    | ~ spl225_103 ),
    inference(avatar_split_clause,[],[f2954,f2920,f2361,f6582]) ).

thf(f6582,plain,
    ( spl225_379
  <=> ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) = X2 )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_379])]) ).

thf(f2920,plain,
    ( spl225_103
  <=> ! [X0: $o,X3: late_subject,X2: late_subject,X1: list_P227219501e_name] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_103])]) ).

thf(f2954,plain,
    ( ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) = X2 )
        | ( $true = X0 ) )
    | ~ spl225_17
    | ~ spl225_103 ),
    inference(forward_demodulation,[],[f2950,f2362]) ).

thf(f2950,plain,
    ( ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X2) = vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) )
        | ( $true = X0 ) )
    | ~ spl225_17
    | ~ spl225_103 ),
    inference(superposition,[],[f2921,f2362]) ).

thf(f2921,plain,
    ( ! [X2: late_subject,X3: late_subject,X0: $o,X1: list_P227219501e_name] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) )
        | ( $true = X0 ) )
    | ~ spl225_103 ),
    inference(avatar_component_clause,[],[f2920]) ).

thf(f6580,plain,
    ( spl225_378
    | ~ spl225_16
    | ~ spl225_102 ),
    inference(avatar_split_clause,[],[f2945,f2916,f2357,f6578]) ).

thf(f6578,plain,
    ( spl225_378
  <=> ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X2 )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_378])]) ).

thf(f2916,plain,
    ( spl225_102
  <=> ! [X0: $o,X3: late_freeRes,X2: late_freeRes,X1: list_P227219501e_name] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_102])]) ).

thf(f2945,plain,
    ( ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X2 )
        | ( $true = X0 ) )
    | ~ spl225_16
    | ~ spl225_102 ),
    inference(forward_demodulation,[],[f2941,f2358]) ).

thf(f2941,plain,
    ( ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X2) = vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) )
        | ( $true = X0 ) )
    | ~ spl225_16
    | ~ spl225_102 ),
    inference(superposition,[],[f2917,f2358]) ).

thf(f2917,plain,
    ( ! [X2: late_freeRes,X3: late_freeRes,X0: $o,X1: list_P227219501e_name] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) )
        | ( $true = X0 ) )
    | ~ spl225_102 ),
    inference(avatar_component_clause,[],[f2916]) ).

thf(f6576,plain,
    ( spl225_377
    | ~ spl225_15
    | ~ spl225_100 ),
    inference(avatar_split_clause,[],[f2936,f2908,f2353,f6574]) ).

thf(f6574,plain,
    ( spl225_377
  <=> ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X2 )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_377])]) ).

thf(f2908,plain,
    ( spl225_100
  <=> ! [X0: $o,X3: pi_Rep,X2: pi_Rep,X1: list_P227219501e_name] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_100])]) ).

thf(f2936,plain,
    ( ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X2 )
        | ( $true = X0 ) )
    | ~ spl225_15
    | ~ spl225_100 ),
    inference(forward_demodulation,[],[f2932,f2354]) ).

thf(f2932,plain,
    ( ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X2) = vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) )
        | ( $true = X0 ) )
    | ~ spl225_15
    | ~ spl225_100 ),
    inference(superposition,[],[f2909,f2354]) ).

thf(f2909,plain,
    ( ! [X2: pi_Rep,X3: pi_Rep,X0: $o,X1: list_P227219501e_name] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) )
        | ( $true = X0 ) )
    | ~ spl225_100 ),
    inference(avatar_component_clause,[],[f2908]) ).

thf(f6572,plain,
    ( spl225_376
    | ~ spl225_8
    | ~ spl225_50 ),
    inference(avatar_split_clause,[],[f2526,f2507,f2296,f6570]) ).

thf(f6570,plain,
    ( spl225_376
  <=> ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) = X1 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_376])]) ).

thf(f2526,plain,
    ( ! [X2: pi,X0: $o,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X1),X2) = X1 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_50 ),
    inference(superposition,[],[f2508,f2297]) ).

thf(f6568,plain,
    ( spl225_375
    | ~ spl225_8
    | ~ spl225_48 ),
    inference(avatar_split_clause,[],[f2523,f2499,f2296,f6566]) ).

thf(f6566,plain,
    ( spl225_375
  <=> ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) = X1 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_375])]) ).

thf(f2523,plain,
    ( ! [X2: name,X0: $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X1),X2) = X1 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_48 ),
    inference(superposition,[],[f2500,f2297]) ).

thf(f6564,plain,
    ( spl225_374
    | ~ spl225_8
    | ~ spl225_45 ),
    inference(avatar_split_clause,[],[f2520,f2487,f2296,f6562]) ).

thf(f6562,plain,
    ( spl225_374
  <=> ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) = X1 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_374])]) ).

thf(f2520,plain,
    ( ! [X2: late_subject,X0: $o,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X1),X2) = X1 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_45 ),
    inference(superposition,[],[f2488,f2297]) ).

thf(f6558,plain,
    ( spl225_373
    | ~ spl225_8
    | ~ spl225_43 ),
    inference(avatar_split_clause,[],[f2517,f2479,f2296,f6556]) ).

thf(f6556,plain,
    ( spl225_373
  <=> ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X1 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_373])]) ).

thf(f2517,plain,
    ( ! [X2: late_freeRes,X0: $o,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X1),X2) = X1 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_43 ),
    inference(superposition,[],[f2480,f2297]) ).

thf(f6554,plain,
    spl225_372,
    inference(avatar_split_clause,[],[f1889,f6552]) ).

thf(f6552,plain,
    ( spl225_372
  <=> ! [X0: set_Pr1834926343_pi_pi,X3: pi,X2: pi,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),sCOMB,vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),sTfun(pi,sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),sTfun(pi,sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))))),bCOMB,sCOMB),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(pi,$o)),sTfun(pi,$o)),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),bCOMB,vAPP(sTfun(sTfun(pi,$o),$o),sTfun(sTfun(pi,sTfun(pi,$o)),sTfun(pi,$o)),bCOMB,vPI(pi)))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o)))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(pi,sTfun(name,$o))),sTfun(pi,sTfun(pi,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o)))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(name,$o)),sTfun(pi,$o)),sTfun(sTfun(pi,sTfun(pi,sTfun(name,$o))),sTfun(pi,sTfun(pi,$o))),bCOMB,vAPP(sTfun(sTfun(name,$o),$o),sTfun(sTfun(pi,sTfun(name,$o)),sTfun(pi,$o)),bCOMB,vPI(name))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o))))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o)))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))),sTfun(pi,sTfun(pi,sTfun(name,$o)))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o))))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(name,sTfun(late_subject,$o))),sTfun(pi,sTfun(name,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))),sTfun(pi,sTfun(pi,sTfun(name,$o)))),bCOMB,vAPP(sTfun(sTfun(name,sTfun(late_subject,$o)),sTfun(name,$o)),sTfun(sTfun(pi,sTfun(name,sTfun(late_subject,$o))),sTfun(pi,sTfun(name,$o))),bCOMB,vAPP(sTfun(sTfun(late_subject,$o),$o),sTfun(sTfun(name,sTfun(late_subject,$o)),sTfun(name,$o)),bCOMB,vPI(late_subject)))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o))))),sTfun(pi,sTfun(set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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_372])]) ).

thf(f1889,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(definition_unfolding,[],[f1709,f1360]) ).

thf(f1360,plain,
    strong743114133lation = 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,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),
    inference(cnf_transformation,[],[f368]) ).

thf(f368,plain,
    strong743114133lation = 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,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),
    inference(fool_elimination,[],[f367]) ).

thf(f367,plain,
    ( strong743114133lation
    = ( ^ [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi] :
          ( ! [X3: late_freeRes,X4: pi] :
              ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4))
             => ? [X5: pi] :
                  ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X1)
                  & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) )
          & ! [X6: late_subject,X7: name,X8: pi] :
              ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X0)
                & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
             => ? [X9: pi] :
                  ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X9),X8),X6),X7),X1)
                  & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X9)) ) ) ) ) ),
    inference(rectify,[],[f340]) ).

thf(f340,axiom,
    ( strong743114133lation
    = ( ^ [X101: pi,X102: set_Pr1834926343_pi_pi,X103: pi] :
          ( ! [X106: late_freeRes,X104: pi] :
              ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X103),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X106),X104))
             => ? [X105: pi] :
                  ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X105),X104)),X102)
                  & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X101),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X106),X105)) ) )
          & ! [X16: late_subject,X21: name,X104: pi] :
              ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X21),X101)
                & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X103),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X16),X21),X104)) )
             => ? [X105: pi] :
                  ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X105),X104),X16),X21),X102)
                  & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X101),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X16),X21),X105)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_simulation__def) ).

thf(f1709,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f1313,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) ) )
      | ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) ) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK183,sK184,sK185,sK186,sK187,sK188,sK189,sK190,sK191,sK192,sK193])],[f1309,f1312,f1311,f1310]) ).

thf(f1310,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X4: pi,X5: pi,X6: pi,X7: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5))),X6)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X6) ) )
     => ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1311,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X8: pi,X9: pi,X10: pi,X11: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)),X10))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X9),X10))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X8) ) )
     => ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1312,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X12: pi,X13: pi,X14: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X12),X13)),X14)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X13),X14)))),X0) )
     => ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f1309,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ? [X4: pi,X5: pi,X6: pi,X7: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5))),X6)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X6) ) )
      | ? [X8: pi,X9: pi,X10: pi,X11: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)),X10))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X9),X10))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X8) ) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ? [X12: pi,X13: pi,X14: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X12),X13)),X14)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X13),X14)))),X0) ) ),
    inference(rectify,[],[f1148]) ).

thf(f1148,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ? [X14: pi,X15: pi,X16: pi,X17: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X15))),X16)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X15),X16))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X17),X16) ) )
      | ? [X10: pi,X11: pi,X12: pi,X13: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),X11)),X12))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X11),X12))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X13),X10) ) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ? [X4: pi,X5: pi,X6: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5)),X6)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6)))),X0) ) ),
    inference(definition_folding,[],[f1069,f1147]) ).

thf(f1147,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X7: pi,X8: pi,X9: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X7)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X7),X8)),X0) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1069,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ? [X14: pi,X15: pi,X16: pi,X17: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X15))),X16)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X15),X16))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X17),X16) ) )
      | ? [X10: pi,X11: pi,X12: pi,X13: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),X11)),X12))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X11),X12))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X13),X10) ) )
      | ? [X7: pi,X8: pi,X9: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X7)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X7),X8)),X0) ) )
      | ? [X4: pi,X5: pi,X6: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5)),X6)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6)))),X0) ) ),
    inference(flattening,[],[f1068]) ).

thf(f1068,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ? [X14: pi,X15: pi,X16: pi,X17: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X15))),X16)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X15),X16))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X17),X16) ) )
      | ? [X10: pi,X11: pi,X12: pi,X13: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),X11)),X12))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X11),X12))))),X0) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X13),X10) ) )
      | ? [X7: pi,X8: pi,X9: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X7)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X7),X8)),X0) ) )
      | ? [X4: pi,X5: pi,X6: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5)),X6)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6)))),X0) ) ),
    inference(ennf_transformation,[],[f644]) ).

thf(f644,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ! [X4: pi,X5: pi,X6: pi] : ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5)),X6)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6)))),X0) )
     => ( ! [X7: pi,X8: pi,X9: name] :
            ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X7),X8)),X0) )
           => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X7)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8))),X0) ) )
       => ( ! [X10: pi,X11: pi,X12: pi,X13: name] :
              ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X13),X10) )
             => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),X11)),X12))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X11),X12))))),X0) ) )
         => ( ! [X14: pi,X15: pi,X16: pi,X17: name] :
                ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X17),X16) )
               => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X15))),X16)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X15),X16))))),X0) ) )
           => ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) ) ) ) ) ),
    inference(fool_elimination,[],[f643]) ).

thf(f643,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi,X3: pi] :
      ( ! [X4: pi,X5: pi,X6: pi] : vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X5)),X6)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X6)))),X0)
     => ( ! [X7: pi,X8: pi,X9: name] :
            ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X7),X8)),X0)
           => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X7)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8))),X0) )
       => ( ! [X10: pi,X11: pi,X12: pi,X13: name] :
              ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X13),X10)
             => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),X11)),X12))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X10),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X11),X12))))),X0) )
         => ( ! [X14: pi,X15: pi,X16: pi,X17: name] :
                ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X17),X16)
               => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X15))),X16)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X17),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X15),X16))))),X0) )
           => vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) ) ) ) ),
    inference(rectify,[],[f346]) ).

thf(f346,axiom,
    ! [X100: set_Pr1834926343_pi_pi,X19: pi,X93: pi,X88: pi] :
      ( ! [X110: pi,X111: pi,X112: pi] : vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),X111)),X112)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X111),X112)))),X100)
     => ( ! [X110: pi,X111: pi,X63: name] :
            ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X110),X111)),X100)
           => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),X110)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),X111))),X100) )
       => ( ! [X110: pi,X111: pi,X112: pi,X63: name] :
              ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X110)
             => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),X111)),X112))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X111),X112))))),X100) )
         => ( ! [X110: pi,X111: pi,X112: pi,X63: name] :
                ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X112)
               => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),X111))),X112)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X111),X112))))),X100) )
           => vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),X88)),X100),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X93),X88))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_parAssocLeft) ).

thf(f6546,plain,
    spl225_371,
    inference(avatar_split_clause,[],[f1891,f6544]) ).

thf(f6544,plain,
    ( spl225_371
  <=> ! [X0: set_Pr1834926343_pi_pi,X3: pi,X2: pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_371])]) ).

thf(f1891,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(definition_unfolding,[],[f1707,f1360]) ).

thf(f1707,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK188,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK189,X0)))))),X0) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f6542,plain,
    spl225_370,
    inference(avatar_split_clause,[],[f1890,f6540]) ).

thf(f6540,plain,
    ( spl225_370
  <=> ! [X0: set_Pr1834926343_pi_pi,X3: pi,X2: pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_370])]) ).

thf(f1890,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(definition_unfolding,[],[f1708,f1360]) ).

thf(f1708,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)))),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK183,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK184,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)))))),X0) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f6536,plain,
    spl225_369,
    inference(avatar_split_clause,[],[f1892,f6534]) ).

thf(f6534,plain,
    ( spl225_369
  <=> ! [X0: set_Pr1834926343_pi_pi,X3: pi,X2: pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_369])]) ).

thf(f1892,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(definition_unfolding,[],[f1706,f1360]) ).

thf(f1706,plain,
    ! [X2: pi,X3: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X3)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK186,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK185,X0)) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,sK190,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK187,X0)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0))),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK191,X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK192,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK193,X0))))),X0) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f6530,plain,
    spl225_368,
    inference(avatar_split_clause,[],[f1868,f6528]) ).

thf(f6528,plain,
    ( spl225_368
  <=> ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0)))),X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_368])]) ).

thf(f1868,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0)))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ),
    inference(definition_unfolding,[],[f1578,f1360]) ).

thf(f1578,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0)))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ),
    inference(cnf_transformation,[],[f1248]) ).

thf(f1248,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0)))),X0) )
        & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0))),X0) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94,sK95,sK96,sK97])],[f1245,f1247,f1246]) ).

thf(f1246,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X3: pi,X4: pi,X5: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X4))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X3),X4)),X0) ) )
     => ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK95,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0)))),X0) )
        & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0))),X0) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1247,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X6: pi,X7: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X7)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X7),X6))),X0) )
     => ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f1245,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ? [X3: pi,X4: pi,X5: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X4))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X3),X4)),X0) ) )
      | ? [X6: pi,X7: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X7)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X7),X6))),X0) ) ),
    inference(rectify,[],[f970]) ).

thf(f970,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ? [X5: pi,X6: pi,X7: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X6)),X0) ) )
      | ? [X3: pi,X4: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))),X0) ) ),
    inference(flattening,[],[f969]) ).

thf(f969,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ? [X5: pi,X6: pi,X7: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X6)),X0) ) )
      | ? [X3: pi,X4: pi] : ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))),X0) ) ),
    inference(ennf_transformation,[],[f504]) ).

thf(f504,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ! [X3: pi,X4: pi] : ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))),X0) )
     => ( ! [X5: pi,X6: pi,X7: name] :
            ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X6)),X0) )
           => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6))),X0) ) )
       => ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) ) ) ),
    inference(fool_elimination,[],[f503]) ).

thf(f503,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ! [X3: pi,X4: pi] : vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))),X0)
     => ( ! [X5: pi,X6: pi,X7: name] :
            ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X6)),X0)
           => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6))),X0) )
       => vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) ) ),
    inference(rectify,[],[f345]) ).

thf(f345,axiom,
    ! [X100: set_Pr1834926343_pi_pi,X19: pi,X93: pi] :
      ( ! [X109: pi,X110: pi] : vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X109),X110)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X110),X109))),X100)
     => ( ! [X109: pi,X110: pi,X63: name] :
            ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X109),X110)),X100)
           => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),X109)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X63),X110))),X100) )
       => vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),X100),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X93),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_parSym) ).

thf(f6522,plain,
    ( spl225_367
    | ~ spl225_8
    | ~ spl225_41 ),
    inference(avatar_split_clause,[],[f2514,f2471,f2296,f6520]) ).

thf(f6520,plain,
    ( spl225_367
  <=> ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X1 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_367])]) ).

thf(f2514,plain,
    ( ! [X2: pi_Rep,X0: $o,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X1),X2) = X1 )
        | ( $false = X0 ) )
    | ~ spl225_8
    | ~ spl225_41 ),
    inference(superposition,[],[f2472,f2297]) ).

thf(f6518,plain,
    spl225_366,
    inference(avatar_split_clause,[],[f1895,f6516]) ).

thf(f6516,plain,
    ( spl225_366
  <=> ! [X2: pi,X3: late_subject,X4: name,X0: pi,X5: pi,X1: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0)),X5),X3),X4),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
        | ( $true != 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_366])]) ).

thf(f1895,plain,
    ! [X2: pi,X3: late_subject,X0: pi,X1: set_Pr1834926343_pi_pi,X4: name,X5: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0)),X5),X3),X4),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ),
    inference(definition_unfolding,[],[f1769,f1360]) ).

thf(f1769,plain,
    ! [X2: pi,X3: late_subject,X0: pi,X1: set_Pr1834926343_pi_pi,X4: name,X5: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0)),X5),X3),X4),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1336]) ).

thf(f1336,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0)),X5),X3),X4),X1) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0))) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK219])],[f1114,f1335]) ).

thf(f1335,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X3: late_subject,X4: name,X5: pi] :
      ( ? [X6: pi] :
          ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
     => ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0)),X5),X3),X4),X1) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1114,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ? [X6: pi] :
          ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(flattening,[],[f1113]) ).

thf(f1113,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ? [X6: pi] :
          ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f700]) ).

thf(f700,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) )
     => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
       => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
         => ? [X6: pi] :
              ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X1) )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) ) ) ) ),
    inference(fool_elimination,[],[f699]) ).

thf(f699,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2)
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5))
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0)
         => ? [X6: pi] :
              ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X1)
              & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) ) ) ),
    inference(rectify,[],[f339]) ).

thf(f339,axiom,
    ! [X19: pi,X100: set_Pr1834926343_pi_pi,X93: pi,X0: late_subject,X2: name,X94: pi] :
      ( vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X19),X100),X93)
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X94))
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X19)
         => ? [X47: pi] :
              ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X47),X94),X0),X2),X100)
              & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X47)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_simE_I1_J) ).

thf(f6510,plain,
    spl225_365,
    inference(avatar_split_clause,[],[f1896,f6508]) ).

thf(f6508,plain,
    ( spl225_365
  <=> ! [X5: pi,X4: name,X2: pi,X0: pi,X3: late_subject,X1: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
        | ( $true != 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_365])]) ).

thf(f1896,plain,
    ! [X2: pi,X3: late_subject,X0: pi,X1: set_Pr1834926343_pi_pi,X4: name,X5: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ),
    inference(definition_unfolding,[],[f1768,f1360]) ).

thf(f1768,plain,
    ! [X2: pi,X3: late_subject,X0: pi,X1: set_Pr1834926343_pi_pi,X4: name,X5: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)))),sK219,X5),X4),X3),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1336]) ).

thf(f6504,plain,
    spl225_364,
    inference(avatar_split_clause,[],[f1869,f6502]) ).

thf(f6502,plain,
    ( spl225_364
  <=> ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0))),X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_364])]) ).

thf(f1869,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ),
    inference(definition_unfolding,[],[f1577,f1360]) ).

thf(f1577,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)),X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X1)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK93,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK94,X0))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(set_Pr1834926343_pi_pi,pi,sK97,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK96,X0)))),X0) ) ),
    inference(cnf_transformation,[],[f1248]) ).

thf(f6498,plain,
    spl225_363,
    inference(avatar_split_clause,[],[f1870,f6496]) ).

thf(f6496,plain,
    ( spl225_363
  <=> ! [X0: pi,X5: pi,X2: set_Pr1834926343_pi_pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X1),X2),X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),X5)) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_363])]) ).

thf(f1870,plain,
    ! [X2: set_Pr1834926343_pi_pi,X0: pi,X1: pi,X5: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X1),X2),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),X5)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(definition_unfolding,[],[f1583,f1360]) ).

thf(f1583,plain,
    ! [X2: set_Pr1834926343_pi_pi,X0: pi,X1: pi,X5: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),X5)) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1255]) ).

thf(f1255,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ( ! [X5: pi] :
            ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))),X2) )
            | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),X5)) ) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))) ) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK101,sK102])],[f1253,f1254]) ).

thf(f1254,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ? [X3: late_freeRes,X4: pi] :
          ( ! [X5: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ) )
     => ( ! [X5: pi] :
            ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))),X2) )
            | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),X5)) ) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1253,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ? [X3: late_freeRes,X4: pi] :
          ( ! [X5: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(rectify,[],[f1143]) ).

thf(f1143,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ? [X7: late_freeRes,X8: pi] :
          ( ! [X9: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X9),X8)),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X9)) ) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) ) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(definition_folding,[],[f972,f1142]) ).

thf(f1142,plain,
    ! [X2: set_Pr1834926343_pi_pi,X1: pi,X0: pi] :
      ( ? [X3: late_subject,X4: name,X5: pi] :
          ( ! [X6: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f972,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ? [X7: late_freeRes,X8: pi] :
          ( ! [X9: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X9),X8)),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X9)) ) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) ) )
      | ? [X3: late_subject,X4: name,X5: pi] :
          ( ! [X6: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) ),
    inference(flattening,[],[f971]) ).

thf(f971,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ? [X7: late_freeRes,X8: pi] :
          ( ! [X9: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X9),X8)),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X9)) ) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) ) )
      | ? [X3: late_subject,X4: name,X5: pi] :
          ( ! [X6: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) ),
    inference(ennf_transformation,[],[f506]) ).

thf(f506,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ! [X3: late_subject,X4: name,X5: pi] :
          ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
         => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
           => ? [X6: pi] :
                ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X2) )
                & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) ) ) )
     => ( ! [X7: late_freeRes,X8: pi] :
            ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
           => ? [X9: pi] :
                ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X9),X8)),X2) )
                & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X9)) ) ) )
       => ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) ) ) ),
    inference(fool_elimination,[],[f505]) ).

thf(f505,plain,
    ! [X0: pi,X1: pi,X2: set_Pr1834926343_pi_pi] :
      ( ! [X3: late_subject,X4: name,X5: pi] :
          ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5))
         => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1)
           => ? [X6: pi] :
                ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X2)
                & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi] :
            ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
           => ? [X9: pi] :
                ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X9),X8)),X2)
                & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X9)) ) )
       => vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) ) ),
    inference(rectify,[],[f341]) ).

thf(f341,axiom,
    ! [X93: pi,X19: pi,X100: set_Pr1834926343_pi_pi] :
      ( ! [X61: late_subject,X50: name,X97: pi] :
          ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X50),X97))
         => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X50),X19)
           => ? [X107: pi] :
                ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X107),X97),X61),X50),X100)
                & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X50),X107)) ) ) )
     => ( ! [X49: late_freeRes,X97: pi] :
            ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X49),X97))
           => ? [X107: pi] :
                ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X107),X97)),X100)
                & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X49),X107)) ) )
       => vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X19),X100),X93) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_simCases) ).

thf(f6446,plain,
    spl225_362,
    inference(avatar_split_clause,[],[f1871,f6444]) ).

thf(f6444,plain,
    ( spl225_362
  <=> ! [X2: set_Pr1834926343_pi_pi,X0: pi,X1: pi] :
        ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X1),X2),X0) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))) )
        | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_362])]) ).

thf(f1871,plain,
    ! [X2: set_Pr1834926343_pi_pi,X0: pi,X1: pi] :
      ( ( $true = 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X1),X2),X0) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(definition_unfolding,[],[f1582,f1360]) ).

thf(f1582,plain,
    ! [X2: set_Pr1834926343_pi_pi,X0: pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X1),X2),X0) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(pi,late_freeRes,vAPP(pi,sTfun(pi,late_freeRes),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,late_freeRes)),sK101,X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,pi)),sK102,X2),X1),X0))) )
      | ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1255]) ).

thf(f6433,plain,
    spl225_361,
    inference(avatar_split_clause,[],[f1894,f6431]) ).

thf(f6431,plain,
    ( spl225_361
  <=> ! [X2: pi,X4: pi,X0: pi,X3: late_freeRes,X1: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
        | ( $true != 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_361])]) ).

thf(f1894,plain,
    ! [X2: pi,X3: late_freeRes,X0: pi,X1: set_Pr1834926343_pi_pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ),
    inference(definition_unfolding,[],[f1730,f1360]) ).

thf(f1730,plain,
    ! [X2: pi,X3: late_freeRes,X0: pi,X1: set_Pr1834926343_pi_pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1317]) ).

thf(f1317,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_freeRes,X4: pi] :
      ( ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0)),X4)),X1) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0))) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK198])],[f1090,f1316]) ).

thf(f1316,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X3: late_freeRes,X4: pi] :
      ( ? [X5: pi] :
          ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) )
     => ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0)),X4)),X1) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1090,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_freeRes,X4: pi] :
      ( ? [X5: pi] :
          ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(flattening,[],[f1089]) ).

thf(f1089,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_freeRes,X4: pi] :
      ( ? [X5: pi] :
          ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f674]) ).

thf(f674,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_freeRes,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) )
     => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
       => ? [X5: pi] :
            ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X1) )
            & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) ) ) ),
    inference(fool_elimination,[],[f673]) ).

thf(f673,plain,
    ! [X0: pi,X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_freeRes,X4: pi] :
      ( vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2)
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4))
       => ? [X5: pi] :
            ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X5),X4)),X1)
            & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X5)) ) ) ),
    inference(rectify,[],[f338]) ).

thf(f338,axiom,
    ! [X19: pi,X100: set_Pr1834926343_pi_pi,X93: pi,X30: late_freeRes,X94: pi] :
      ( vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X19),X100),X93)
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X94))
       => ? [X47: pi] :
            ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X47),X94)),X100)
            & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X47)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_simE_I2_J) ).

thf(f6429,plain,
    spl225_360,
    inference(avatar_split_clause,[],[f1893,f6427]) ).

thf(f6427,plain,
    ( spl225_360
  <=> ! [X2: pi,X4: pi,X0: pi,X3: late_freeRes,X1: set_Pr1834926343_pi_pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0)),X4)),X1) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
        | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),sCOMB,vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),sTfun(pi,sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),sTfun(pi,sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))))),bCOMB,sCOMB),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(sTfun(pi,$o),sTfun(pi,$o)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(pi,$o)),sTfun(pi,$o)),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),bCOMB,vAPP(sTfun(sTfun(pi,$o),$o),sTfun(sTfun(pi,sTfun(pi,$o)),sTfun(pi,$o)),bCOMB,vPI(pi)))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o)))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(pi,sTfun(name,$o))),sTfun(pi,sTfun(pi,$o))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o)))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o)))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(name,$o)),sTfun(pi,$o)),sTfun(sTfun(pi,sTfun(pi,sTfun(name,$o))),sTfun(pi,sTfun(pi,$o))),bCOMB,vAPP(sTfun(sTfun(name,$o),$o),sTfun(sTfun(pi,sTfun(name,$o)),sTfun(pi,$o)),bCOMB,vPI(name))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),vAPP(sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o))))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o)))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))),sTfun(pi,sTfun(pi,sTfun(name,$o)))),sTfun(sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o))))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,sTfun(name,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,sTfun(name,sTfun(late_subject,$o))),sTfun(pi,sTfun(name,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o)))),sTfun(pi,sTfun(pi,sTfun(name,$o)))),bCOMB,vAPP(sTfun(sTfun(name,sTfun(late_subject,$o)),sTfun(name,$o)),sTfun(sTfun(pi,sTfun(name,sTfun(late_subject,$o))),sTfun(pi,sTfun(name,$o))),bCOMB,vAPP(sTfun(sTfun(late_subject,$o),$o),sTfun(sTfun(name,sTfun(late_subject,$o)),sTfun(name,$o)),bCOMB,vPI(late_subject)))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(name,sTfun(late_subject,$o))))),sTfun(pi,sTfun(set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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_360])]) ).

thf(f1893,plain,
    ! [X2: pi,X3: late_freeRes,X0: pi,X1: set_Pr1834926343_pi_pi,X4: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0)),X4)),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != 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)))),bCOMB,sCOMB)),vAPP(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),vAPP(sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),sTfun(sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),sTfun(pi,sTfun(late_freeRes,sTfun(pi,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),sTfun(sTfun(late_freeRes,sTfun(pi,$o)),sTfun(late_freeRes,sTfun(pi,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(pi,$o),sTfun(pi,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o))),vAPP(sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(pi,sTfun(late_freeRes,sTfun(pi,$o)))),cCOMB,vAPP(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),vAPP(sTfun(sTfun(sTfun(pi,late_residual),sTfun(pi,$o)),sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o)))),sTfun(sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(pi,sTfun(sTfun(late_freeRes,sTfun(pi,late_residual)),sTfun(late_freeRes,sTfun(pi,$o))))),bCOMB,bCOMB),vAPP(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),vAPP(sTfun(sTfun(late_residual,$o),sTfun(sTfun(pi,late_residual),sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(late_residual,$o)),sTfun(pi,sTfun(sTfun(pi,late_residual),sTfun(pi,$o)))),bCOMB,bCOMB),late_transitions))),late_FreeR))))))),vAPP(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,sTfun(pi,$o))),cCOMB,vAPP(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),vAPP(sTfun(sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o))),sTfun(sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)))),bCOMB,cCOMB),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),sTfun(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)))),bCOMB,vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(sTfun(pi,product_prod_pi_pi),sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o))),bCOMB,member558706512_pi_pi)),vAPP(sTfun(pi,sTfun(pi,product_prod_pi_pi)),sTfun(pi,sTfun(pi,product_prod_pi_pi)),cCOMB,product_Pair_pi_pi)))))))))),X0),X1),X2) ) ),
    inference(definition_unfolding,[],[f1731,f1360]) ).

thf(f1731,plain,
    ! [X2: pi,X3: late_freeRes,X0: pi,X1: set_Pr1834926343_pi_pi,X4: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,pi),vAPP(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,pi))),sK198,X4),X3),X1),X0)),X4)),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ( $true != vAPP(pi,$o,vAPP(set_Pr1834926343_pi_pi,sTfun(pi,$o),vAPP(pi,sTfun(set_Pr1834926343_pi_pi,sTfun(pi,$o)),strong743114133lation,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1317]) ).

thf(f6417,plain,
    spl225_359,
    inference(avatar_split_clause,[],[f1752,f6415]) ).

thf(f6415,plain,
    ( spl225_359
  <=> ! [X4: pi,X0: name,X3: name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0)),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0))),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_359])]) ).

thf(f1752,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0)),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0))),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1326]) ).

thf(f1326,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
      | ( ( vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0) != vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0)),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0))),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0))),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0)) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK205,sK206,sK207,sK208])],[f1150,f1325,f1324]) ).

thf(f1324,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ? [X5: pi,X6: name,X7: name] :
          ( ? [X8: pi] :
              ( ( X6 != X7 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) ) )
     => ( ? [X8: pi] :
            ( ( vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0) != vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0) )
            & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0)),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0))),X8)) )
            & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0))),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),X8) ) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1325,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ? [X8: pi] :
          ( ( vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0) != vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0)),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0))),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0))),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),X8) ) )
     => ( ( vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0) != vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0)),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0))),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0))),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1150,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
      | ? [X5: pi,X6: name,X7: name] :
          ( ? [X8: pi] :
              ( ( X6 != X7 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(definition_folding,[],[f1110,f1149]) ).

thf(f1149,plain,
    ! [X4: pi,X3: name,X2: late_subject,X1: pi,X0: name] :
      ( ? [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9) )
          & ( X11 != X13 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1110,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ? [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9) )
          & ( X11 != X13 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) ) )
      | ? [X5: pi,X6: name,X7: name] :
          ( ? [X8: pi] :
              ( ( X6 != X7 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(flattening,[],[f1109]) ).

thf(f1109,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ? [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9) )
          & ( X11 != X13 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) ) )
      | ? [X5: pi,X6: name,X7: name] :
          ( ? [X8: pi] :
              ( ( X6 != X7 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(ennf_transformation,[],[f910]) ).

thf(f910,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ! [X5: pi,X6: name,X7: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) )
           => ! [X8: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8)) )
                 => ( X6 = X7 ) ) ) )
       => ~ ! [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12)) )
                 => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10) )
                   => ( ( X11 != X13 )
                     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9) )
                       => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) ) ) ) ) ) ) ) ) ),
    inference(flattening,[],[f694]) ).

thf(f694,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ! [X5: pi,X6: name,X7: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) )
           => ! [X8: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8)) )
                 => ( X6 = X7 ) ) ) )
       => ~ ! [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12)) )
                 => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10) )
                   => ( ( X11 != X13 )
                     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9) )
                       => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f693]) ).

thf(f693,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4))
     => ( ! [X5: pi,X6: name,X7: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X5) )
           => ! [X8: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X6)),X7),X8) )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X7)),X8))
                 => ( X6 = X7 ) ) ) )
       => ~ ! [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12))
                 => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10)
                   => ( ( X11 != X13 )
                     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9)
                       => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f210]) ).

thf(f210,axiom,
    ! [X66: name,X19: pi,X0: late_subject,X67: name,X31: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X66),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X67),X31))
     => ( ! [X48: pi,X61: name,X62: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X62),X48) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X66),X19) )
           => ! [X47: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X61)),X62),X47) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X67),X31) )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X61),X62)),X47))
                 => ( X61 = X62 ) ) ) )
       => ~ ! [X48: pi,X61: late_subject,X63: name,X47: pi,X50: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X48) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X66),X19) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X47)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X67),X31) )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),X47))
                 => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X50),X61)
                   => ( ( X50 != X63 )
                     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X48)
                       => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X63),X61) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_resCasesB_H) ).

thf(f6407,plain,
    spl225_358,
    inference(avatar_split_clause,[],[f1761,f6405]) ).

thf(f6405,plain,
    ( spl225_358
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_358])]) ).

thf(f1761,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1334]) ).

thf(f1334,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: pi] :
      ( ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK214,sK215,sK216,sK217,sK218])],[f1332,f1333]) ).

thf(f1333,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: pi] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) ) )
     => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1332,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: pi] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(rectify,[],[f1331]) ).

thf(f1331,plain,
    ! [X4: pi,X3: name,X2: late_subject,X1: pi,X0: pi] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X0),X1),X2),X3),X4) ) ),
    inference(nnf_transformation,[],[f1151]) ).

thf(f1151,plain,
    ! [X4: pi,X3: name,X2: late_subject,X1: pi,X0: pi] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X0),X1),X2),X3),X4) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6403,plain,
    spl225_357,
    inference(avatar_split_clause,[],[f1755,f6401]) ).

thf(f6401,plain,
    ( spl225_357
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_357])]) ).

thf(f1755,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

thf(f1330,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: pi] :
      ( ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK209,sK210,sK211,sK212,sK213])],[f1328,f1329]) ).

thf(f1329,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: pi] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X9),X8)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X9),X5) ) )
     => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1328,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: pi] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X9),X8)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X9),X5) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(rectify,[],[f1327]) ).

thf(f1327,plain,
    ! [X4: pi,X3: name,X2: late_subject,X1: pi,X0: pi] :
      ( ? [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X0),X1),X2),X3),X4) ) ),
    inference(nnf_transformation,[],[f1152]) ).

thf(f1152,plain,
    ! [X4: pi,X3: name,X2: late_subject,X1: pi,X0: pi] :
      ( ? [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X0),X1),X2),X3),X4) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6399,plain,
    ( spl225_356
    | ~ spl225_8
    | spl225_59 ),
    inference(avatar_split_clause,[],[f2569,f2564,f2296,f6396]) ).

thf(f2564,plain,
    ( spl225_59
  <=> ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_59])]) ).

thf(f2569,plain,
    ( ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))) )
    | ~ spl225_8
    | spl225_59 ),
    inference(trivial_inequality_removal,[],[f2568]) ).

thf(f2568,plain,
    ( ( $true != $true )
    | ( $false = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))) )
    | ~ spl225_8
    | spl225_59 ),
    inference(superposition,[],[f2566,f2297]) ).

thf(f2566,plain,
    ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))) )
    | spl225_59 ),
    inference(avatar_component_clause,[],[f2564]) ).

thf(f6394,plain,
    spl225_355,
    inference(avatar_split_clause,[],[f1744,f6392]) ).

thf(f6392,plain,
    ( spl225_355
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_355])]) ).

thf(f1744,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f1323,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: name] :
      ( ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) )
        & ( vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0) != vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK200,sK201,sK202,sK203,sK204])],[f1321,f1322]) ).

thf(f1322,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: name] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( X7 != X9 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X6) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X5) ) )
     => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) )
        & ( vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0) != vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1321,plain,
    ! [X0: pi,X1: name,X2: late_subject,X3: pi,X4: name] :
      ( ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( X7 != X9 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X6) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X1),X0) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X5) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(rectify,[],[f1320]) ).

thf(f1320,plain,
    ! [X4: pi,X3: name,X2: late_subject,X1: pi,X0: name] :
      ( ? [X9: pi,X10: late_subject,X11: name,X12: pi,X13: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X11),X9) )
          & ( X11 != X13 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X13),X10) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),X12)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X10),X11),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X12)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X13),X9) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) ) ),
    inference(nnf_transformation,[],[f1149]) ).

thf(f6382,plain,
    spl225_354,
    inference(avatar_split_clause,[],[f1751,f6380]) ).

thf(f6380,plain,
    ( spl225_354
  <=> ! [X4: pi,X0: name,X3: name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
        | ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0))),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_354])]) ).

thf(f1751,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
      | ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0))),vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK208,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1326]) ).

thf(f6372,plain,
    spl225_353,
    inference(avatar_split_clause,[],[f1762,f6370]) ).

thf(f6370,plain,
    ( spl225_353
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_353])]) ).

thf(f1762,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK217,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1334]) ).

thf(f6368,plain,
    spl225_352,
    inference(avatar_split_clause,[],[f1756,f6366]) ).

thf(f6366,plain,
    ( spl225_352
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_352])]) ).

thf(f1756,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK212,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

thf(f6364,plain,
    spl225_351,
    inference(avatar_split_clause,[],[f1745,f6362]) ).

thf(f6362,plain,
    ( spl225_351
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_351])]) ).

thf(f1745,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)),vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK203,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f6343,plain,
    spl225_350,
    inference(avatar_split_clause,[],[f2259,f6341]) ).

thf(f6341,plain,
    ( spl225_350
  <=> ! [X0: name,X3: name,X2: name,X1: name] :
        ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X1)),X2)) )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X1),X2) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_350])]) ).

thf(f2259,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X1)),X2)) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X1),X2) )
      | ( X0 = X1 ) ),
    inference(forward_demodulation,[],[f1888,f2255]) ).

thf(f1888,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X1),X2) )
      | ( X0 = X1 ) ),
    inference(definition_unfolding,[],[f1697,f1361,f1358,f1361,f1361]) ).

thf(f1361,plain,
    fresh_name_name = vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),
    inference(cnf_transformation,[],[f370]) ).

thf(f370,plain,
    fresh_name_name = vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),
    inference(fool_elimination,[],[f369]) ).

thf(f369,plain,
    ( fresh_name_name
    = ( ^ [X0: name,X1: name] : ( X0 != X1 ) ) ),
    inference(rectify,[],[f61]) ).

thf(f61,axiom,
    ( fresh_name_name
    = ( ^ [X16: name,X17: name] : ( X16 != X17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_name__fresh) ).

thf(f1697,plain,
    ! [X2: name,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) != $true )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1061]) ).

thf(f1061,plain,
    ! [X0: name,X1: name,X2: name,X3: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) != $true )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1060]) ).

thf(f1060,plain,
    ! [X0: name,X1: name,X2: name,X3: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) != $true )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f638]) ).

thf(f638,plain,
    ! [X0: name,X1: name,X2: name,X3: name] :
      ( ( X0 != X1 )
     => ( ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X2) = $true )
       => ( ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) = $true )
         => ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ) ),
    inference(fool_elimination,[],[f637]) ).

thf(f637,plain,
    ! [X0: name,X1: name,X2: name,X3: name] :
      ( ( X0 != X1 )
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X2)
       => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2)
         => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ),
    inference(rectify,[],[f113]) ).

thf(f113,axiom,
    ! [X32: name,X0: name,X2: name,X1: name] :
      ( ( X0 != X32 )
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2)
       => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X32),X2)
         => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X32),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_fresh__aux) ).

thf(f6334,plain,
    spl225_349,
    inference(avatar_split_clause,[],[f1777,f6332]) ).

thf(f6332,plain,
    ( spl225_349
  <=> ! [X2: late_subject,X3: name,X4: pi,X0: pi,X5: pi > $o,X1: pi] :
        ( ( $true = vAPP(pi,$o,X5,X4) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_349])]) ).

thf(f1777,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1347]) ).

thf(f1347,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) ) )
      | ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0)),X1)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0))) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK223,sK224])],[f1344,f1346,f1345]) ).

thf(f1345,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X5: pi > $o] :
      ( ? [X6: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X6)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) ) )
     => ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1346,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X5: pi > $o] :
      ( ? [X7: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X7),X1)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X7)) ) )
     => ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0)),X1)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1344,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ? [X6: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X6)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) ) )
      | ? [X7: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X7),X1)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X7)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(rectify,[],[f1118]) ).

thf(f1118,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ? [X7: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X7)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X7)) ) )
      | ? [X6: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X1)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(flattening,[],[f1117]) ).

thf(f1117,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ? [X7: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X7)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X7)) ) )
      | ? [X6: pi] :
          ( ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X1)) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(ennf_transformation,[],[f704]) ).

thf(f704,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
       => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
         => ( ! [X6: pi] :
                ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) )
               => ( $true = vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X1)) ) )
           => ( ! [X7: pi] :
                  ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X7)) )
                 => ( $true = vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X7)) ) )
             => ( $true = vAPP(pi,$o,X5,X4) ) ) ) ) ) ),
    inference(fool_elimination,[],[f703]) ).

thf(f703,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi,X5: pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0)
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1)
         => ( ! [X6: pi] :
                ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6))
               => vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X6),X1)) )
           => ( ! [X7: pi] :
                  ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X7))
                 => vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X7)) )
             => vAPP(pi,$o,X5,X4) ) ) ) ) ),
    inference(rectify,[],[f305]) ).

thf(f305,axiom,
    ! [X19: pi,X93: pi,X0: late_subject,X2: name,X95: pi,X96: pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X95))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X19)
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X93)
         => ( ! [X47: pi] :
                ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X47))
               => vAPP(pi,$o,X96,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X47),X93)) )
           => ( ! [X97: pi] :
                  ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X97))
                 => vAPP(pi,$o,X96,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X97)) )
             => vAPP(pi,$o,X96,X95) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_parCasesB) ).

thf(f6307,plain,
    spl225_348,
    inference(avatar_split_clause,[],[f1779,f6305]) ).

thf(f6305,plain,
    ( spl225_348
  <=> ! [X2: late_subject,X3: name,X4: pi,X0: pi,X5: pi > $o,X1: pi] :
        ( ( $true = vAPP(pi,$o,X5,X4) )
        | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_348])]) ).

thf(f1779,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1347]) ).

thf(f6303,plain,
    spl225_347,
    inference(avatar_split_clause,[],[f1778,f6301]) ).

thf(f6301,plain,
    ( spl225_347
  <=> ! [X2: late_subject,X3: name,X4: pi,X0: pi,X5: pi > $o,X1: pi] :
        ( ( $true = vAPP(pi,$o,X5,X4) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0)),X1)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_347])]) ).

thf(f1778,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1347]) ).

thf(f6299,plain,
    spl225_346,
    inference(avatar_split_clause,[],[f1773,f6297]) ).

thf(f6297,plain,
    ( spl225_346
  <=> ! [X4: pi,X0: name,X3: late_subject,X2: late_subject > pi > $o,X1: name] :
        ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X2,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0))),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_346])]) ).

thf(f1773,plain,
    ! [X2: late_subject > pi > $o,X3: late_subject,X0: name,X1: name,X4: pi] :
      ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X2,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0))),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1340]) ).

thf(f1340,plain,
    ! [X0: name,X1: name,X2: late_subject > pi > $o,X3: late_subject,X4: pi] :
      ( ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X2,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0))),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) )
        & ( vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)) = X3 )
        & ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0) != X0 )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)),X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) ) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK220,sK221])],[f1338,f1339]) ).

thf(f1339,plain,
    ! [X0: name,X1: name,X2: late_subject > pi > $o,X3: late_subject,X4: pi] :
      ( ? [X5: name,X6: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X2,vAPP(name,late_subject,late_BoundOutputS,X5)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X6)) )
          & ( vAPP(name,late_subject,late_BoundOutputS,X5) = X3 )
          & ( X0 != X5 )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X5),X0)),X6)) ) )
     => ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X2,vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0))),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) )
        & ( vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)) = X3 )
        & ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0) != X0 )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)),X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1338,plain,
    ! [X0: name,X1: name,X2: late_subject > pi > $o,X3: late_subject,X4: pi] :
      ( ? [X5: name,X6: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X2,vAPP(name,late_subject,late_BoundOutputS,X5)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X6)) )
          & ( vAPP(name,late_subject,late_BoundOutputS,X5) = X3 )
          & ( X0 != X5 )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X5),X0)),X6)) ) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ),
    inference(rectify,[],[f1337]) ).

thf(f1337,plain,
    ! [X0: name,X3: name,X5: late_subject > pi > $o,X2: late_subject,X1: pi] :
      ( ? [X6: name,X7: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,vAPP(name,late_subject,late_BoundOutputS,X6)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X7)) )
          & ( vAPP(name,late_subject,late_BoundOutputS,X6) = X2 )
          & ( X0 != X6 )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X0)),X7)) ) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) ) ),
    inference(nnf_transformation,[],[f1154]) ).

thf(f1154,plain,
    ! [X0: name,X3: name,X5: late_subject > pi > $o,X2: late_subject,X1: pi] :
      ( ? [X6: name,X7: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,vAPP(name,late_subject,late_BoundOutputS,X6)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X7)) )
          & ( vAPP(name,late_subject,late_BoundOutputS,X6) = X2 )
          & ( X0 != X6 )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X0)),X7)) ) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6285,plain,
    ( spl225_345
    | ~ spl225_61
    | ~ spl225_303 ),
    inference(avatar_split_clause,[],[f6233,f5904,f2575,f6283]) ).

thf(f6283,plain,
    ( spl225_345
  <=> ! [X0: late_freeRes,X1: list_P227219501e_name] :
        ( ( late_TauR != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X0) )
        | ( late_TauR = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_345])]) ).

thf(f2575,plain,
    ( spl225_61
  <=> ! [X0: late_freeRes] :
        ( ( late_TauR = X0 )
        | ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_freeRes,name,sK42,X0)),vAPP(late_freeRes,name,sK43,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_61])]) ).

thf(f5904,plain,
    ( spl225_303
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name] : ( late_TauR != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_303])]) ).

thf(f6233,plain,
    ( ! [X0: late_freeRes,X1: list_P227219501e_name] :
        ( ( late_TauR != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X0) )
        | ( late_TauR = X0 ) )
    | ~ spl225_61
    | ~ spl225_303 ),
    inference(superposition,[],[f5905,f2576]) ).

thf(f2576,plain,
    ( ! [X0: late_freeRes] :
        ( ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_freeRes,name,sK42,X0)),vAPP(late_freeRes,name,sK43,X0)) = X0 )
        | ( late_TauR = X0 ) )
    | ~ spl225_61 ),
    inference(avatar_component_clause,[],[f2575]) ).

thf(f5905,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: name] : ( late_TauR != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) )
    | ~ spl225_303 ),
    inference(avatar_component_clause,[],[f5904]) ).

thf(f6281,plain,
    spl225_344,
    inference(avatar_split_clause,[],[f1774,f6279]) ).

thf(f6279,plain,
    ( spl225_344
  <=> ! [X3: name,X4: pi,X0: name,X5: late_subject > pi > $o,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) )
        | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( X0 = X3 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_344])]) ).

thf(f1774,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1343]) ).

thf(f1343,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) )
        & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) ) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK222])],[f1341,f1342]) ).

thf(f1342,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X5: late_subject > pi > $o] :
      ( ? [X6: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X6)) )
          & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) ) )
     => ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) )
        & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1341,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ? [X6: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X6)) )
          & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X6)) ) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(rectify,[],[f1155]) ).

thf(f1155,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ? [X8: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X8)) )
          & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X8)) ) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(definition_folding,[],[f1116,f1154]) ).

thf(f1116,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ? [X8: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X8)) )
          & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X8)) ) )
      | ? [X6: name,X7: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,vAPP(name,late_subject,late_BoundOutputS,X6)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X7)) )
          & ( vAPP(name,late_subject,late_BoundOutputS,X6) = X2 )
          & ( X0 != X6 )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X0)),X7)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(flattening,[],[f1115]) ).

thf(f1115,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ? [X8: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X8)) )
          & ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X8)) ) )
      | ? [X6: name,X7: pi] :
          ( ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,vAPP(name,late_subject,late_BoundOutputS,X6)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X7)) )
          & ( vAPP(name,late_subject,late_BoundOutputS,X6) = X2 )
          & ( X0 != X6 )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X0)),X7)) ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(ennf_transformation,[],[f702]) ).

thf(f702,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ( X0 != X3 )
       => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
         => ( ! [X6: name,X7: pi] :
                ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X0)),X7)) )
               => ( ( X0 != X6 )
                 => ( ( vAPP(name,late_subject,late_BoundOutputS,X6) = X2 )
                   => ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,vAPP(name,late_subject,late_BoundOutputS,X6)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X7)) ) ) ) )
           => ( ! [X8: pi] :
                  ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X8)) )
                 => ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
                   => ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X8)) ) ) )
             => ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) ) ) ) ) ) ),
    inference(fool_elimination,[],[f701]) ).

thf(f701,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name,X4: pi,X5: late_subject > pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4))
     => ( ( X0 != X3 )
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1)
         => ( ! [X6: name,X7: pi] :
                ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X6),X0)),X7))
               => ( ( X0 != X6 )
                 => ( ( vAPP(name,late_subject,late_BoundOutputS,X6) = X2 )
                   => vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,vAPP(name,late_subject,late_BoundOutputS,X6)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X7)) ) ) )
           => ( ! [X8: pi] :
                  ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X8))
                 => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2)
                   => vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X8)) ) )
             => vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) ) ) ) ) ),
    inference(rectify,[],[f222]) ).

thf(f222,axiom,
    ! [X22: name,X19: pi,X0: late_subject,X2: name,X70: pi,X46: late_subject > pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X70))
     => ( ( X2 != X22 )
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X19)
         => ( ! [X62: name,X47: pi] :
                ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X62),X22)),X47))
               => ( ( X22 != X62 )
                 => ( ( vAPP(name,late_subject,late_BoundOutputS,X62) = X0 )
                   => vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X46,vAPP(name,late_subject,late_BoundOutputS,X62)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X22)),nil_Pr743626285e_name)),X47)) ) ) )
           => ( ! [X47: pi] :
                  ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X47))
                 => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X22),X0)
                   => vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X46,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X47)) ) )
             => vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X46,X0),X70) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_resCasesB) ).

thf(f6264,plain,
    spl225_343,
    inference(avatar_split_clause,[],[f1780,f6262]) ).

thf(f6262,plain,
    ( spl225_343
  <=> ! [X2: late_subject,X3: name,X4: pi,X0: pi,X5: pi > $o,X1: pi] :
        ( ( $true = vAPP(pi,$o,X5,X4) )
        | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
        | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0)),X1)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_343])]) ).

thf(f1780,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: pi,X5: pi > $o] :
      ( ( $true = vAPP(pi,$o,X5,X4) )
      | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK223,X5),X3),X2),X1),X0))) )
      | ( $true != vAPP(pi,$o,X5,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP(late_subject,sTfun(pi,sTfun(pi,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi))),vAPP(sTfun(pi,$o),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(pi,pi)))),sK224,X5),X3),X2),X1),X0)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1347]) ).

thf(f6260,plain,
    spl225_342,
    inference(avatar_split_clause,[],[f1776,f6258]) ).

thf(f6258,plain,
    ( spl225_342
  <=> ! [X3: name,X4: pi,X0: name,X5: late_subject > pi > $o,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
        | ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) )
        | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( X0 = X3 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_342])]) ).

thf(f1776,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ( $true != vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK222,X5),X3),X2),X1),X0))) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1343]) ).

thf(f6256,plain,
    spl225_341,
    inference(avatar_split_clause,[],[f1770,f6254]) ).

thf(f6254,plain,
    ( spl225_341
  <=> ! [X4: pi,X0: name,X3: late_subject,X2: late_subject > pi > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)),X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_341])]) ).

thf(f1770,plain,
    ! [X2: late_subject > pi > $o,X3: late_subject,X0: name,X1: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)),X0)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,pi)))),sK221,X4),X3),X2),X1),X0))) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1340]) ).

thf(f6244,plain,
    spl225_340,
    inference(avatar_split_clause,[],[f1750,f6242]) ).

thf(f6242,plain,
    ( spl225_340
  <=> ! [X4: pi,X0: name,X3: name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
        | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_340])]) ).

thf(f1750,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
      | ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_subject,sTfun(pi,sTfun(name,pi)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,pi)))),sK205,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1326]) ).

thf(f6232,plain,
    spl225_339,
    inference(avatar_split_clause,[],[f1581,f6230]) ).

thf(f6230,plain,
    ( spl225_339
  <=> ! [X0: set_Pr1834926343_pi_pi,X6: pi,X2: pi,X1: pi] :
        ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X6)) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_339])]) ).

thf(f1581,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi,X6: pi] :
      ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X6)) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1252]) ).

thf(f1252,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ( ! [X6: pi] :
            ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X0) )
            | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X6)) ) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X1) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0))) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99,sK100])],[f1250,f1251]) ).

thf(f1251,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ? [X3: late_subject,X4: name,X5: pi] :
          ( ! [X6: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X0) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X6: pi] :
            ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X0) )
            | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X6)) ) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X1) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1250,plain,
    ! [X0: set_Pr1834926343_pi_pi,X1: pi,X2: pi] :
      ( ? [X3: late_subject,X4: name,X5: pi] :
          ( ! [X6: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X0) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ),
    inference(rectify,[],[f1249]) ).

thf(f1249,plain,
    ! [X2: set_Pr1834926343_pi_pi,X1: pi,X0: pi] :
      ( ? [X3: late_subject,X4: name,X5: pi] :
          ( ! [X6: pi] :
              ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X6),X5),X3),X4),X2) )
              | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X6)) ) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X1) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f1142]) ).

thf(f6209,plain,
    spl225_338,
    inference(avatar_split_clause,[],[f1875,f6207]) ).

thf(f6207,plain,
    ( spl225_338
  <=> ! [X2: name,X0: name,X1: name] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X2),X1) )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_338])]) ).

thf(f1875,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X2),X1) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X1) ) ),
    inference(definition_unfolding,[],[f1624,f1358,f1361,f1361]) ).

thf(f1624,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X2),X1) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1019]) ).

thf(f1019,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X2),X1) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) ) ),
    inference(flattening,[],[f1018]) ).

thf(f1018,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X2),X1) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f554]) ).

thf(f554,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) )
     => ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X2),X1) )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(fool_elimination,[],[f553]) ).

thf(f553,plain,
    ! [X0: name,X1: name,X2: name] :
      ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1)
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X2),X1)
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f72]) ).

thf(f72,axiom,
    ! [X0: name,X2: name,X1: name] :
      ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2)
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X2)
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_name__fresh__fresh) ).

thf(f6205,plain,
    spl225_337,
    inference(avatar_split_clause,[],[f1609,f6203]) ).

thf(f6203,plain,
    ( spl225_337
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK159,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK161,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK163,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK164,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK165,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK166,X0))),nil_Pr743626285e_name) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_337])]) ).

thf(f1609,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK159,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK161,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK163,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK164,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK165,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK166,X0))),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1292]) ).

thf(f1292,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK159,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK161,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0)) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK163,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK164,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK165,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK166,X0))),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK159,sK160,sK161,sK162,sK163,sK164,sK165,sK166])],[f1288,f1291,f1290,f1289]) ).

thf(f1289,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),X6) ) )
     => ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK159,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK161,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1290,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X7: produc367475239e_name,X8: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) )
     => ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK163,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK164,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1291,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X9: produc367475239e_name,X10: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X9),X10)),nil_Pr743626285e_name) )
     => ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK165,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK166,X0))),nil_Pr743626285e_name) ) ),
    introduced(choice_axiom,[]) ).

thf(f1288,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),X6) ) )
      | ? [X7: produc367475239e_name,X8: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) )
      | ? [X9: produc367475239e_name,X10: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X9),X10)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ),
    inference(rectify,[],[f990]) ).

thf(f990,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X7: produc367475239e_name,X8: list_P227219501e_name,X9: produc367475239e_name,X10: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X9),X10)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X8),X10) ) )
      | ? [X5: produc367475239e_name,X6: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
      | ? [X3: produc367475239e_name,X4: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ),
    inference(flattening,[],[f989]) ).

thf(f989,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X7: produc367475239e_name,X8: list_P227219501e_name,X9: produc367475239e_name,X10: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X9),X10)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X8),X10) ) )
      | ? [X5: produc367475239e_name,X6: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
      | ? [X3: produc367475239e_name,X4: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ),
    inference(ennf_transformation,[],[f524]) ).

thf(f524,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) )
     => ( ! [X3: produc367475239e_name,X4: list_P227219501e_name] : ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),nil_Pr743626285e_name) )
       => ( ! [X5: produc367475239e_name,X6: list_P227219501e_name] : ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
         => ( ! [X7: produc367475239e_name,X8: list_P227219501e_name,X9: produc367475239e_name,X10: list_P227219501e_name] :
                ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X8),X10) )
               => ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X9),X10)) ) )
           => ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f523]) ).

thf(f523,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name)
     => ( ! [X3: produc367475239e_name,X4: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),nil_Pr743626285e_name)
       => ( ! [X5: produc367475239e_name,X6: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6))
         => ( ! [X7: produc367475239e_name,X8: list_P227219501e_name,X9: produc367475239e_name,X10: list_P227219501e_name] :
                ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X8),X10)
               => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X9),X10)) )
           => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ) ) ),
    inference(rectify,[],[f268]) ).

thf(f268,axiom,
    ! [X19: list_P227219501e_name > list_P227219501e_name > $o,X43: list_P227219501e_name,X83: list_P227219501e_name] :
      ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,nil_Pr743626285e_name),nil_Pr743626285e_name)
     => ( ! [X63: produc367475239e_name,X65: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),nil_Pr743626285e_name)
       => ( ! [X50: produc367475239e_name,X64: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X64))
         => ( ! [X63: produc367475239e_name,X65: list_P227219501e_name,X50: produc367475239e_name,X64: list_P227219501e_name] :
                ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X65),X64)
               => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X64)) )
           => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X43),X83) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_list__induct2_H) ).

thf(f6201,plain,
    spl225_336,
    inference(avatar_split_clause,[],[f1753,f6199]) ).

thf(f6199,plain,
    ( spl225_336
  <=> ! [X4: pi,X0: name,X3: name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
        | ( vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0) != vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_336])]) ).

thf(f1753,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X0),X1),X2),X3),X4) )
      | ( vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK206,X4),X3),X2),X1),X0) != vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_subject,sTfun(pi,sTfun(name,name)),vAPP(name,sTfun(late_subject,sTfun(pi,sTfun(name,name))),vAPP(pi,sTfun(name,sTfun(late_subject,sTfun(pi,sTfun(name,name)))),sK207,X4),X3),X2),X1),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1326]) ).

thf(f6189,plain,
    spl225_335,
    inference(avatar_split_clause,[],[f1874,f6187]) ).

thf(f6187,plain,
    ( spl225_335
  <=> ! [X2: name,X0: name,X1: list_P227219501e_name] :
        ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_335])]) ).

thf(f1874,plain,
    ! [X2: name,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(definition_unfolding,[],[f1621,f1361,f1358,f1361]) ).

thf(f1621,plain,
    ! [X2: name,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1013]) ).

thf(f1013,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(flattening,[],[f1012]) ).

thf(f1012,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) )
      | ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f548]) ).

thf(f548,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) )
     => ( ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) = $true )
       => ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) ) ) ),
    inference(fool_elimination,[],[f547]) ).

thf(f547,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1)
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2)
       => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) ) ),
    inference(rectify,[],[f80]) ).

thf(f80,axiom,
    ! [X0: name,X5: list_P227219501e_name,X2: name] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X5)
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2)
       => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_fresh__perm__app) ).

thf(f6163,plain,
    spl225_334,
    inference(avatar_split_clause,[],[f1793,f6161]) ).

thf(f6161,plain,
    ( spl225_334
  <=> ! [X5: name,X3: pi,X4: pi,X0: pi,X6: pi,X2: name,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2))))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_334])]) ).

thf(f1793,plain,
    ! [X2: name,X3: pi,X0: pi,X1: name,X6: pi,X4: pi,X5: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2))))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1139]) ).

thf(f1139,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2))))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) ) ),
    inference(flattening,[],[f1138]) ).

thf(f1138,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2))))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) ) ),
    inference(ennf_transformation,[],[f730]) ).

thf(f730,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) )
     => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
       => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
         => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2))))) ) ) ) ),
    inference(fool_elimination,[],[f729]) ).

thf(f729,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6))
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4)
         => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2))))) ) ) ),
    inference(rectify,[],[f314]) ).

thf(f314,axiom,
    ! [X19: pi,X0: name,X22: name,X31: pi,X93: pi,X2: name,X94: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X0)),X22),X31))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X2),X94))
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X93)
         => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X31),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X94),X2),X22))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_Late__Semantics_OClose2) ).

thf(f6159,plain,
    spl225_333,
    inference(avatar_split_clause,[],[f1791,f6157]) ).

thf(f6157,plain,
    ( spl225_333
  <=> ! [X5: name,X3: pi,X4: pi,X0: pi,X6: pi,X2: name,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6)))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X5),X6)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_333])]) ).

thf(f1791,plain,
    ! [X2: name,X3: pi,X0: pi,X1: name,X6: pi,X4: pi,X5: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6)))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1135]) ).

thf(f1135,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6)))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ),
    inference(flattening,[],[f1134]) ).

thf(f1134,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6)))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ),
    inference(ennf_transformation,[],[f726]) ).

thf(f726,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) )
     => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X5),X6)) )
       => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X0) )
         => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6)))) ) ) ) ),
    inference(fool_elimination,[],[f725]) ).

thf(f725,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X5),X6))
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X0)
         => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6)))) ) ) ),
    inference(rectify,[],[f313]) ).

thf(f313,axiom,
    ! [X19: pi,X0: name,X2: name,X31: pi,X93: pi,X22: name,X94: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X2),X31))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X0)),X22),X94))
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X19)
         => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X31),X2),X22)),X94)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_Late__Semantics_OClose1) ).

thf(f6149,plain,
    spl225_332,
    inference(avatar_split_clause,[],[f1723,f6147]) ).

thf(f6147,plain,
    ( spl225_332
  <=> ! [X0: name,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_332])]) ).

thf(f1723,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi] :
      ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1315]) ).

thf(f1315,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK194,sK195,sK196,sK197])],[f1088,f1314]) ).

thf(f1314,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( ? [X4: pi,X5: late_freeRes,X6: pi,X7: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X4) ) )
     => ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1088,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( ? [X4: pi,X5: late_freeRes,X6: pi,X7: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X4) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(flattening,[],[f1087]) ).

thf(f1087,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( ? [X4: pi,X5: late_freeRes,X6: pi,X7: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X4) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(ennf_transformation,[],[f905]) ).

thf(f905,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
     => ~ ! [X4: pi,X5: late_freeRes,X6: pi,X7: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X4) )
           => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) )
             => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
               => ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X5) ) ) ) ) ),
    inference(flattening,[],[f670]) ).

thf(f670,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
     => ~ ! [X4: pi,X5: late_freeRes,X6: pi,X7: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X4) )
           => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) )
             => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
               => ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X5) ) ) ) ) ),
    inference(fool_elimination,[],[f669]) ).

thf(f669,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3))
     => ~ ! [X4: pi,X5: late_freeRes,X6: pi,X7: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X4) )
           => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) )
             => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6))
               => ~ vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X5) ) ) ) ),
    inference(rectify,[],[f199]) ).

thf(f199,axiom,
    ! [X2: name,X19: pi,X30: late_freeRes,X31: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31))
     => ~ ! [X48: pi,X49: late_freeRes,X47: pi,X50: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X48) )
           => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X49),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X47)) )
             => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X49),X47))
               => ~ vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X50),X49) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_resCasesF_H) ).

thf(f6139,plain,
    spl225_331,
    inference(avatar_split_clause,[],[f1760,f6137]) ).

thf(f6137,plain,
    ( spl225_331
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_331])]) ).

thf(f1760,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1334]) ).

thf(f6135,plain,
    spl225_330,
    inference(avatar_split_clause,[],[f1754,f6133]) ).

thf(f6133,plain,
    ( spl225_330
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_330])]) ).

thf(f1754,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

thf(f6128,plain,
    spl225_329,
    inference(avatar_split_clause,[],[f1743,f6126]) ).

thf(f6126,plain,
    ( spl225_329
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_329])]) ).

thf(f1743,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f6107,plain,
    spl225_328,
    inference(avatar_split_clause,[],[f1873,f6105]) ).

thf(f6105,plain,
    ( spl225_328
  <=> ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
        | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_328])]) ).

thf(f1873,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)) ) ),
    inference(definition_unfolding,[],[f1599,f1361]) ).

thf(f1599,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)) ) ),
    inference(cnf_transformation,[],[f1279]) ).

thf(f1279,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK143,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)) )
        & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK138,sK139,sK140,sK141,sK142,sK143,sK144])],[f1276,f1278,f1277]) ).

thf(f1277,plain,
    ! [X0: name > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1278,plain,
    ! [X0: name > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK143,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)) )
        & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1276,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X7),X9) ) ) ),
    inference(rectify,[],[f984]) ).

thf(f984,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6) ) ) ),
    inference(flattening,[],[f983]) ).

thf(f983,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f518]) ).

thf(f518,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: name] : ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f517]) ).

thf(f517,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: name] : vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f220]) ).

thf(f220,axiom,
    ! [X19: name > late_residual > $o,X68: name,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: name] :
          ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: name] : vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_residual_Ostrong__induct) ).

thf(f6103,plain,
    spl225_327,
    inference(avatar_split_clause,[],[f1872,f6101]) ).

thf(f6101,plain,
    ( spl225_327
  <=> ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
        | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_327])]) ).

thf(f1872,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)) ) ),
    inference(definition_unfolding,[],[f1596,f1361]) ).

thf(f1596,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)) ) ),
    inference(cnf_transformation,[],[f1275]) ).

thf(f1275,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK136,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)) )
        & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK131,sK132,sK133,sK134,sK135,sK136,sK137])],[f1272,f1274,f1273]) ).

thf(f1273,plain,
    ! [X0: name > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1274,plain,
    ! [X0: name > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK136,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)) )
        & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1272,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X7),X9) ) ) ),
    inference(rectify,[],[f982]) ).

thf(f982,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6) ) ) ),
    inference(flattening,[],[f981]) ).

thf(f981,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: name] : ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f516]) ).

thf(f516,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: name] : ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f515]) ).

thf(f515,plain,
    ! [X0: name > late_residual > $o,X1: name,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: name] :
          ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: name] : vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f216]) ).

thf(f216,axiom,
    ! [X19: name > late_residual > $o,X68: name,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: name] :
          ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: name] : vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_residual_Ostrong__inducts) ).

thf(f6099,plain,
    spl225_326,
    inference(avatar_split_clause,[],[f1796,f6097]) ).

thf(f6097,plain,
    ( spl225_326
  <=> ! [X5: pi,X4: name,X2: pi,X0: name,X6: late_subject > name > pi > $o,X3: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,vAPP(name,late_subject,late_InputS,X0)),X4),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
        | ( X1 = X4 )
        | ( X0 = X4 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_326])]) ).

thf(f1796,plain,
    ! [X2: pi,X3: late_subject,X0: name,X1: name,X6: late_subject > name > pi > $o,X4: name,X5: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,vAPP(name,late_subject,late_InputS,X0)),X4),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
      | ( X1 = X4 )
      | ( X0 = X4 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(cnf_transformation,[],[f1141]) ).

thf(f1141,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi,X6: late_subject > name > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
      | ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,vAPP(name,late_subject,late_InputS,X0)),X4),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2)) )
        & ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2) = X5 )
        & ( vAPP(name,late_subject,late_InputS,X0) = X3 ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
      | ( X1 = X4 )
      | ( X0 = X4 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(flattening,[],[f1140]) ).

thf(f1140,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi,X6: late_subject > name > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
      | ( ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,vAPP(name,late_subject,late_InputS,X0)),X4),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2)) )
        & ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2) = X5 )
        & ( vAPP(name,late_subject,late_InputS,X0) = X3 ) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
      | ( X1 = X4 )
      | ( X0 = X4 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(ennf_transformation,[],[f732]) ).

thf(f732,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi,X6: late_subject > name > pi > $o] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
     => ( ( X0 != X4 )
       => ( ( X1 != X4 )
         => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
           => ( ( ( vAPP(name,late_subject,late_InputS,X0) = X3 )
               => ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2) = X5 )
                 => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,vAPP(name,late_subject,late_InputS,X0)),X4),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2)) ) ) )
             => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) ) ) ) ) ) ),
    inference(fool_elimination,[],[f731]) ).

thf(f731,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi,X6: late_subject > name > pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5))
     => ( ( X0 != X4 )
       => ( ( X1 != X4 )
         => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2)
           => ( ( ( vAPP(name,late_subject,late_InputS,X0) = X3 )
               => ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2) = X5 )
                 => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,vAPP(name,late_subject,late_InputS,X0)),X4),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2)) ) )
             => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) ) ) ) ) ),
    inference(rectify,[],[f311]) ).

thf(f311,axiom,
    ! [X0: name,X2: name,X19: pi,X1: late_subject,X22: name,X70: pi,X96: late_subject > name > pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X2),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X22),X70))
     => ( ( X0 != X22 )
       => ( ( X2 != X22 )
         => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X19)
           => ( ( ( vAPP(name,late_subject,late_InputS,X0) = X1 )
               => ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X22)),nil_Pr743626285e_name)),X19) = X70 )
                 => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X96,vAPP(name,late_subject,late_InputS,X0)),X22),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X22)),nil_Pr743626285e_name)),X19)) ) )
             => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X96,X1),X22),X70) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_inputCases) ).

thf(f6081,plain,
    spl225_325,
    inference(avatar_split_clause,[],[f1653,f6079]) ).

thf(f6079,plain,
    ( spl225_325
  <=> ! [X2: late_residual,X0: name,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_325])]) ).

thf(f1653,plain,
    ! [X2: late_residual,X0: name,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1304]) ).

thf(f1304,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) = X2 )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)) ) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK176,sK177,sK178,sK179])],[f1302,f1303]) ).

thf(f1303,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ? [X3: pi,X4: late_freeRes,X5: pi,X6: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X6),X4) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X6),X5)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X6),X3) ) )
     => ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) = X2 )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1302,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ? [X3: pi,X4: late_freeRes,X5: pi,X6: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X6),X4) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X6),X5)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X6),X3) ) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(rectify,[],[f1146]) ).

thf(f1146,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ? [X12: pi,X13: late_freeRes,X14: pi,X15: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X15),X13) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X12),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X14)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X12) ) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(definition_folding,[],[f1041,f1145,f1144]) ).

thf(f1144,plain,
    ! [X2: late_residual,X1: pi,X0: name] :
      ( ? [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7) )
          & ( X9 != X11 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1145,plain,
    ! [X2: late_residual,X1: pi,X0: name] :
      ( ? [X3: pi,X4: name,X5: name] :
          ( ? [X6: pi] :
              ( ( X4 != X5 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1041,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ? [X12: pi,X13: late_freeRes,X14: pi,X15: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X15),X13) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X12),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X14)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X12) ) )
      | ? [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7) )
          & ( X9 != X11 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) ) )
      | ? [X3: pi,X4: name,X5: name] :
          ( ? [X6: pi] :
              ( ( X4 != X5 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(flattening,[],[f1040]) ).

thf(f1040,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ? [X12: pi,X13: late_freeRes,X14: pi,X15: name] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X15),X13) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X12),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14)) )
          & ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X14)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X12) ) )
      | ? [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7) )
          & ( X9 != X11 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) ) )
      | ? [X3: pi,X4: name,X5: name] :
          ( ? [X6: pi] :
              ( ( X4 != X5 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(ennf_transformation,[],[f885]) ).

thf(f885,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) )
     => ( ! [X3: pi,X4: name,X5: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) )
           => ! [X6: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
                 => ( X4 = X5 ) ) ) )
       => ( ! [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10)) )
                 => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8) )
                   => ( ( X9 != X11 )
                     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7) )
                       => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) ) ) ) ) ) ) )
         => ~ ! [X12: pi,X13: late_freeRes,X14: pi,X15: name] :
                ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X12) )
               => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X14)) = X2 )
                 => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X12),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14)) )
                   => ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X15),X13) ) ) ) ) ) ) ),
    inference(flattening,[],[f586]) ).

thf(f586,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) )
     => ( ! [X3: pi,X4: name,X5: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) )
           => ! [X6: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
                 => ( X4 = X5 ) ) ) )
       => ( ! [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10)) )
                 => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8) )
                   => ( ( X9 != X11 )
                     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7) )
                       => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) ) ) ) ) ) ) )
         => ~ ! [X12: pi,X13: late_freeRes,X14: pi,X15: name] :
                ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X12) )
               => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X14)) = X2 )
                 => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X12),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14)) )
                   => ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X15),X13) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f585]) ).

thf(f585,plain,
    ! [X0: name,X1: pi,X2: late_residual] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2)
     => ( ! [X3: pi,X4: name,X5: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) )
           => ! [X6: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6))
                 => ( X4 = X5 ) ) ) )
       => ( ! [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10))
                 => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8)
                   => ( ( X9 != X11 )
                     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7)
                       => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) ) ) ) ) ) )
         => ~ ! [X12: pi,X13: late_freeRes,X14: pi,X15: name] :
                ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X12) )
               => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X15),X14)) = X2 )
                 => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X12),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14))
                   => ~ vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X15),X13) ) ) ) ) ) ),
    inference(rectify,[],[f205]) ).

thf(f205,axiom,
    ! [X2: name,X19: pi,X60: late_residual] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19)),X60)
     => ( ! [X48: pi,X61: name,X62: name] :
            ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X62),X48) )
           => ! [X47: pi] :
                ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X61)),X62),X47) = X60 )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X61),X62)),X47))
                 => ( X61 = X62 ) ) ) )
       => ( ! [X48: pi,X61: late_subject,X63: name,X47: pi,X50: name] :
              ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X48) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X47)) = X60 )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),X47))
                 => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X50),X61)
                   => ( ( X50 != X63 )
                     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X48)
                       => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X63),X61) ) ) ) ) ) )
         => ~ ! [X48: pi,X49: late_freeRes,X47: pi,X50: name] :
                ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X48) )
               => ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X49),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X50),X47)) = X60 )
                 => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X49),X47))
                   => ~ vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X50),X49) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_resCases_H) ).

thf(f6074,plain,
    spl225_324,
    inference(avatar_split_clause,[],[f1652,f6072]) ).

thf(f6072,plain,
    ( spl225_324
  <=> ! [X2: late_residual,X0: name,X1: pi] :
        ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) = X2 )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_324])]) ).

thf(f1652,plain,
    ! [X2: late_residual,X0: name,X1: pi] :
      ( ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK178,X2),X1),X0))) = X2 )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1304]) ).

thf(f6064,plain,
    spl225_323,
    inference(avatar_split_clause,[],[f1724,f6062]) ).

thf(f6062,plain,
    ( spl225_323
  <=> ! [X0: name,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_323])]) ).

thf(f1724,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK196,X3),X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1315]) ).

thf(f6050,plain,
    spl225_322,
    inference(avatar_split_clause,[],[f1775,f6048]) ).

thf(f6048,plain,
    ( spl225_322
  <=> ! [X3: name,X4: pi,X0: name,X5: late_subject > pi > $o,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
        | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
        | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
        | ( X0 = X3 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_322])]) ).

thf(f1775,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi,X4: pi,X5: late_subject > pi > $o] :
      ( ( $true = vAPP(pi,$o,vAPP(late_subject,sTfun(pi,$o),X5,X2),X4) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
      | ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X1),X2),X5),X3),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X1) )
      | ( X0 = X3 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1343]) ).

thf(f6036,plain,
    ( spl225_321
    | ~ spl225_37
    | ~ spl225_290 ),
    inference(avatar_split_clause,[],[f5942,f5834,f2455,f6034]) ).

thf(f6034,plain,
    ( spl225_321
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK52,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK53,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_321])]) ).

thf(f5834,plain,
    ( spl225_290
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_290])]) ).

thf(f5942,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK52,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK53,X0)) )
    | ~ spl225_37
    | ~ spl225_290 ),
    inference(superposition,[],[f5835,f2456]) ).

thf(f5835,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X1) = X0 )
    | ~ spl225_290 ),
    inference(avatar_component_clause,[],[f5834]) ).

thf(f6024,plain,
    spl225_320,
    inference(avatar_split_clause,[],[f1765,f6022]) ).

thf(f6022,plain,
    ( spl225_320
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_320])]) ).

thf(f1765,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK215,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1334]) ).

thf(f6020,plain,
    spl225_319,
    inference(avatar_split_clause,[],[f1764,f6018]) ).

thf(f6018,plain,
    ( spl225_319
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_319])]) ).

thf(f1764,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK218,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1334]) ).

thf(f6016,plain,
    spl225_318,
    inference(avatar_split_clause,[],[f1763,f6014]) ).

thf(f6014,plain,
    ( spl225_318
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_318])]) ).

thf(f1763,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK216,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK214,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1334]) ).

thf(f6012,plain,
    spl225_317,
    inference(avatar_split_clause,[],[f1759,f6010]) ).

thf(f6010,plain,
    ( spl225_317
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_317])]) ).

thf(f1759,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK210,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

thf(f6008,plain,
    spl225_316,
    inference(avatar_split_clause,[],[f1758,f6006]) ).

thf(f6006,plain,
    ( spl225_316
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_316])]) ).

thf(f1758,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK209,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

thf(f6004,plain,
    spl225_315,
    inference(avatar_split_clause,[],[f1757,f6002]) ).

thf(f6002,plain,
    ( spl225_315
  <=> ! [X4: pi,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_315])]) ).

thf(f1757,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK211,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK213,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

thf(f6000,plain,
    ( spl225_314
    | ~ spl225_34
    | ~ spl225_290 ),
    inference(avatar_split_clause,[],[f5941,f5834,f2443,f5998]) ).

thf(f5998,plain,
    ( spl225_314
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK48,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK49,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_314])]) ).

thf(f5941,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK48,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK49,X0)) )
    | ~ spl225_34
    | ~ spl225_290 ),
    inference(superposition,[],[f5835,f2444]) ).

thf(f5996,plain,
    spl225_313,
    inference(avatar_split_clause,[],[f1749,f5994]) ).

thf(f5994,plain,
    ( spl225_313
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_313])]) ).

thf(f1749,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f5992,plain,
    spl225_312,
    inference(avatar_split_clause,[],[f1748,f5990]) ).

thf(f5990,plain,
    ( spl225_312
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_312])]) ).

thf(f1748,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(late_subject,sTfun(name,sTfun(pi,pi)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,pi)))),sK200,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f5988,plain,
    spl225_311,
    inference(avatar_split_clause,[],[f1746,f5986]) ).

thf(f5986,plain,
    ( spl225_311
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_311])]) ).

thf(f1746,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0)),vAPP(pi,late_subject,vAPP(name,sTfun(pi,late_subject),vAPP(late_subject,sTfun(name,sTfun(pi,late_subject)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,late_subject)))),sK201,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f5973,plain,
    spl225_310,
    inference(avatar_split_clause,[],[f1898,f5971]) ).

thf(f5971,plain,
    ( spl225_310
  <=> ! [X3: name,X4: set_Pr1834926343_pi_pi,X0: pi,X5: list_P227219501e_name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X5),X3)),X4) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_310])]) ).

thf(f1898,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(definition_unfolding,[],[f1782,f1358]) ).

thf(f1782,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(cnf_transformation,[],[f1122]) ).

thf(f1122,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(flattening,[],[f1121]) ).

thf(f1121,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(ennf_transformation,[],[f708]) ).

thf(f708,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) )
     => ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
       => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) ) ) ),
    inference(fool_elimination,[],[f707]) ).

thf(f707,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4)
     => ( vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4)
       => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) ) ),
    inference(rectify,[],[f347]) ).

thf(f347,axiom,
    ! [X19: pi,X93: pi,X0: late_subject,X2: name,X100: set_Pr1834926343_pi_pi,X108: list_P227219501e_name] :
      ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X19),X93),X0),X2),X100)
     => ( vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X100)
       => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X108),X19)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X108),X93)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X108),X0)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X108),X2)),X100) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_derivativeEqvtI) ).

thf(f5969,plain,
    spl225_309,
    inference(avatar_split_clause,[],[f1608,f5967]) ).

thf(f5967,plain,
    ( spl225_309
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK163,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK164,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK165,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK166,X0))),nil_Pr743626285e_name) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_309])]) ).

thf(f1608,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK160,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK162,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK163,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK164,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK165,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK166,X0))),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1292]) ).

thf(f5949,plain,
    spl225_308,
    inference(avatar_split_clause,[],[f1789,f5947]) ).

thf(f5947,plain,
    ( spl225_308
  <=> ! [X5: name,X3: pi,X4: pi,X0: pi,X6: pi,X2: name,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X5)),X6)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_308])]) ).

thf(f1789,plain,
    ! [X2: name,X3: pi,X0: pi,X1: name,X6: pi,X4: pi,X5: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X5)),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1131]) ).

thf(f1131,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X5)),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ),
    inference(flattening,[],[f1130]) ).

thf(f1130,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X5)),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) ) ),
    inference(ennf_transformation,[],[f722]) ).

thf(f722,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3)) )
     => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X5)),X6)) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6))) ) ) ),
    inference(fool_elimination,[],[f721]) ).

thf(f721,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X2),X3))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X5)),X6))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X2),X5)),X6))) ) ),
    inference(rectify,[],[f330]) ).

thf(f330,axiom,
    ! [X19: pi,X0: name,X2: name,X31: pi,X93: pi,X1: name,X94: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X2),X31))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),X94))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X31),X2),X1)),X94))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_Late__Semantics_OComm1) ).

thf(f5940,plain,
    spl225_307,
    inference(avatar_split_clause,[],[f1787,f5938]) ).

thf(f5938,plain,
    ( spl225_307
  <=> ! [X5: name,X3: pi,X4: pi,X0: pi,X6: pi,X2: name,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2)))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_307])]) ).

thf(f1787,plain,
    ! [X2: name,X3: pi,X0: pi,X1: name,X6: pi,X4: pi,X5: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2)))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ),
    inference(cnf_transformation,[],[f1127]) ).

thf(f1127,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2)))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ),
    inference(flattening,[],[f1126]) ).

thf(f1126,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2)))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ),
    inference(ennf_transformation,[],[f718]) ).

thf(f718,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) )
     => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6)) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2)))) ) ) ),
    inference(fool_elimination,[],[f717]) ).

thf(f717,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi,X4: pi,X5: name,X6: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X4),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X1)),X5),X6))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X6),X5),X2)))) ) ),
    inference(rectify,[],[f331]) ).

thf(f331,axiom,
    ! [X19: pi,X0: name,X1: name,X31: pi,X93: pi,X2: name,X94: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),X31))
     => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X2),X94))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X31),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X94),X2),X1)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Late__Semantics_OComm2) ).

thf(f5931,plain,
    spl225_306,
    inference(avatar_split_clause,[],[f1766,f5929]) ).

thf(f5929,plain,
    ( spl225_306
  <=> ! [X4: pi,X0: pi,X3: name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X0),X1),X2),X3),X4) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X0),X1),X2),X3),X4) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_306])]) ).

thf(f1766,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X0),X1),X2),X3),X4) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X0),X1),X2),X3),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(cnf_transformation,[],[f1153]) ).

thf(f1153,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP6,X0),X1),X2),X3),X4) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP5,X0),X1),X2),X3),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(definition_folding,[],[f1112,f1152,f1151]) ).

thf(f1112,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ? [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) ) )
      | ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(flattening,[],[f1111]) ).

thf(f1111,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ? [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) ) )
      | ? [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
          & ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(ennf_transformation,[],[f911]) ).

thf(f911,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ! [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
            ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) )
           => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
             => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
               => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
                 => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
                   => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) ) ) ) ) ) )
       => ~ ! [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
              ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13)) )
                 => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14) )
                   => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10) )
                     => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) ) ) ) ) ) ) ) ),
    inference(flattening,[],[f696]) ).

thf(f696,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ! [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
            ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) )
           => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
             => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
               => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5) )
                 => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) )
                   => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) ) ) ) ) ) )
       => ~ ! [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
              ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
               => ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13)) )
                 => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14) )
                   => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10) )
                     => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f695]) ).

thf(f695,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4))
     => ( ! [X5: pi,X6: late_subject,X7: name,X8: pi,X9: pi] :
            ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X5),X9) )
           => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X8),X9)) )
             => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8))
               => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X5)
                 => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9)
                   => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) ) ) ) ) )
       => ~ ! [X10: pi,X11: late_subject,X12: name,X13: pi,X14: pi] :
              ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X10) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X13)) )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X10),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X11),X12),X13))
                 => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X14)
                   => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X12),X10)
                     => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X12),X11) ) ) ) ) ) ) ),
    inference(rectify,[],[f306]) ).

thf(f306,axiom,
    ! [X19: pi,X93: pi,X1: late_subject,X22: name,X31: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X22),X31))
     => ( ! [X48: pi,X61: late_subject,X63: name,X47: pi,X98: pi] :
            ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X48),X98) )
           => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X22),X31) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X47),X98)) )
             => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X48),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),X47))
               => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X48)
                 => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X98)
                   => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X63),X61) ) ) ) ) )
       => ~ ! [X98: pi,X61: late_subject,X63: name,X97: pi,X48: pi] :
              ( ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X48),X98) )
             => ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X22),X31) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X48),X97)) )
               => ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X98),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X61),X63),X97))
                 => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X48)
                   => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X63),X98)
                     => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X63),X61) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_parCasesB_H) ).

thf(f5925,plain,
    spl225_305,
    inference(avatar_split_clause,[],[f1747,f5923]) ).

thf(f5923,plain,
    ( spl225_305
  <=> ! [X4: name,X0: pi,X3: pi,X2: late_subject,X1: name] :
        ( ( vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0) != vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_305])]) ).

thf(f1747,plain,
    ! [X2: late_subject,X3: pi,X0: pi,X1: name,X4: name] :
      ( ( vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK202,X4),X3),X2),X1),X0) != vAPP(pi,name,vAPP(name,sTfun(pi,name),vAPP(late_subject,sTfun(name,sTfun(pi,name)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,name)))),sK204,X4),X3),X2),X1),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o))),vAPP(name,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(pi,$o)))),sP4,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f5921,plain,
    spl225_304,
    inference(avatar_split_clause,[],[f1642,f5919]) ).

thf(f5919,plain,
    ( spl225_304
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0))),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_304])]) ).

thf(f1642,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0))),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f1297,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0))),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0))),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0)) = X0 )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK167,sK168,sK169,sK170])],[f1294,f1296,f1295]) ).

thf(f1295,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ? [X3: pi,X4: name,X5: name] :
          ( ? [X6: pi] :
              ( ( X4 != X5 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X0 ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) ) )
     => ( ? [X6: pi] :
            ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0) )
            & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0))),X6)) )
            & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0))),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),X6) = X0 ) )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1296,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ? [X6: pi] :
          ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0))),X6)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0))),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),X6) = X0 ) )
     => ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0))),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0))),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1294,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ? [X3: pi,X4: name,X5: name] :
          ( ? [X6: pi] :
              ( ( X4 != X5 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X0 ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ),
    inference(rectify,[],[f1293]) ).

thf(f1293,plain,
    ! [X2: late_residual,X1: pi,X0: name] :
      ( ? [X3: pi,X4: name,X5: name] :
          ( ? [X6: pi] :
              ( ( X4 != X5 )
              & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X5)),X6)) )
              & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6) = X2 ) )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X5),X3) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f1145]) ).

thf(f5906,plain,
    ( spl225_303
    | ~ spl225_21
    | ~ spl225_158 ),
    inference(avatar_split_clause,[],[f3857,f3516,f2377,f5904]) ).

thf(f3516,plain,
    ( spl225_158
  <=> ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_158])]) ).

thf(f3857,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: name] : ( late_TauR != vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) )
    | ~ spl225_21
    | ~ spl225_158 ),
    inference(superposition,[],[f2378,f3517]) ).

thf(f3517,plain,
    ( ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) )
    | ~ spl225_158 ),
    inference(avatar_component_clause,[],[f3516]) ).

thf(f5902,plain,
    spl225_302,
    inference(avatar_split_clause,[],[f1651,f5900]) ).

thf(f5900,plain,
    ( spl225_302
  <=> ! [X2: late_residual,X0: name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_302])]) ).

thf(f1651,plain,
    ! [X2: late_residual,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_residual,sTfun(pi,sTfun(name,pi)),sK176,X2),X1),X0)) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1304]) ).

thf(f5898,plain,
    spl225_301,
    inference(avatar_split_clause,[],[f1646,f5896]) ).

thf(f5896,plain,
    ( spl225_301
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_301])]) ).

thf(f1646,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f1301,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) )
        & ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) = X0 )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK171,sK172,sK173,sK174,sK175])],[f1299,f1300]) ).

thf(f1300,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ? [X3: pi,X4: late_subject,X5: name,X6: pi,X7: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X5),X4) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X3) )
          & ( X5 != X7 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X4) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X4),X5),X6)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X4),X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) = X0 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X3) ) )
     => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) )
        & ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) )
        & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) = X0 )
        & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1299,plain,
    ! [X0: late_residual,X1: pi,X2: name] :
      ( ? [X3: pi,X4: late_subject,X5: name,X6: pi,X7: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X5),X4) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X5),X3) )
          & ( X5 != X7 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X4) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X4),X5),X6)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X4),X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X6)) = X0 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X7),X3) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(rectify,[],[f1298]) ).

thf(f1298,plain,
    ! [X2: late_residual,X1: pi,X0: name] :
      ( ? [X7: pi,X8: late_subject,X9: name,X10: pi,X11: name] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X9),X8) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X9),X7) )
          & ( X9 != X11 )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X11),X8) )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X7),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),X10)) )
          & ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X8),X9),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X10)) = X2 )
          & ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X11),X7) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f1144]) ).

thf(f5894,plain,
    spl225_300,
    inference(avatar_split_clause,[],[f1645,f5892]) ).

thf(f5892,plain,
    ( spl225_300
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) = X0 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_300])]) ).

thf(f1645,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK174,X2),X1),X0))) = X0 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f5876,plain,
    ( spl225_299
    | ~ spl225_18
    | ~ spl225_79
    | ~ spl225_98 ),
    inference(avatar_split_clause,[],[f2899,f2862,f2678,f2365,f5874]) ).

thf(f5874,plain,
    ( spl225_299
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_299])]) ).

thf(f2678,plain,
    ( spl225_79
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_79])]) ).

thf(f2899,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),X1) = X1 )
    | ~ spl225_18
    | ~ spl225_79
    | ~ spl225_98 ),
    inference(forward_demodulation,[],[f2891,f2366]) ).

thf(f2891,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1)) = X1 )
    | ~ spl225_79
    | ~ spl225_98 ),
    inference(superposition,[],[f2863,f2679]) ).

thf(f2679,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 )
    | ~ spl225_79 ),
    inference(avatar_component_clause,[],[f2678]) ).

thf(f5868,plain,
    spl225_298,
    inference(avatar_split_clause,[],[f1897,f5866]) ).

thf(f5866,plain,
    ( spl225_298
  <=> ! [X3: name,X4: set_Pr1834926343_pi_pi,X0: pi,X5: list_P227219501e_name,X2: late_subject,X1: pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X5),X3)),X4) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_298])]) ).

thf(f1897,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(definition_unfolding,[],[f1781,f1358]) ).

thf(f1781,plain,
    ! [X2: late_subject,X3: name,X0: pi,X1: pi,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(cnf_transformation,[],[f1120]) ).

thf(f1120,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(flattening,[],[f1119]) ).

thf(f1119,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) ) ),
    inference(ennf_transformation,[],[f706]) ).

thf(f706,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4) )
     => ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4) )
       => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) ) ) ),
    inference(fool_elimination,[],[f705]) ).

thf(f705,plain,
    ! [X0: pi,X1: pi,X2: late_subject,X3: name,X4: set_Pr1834926343_pi_pi,X5: list_P227219501e_name] :
      ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X0),X1),X2),X3),X4)
     => ( vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X4)
       => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X0)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X1)),X2),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),X4) ) ),
    inference(rectify,[],[f343]) ).

thf(f343,axiom,
    ! [X19: pi,X93: pi,X0: late_subject,X2: name,X100: set_Pr1834926343_pi_pi,X108: list_P227219501e_name] :
      ( vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,X19),X93),X0),X2),X100)
     => ( vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,X100)
       => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(name,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)),vAPP(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o))),vAPP(pi,sTfun(pi,sTfun(late_subject,sTfun(name,sTfun(set_Pr1834926343_pi_pi,$o)))),strong2129052853vative,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X108),X19)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X108),X93)),X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X108),X2)),X100) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_derivativeEqvtI2) ).

thf(f5864,plain,
    spl225_297,
    inference(avatar_split_clause,[],[f1607,f5862]) ).

thf(f5862,plain,
    ( spl225_297
  <=> ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK157,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_297])]) ).

thf(f1607,plain,
    ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK157,X0))) ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f1287,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK157,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153,sK154,sK155,sK156,sK157,sK158])],[f1284,f1286,f1285]) ).

thf(f1285,plain,
    ! [X0: pi > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1286,plain,
    ! [X0: pi > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK157,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1284,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) ) ) ),
    inference(rectify,[],[f988]) ).

thf(f988,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6) ) ) ),
    inference(flattening,[],[f987]) ).

thf(f987,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f522]) ).

thf(f522,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: pi] : ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f521]) ).

thf(f521,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: pi] : vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f221]) ).

thf(f221,axiom,
    ! [X19: pi > late_residual > $o,X68: pi,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: pi] :
          ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: pi] : vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_residual_Ostrong__induct) ).

thf(f5860,plain,
    spl225_296,
    inference(avatar_split_clause,[],[f1604,f5858]) ).

thf(f5858,plain,
    ( spl225_296
  <=> ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK150,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_296])]) ).

thf(f1604,plain,
    ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK150,X0))) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f1283,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK150,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK145,sK146,sK147,sK148,sK149,sK150,sK151])],[f1280,f1282,f1281]) ).

thf(f1281,plain,
    ! [X0: pi > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1282,plain,
    ! [X0: pi > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK150,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)) )
        & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1280,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X7),X9) ) ) ),
    inference(rectify,[],[f986]) ).

thf(f986,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6) ) ) ),
    inference(flattening,[],[f985]) ).

thf(f985,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f520]) ).

thf(f520,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: pi] : ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f519]) ).

thf(f519,plain,
    ! [X0: pi > late_residual > $o,X1: pi,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: pi] :
          ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: pi] : vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f217]) ).

thf(f217,axiom,
    ! [X19: pi > late_residual > $o,X68: pi,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: pi] :
          ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: pi] : vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_residual_Ostrong__inducts) ).

thf(f5856,plain,
    spl225_295,
    inference(avatar_split_clause,[],[f1601,f5854]) ).

thf(f5854,plain,
    ( spl225_295
  <=> ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK143,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_295])]) ).

thf(f1601,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK144,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK143,X0))) ) ),
    inference(cnf_transformation,[],[f1279]) ).

thf(f5852,plain,
    spl225_294,
    inference(avatar_split_clause,[],[f1598,f5850]) ).

thf(f5850,plain,
    ( spl225_294
  <=> ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK136,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_294])]) ).

thf(f1598,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK137,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK136,X0))) ) ),
    inference(cnf_transformation,[],[f1275]) ).

thf(f5848,plain,
    spl225_293,
    inference(avatar_split_clause,[],[f1595,f5846]) ).

thf(f5846,plain,
    ( spl225_293
  <=> ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK129,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_293])]) ).

thf(f1595,plain,
    ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK129,X0))) ) ),
    inference(cnf_transformation,[],[f1271]) ).

thf(f1271,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK129,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125,sK126,sK127,sK128,sK129,sK130])],[f1268,f1270,f1269]) ).

thf(f1269,plain,
    ! [X0: late_subject > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1270,plain,
    ! [X0: late_subject > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK129,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1268,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X9) ) ) ),
    inference(rectify,[],[f980]) ).

thf(f980,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6) ) ) ),
    inference(flattening,[],[f979]) ).

thf(f979,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f514]) ).

thf(f514,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_subject] : ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f513]) ).

thf(f513,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_subject] : vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f218]) ).

thf(f218,axiom,
    ! [X19: late_subject > late_residual > $o,X68: late_subject,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: late_subject] :
          ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: late_subject] : vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_residual_Ostrong__induct) ).

thf(f5844,plain,
    spl225_292,
    inference(avatar_split_clause,[],[f1592,f5842]) ).

thf(f5842,plain,
    ( spl225_292
  <=> ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK122,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_292])]) ).

thf(f1592,plain,
    ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK122,X0))) ) ),
    inference(cnf_transformation,[],[f1267]) ).

thf(f1267,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK122,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK117,sK118,sK119,sK120,sK121,sK122,sK123])],[f1264,f1266,f1265]) ).

thf(f1265,plain,
    ! [X0: late_subject > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1266,plain,
    ! [X0: late_subject > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK122,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1264,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X9) ) ) ),
    inference(rectify,[],[f978]) ).

thf(f978,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6) ) ) ),
    inference(flattening,[],[f977]) ).

thf(f977,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_subject] : ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f512]) ).

thf(f512,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_subject] : ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f511]) ).

thf(f511,plain,
    ! [X0: late_subject > late_residual > $o,X1: late_subject,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_subject] :
          ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_subject] : vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f214]) ).

thf(f214,axiom,
    ! [X19: late_subject > late_residual > $o,X68: late_subject,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: late_subject] :
          ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: late_subject] : vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_residual_Ostrong__inducts) ).

thf(f5840,plain,
    spl225_291,
    inference(avatar_split_clause,[],[f1589,f5838]) ).

thf(f5838,plain,
    ( spl225_291
  <=> ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK115,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_291])]) ).

thf(f1589,plain,
    ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK115,X0))) ) ),
    inference(cnf_transformation,[],[f1263]) ).

thf(f1263,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK115,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)) )
        & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111,sK112,sK113,sK114,sK115,sK116])],[f1260,f1262,f1261]) ).

thf(f1261,plain,
    ! [X0: late_freeRes > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1262,plain,
    ! [X0: late_freeRes > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK115,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)) )
        & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1260,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X9) ) ) ),
    inference(rectify,[],[f976]) ).

thf(f976,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6) ) ) ),
    inference(flattening,[],[f975]) ).

thf(f975,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f510]) ).

thf(f510,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_freeRes] : ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f509]) ).

thf(f509,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_freeRes] : vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f215]) ).

thf(f215,axiom,
    ! [X19: late_freeRes > late_residual > $o,X68: late_freeRes,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: late_freeRes] :
          ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: late_freeRes] : vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_residual_Ostrong__inducts) ).

thf(f5836,plain,
    ( spl225_290
    | ~ spl225_18
    | ~ spl225_78
    | ~ spl225_98 ),
    inference(avatar_split_clause,[],[f2898,f2862,f2674,f2365,f5834]) ).

thf(f2898,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X1) = X0 )
    | ~ spl225_18
    | ~ spl225_78
    | ~ spl225_98 ),
    inference(forward_demodulation,[],[f2890,f2366]) ).

thf(f2890,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,nil_Pr743626285e_name),X1)) = X0 )
    | ~ spl225_78
    | ~ spl225_98 ),
    inference(superposition,[],[f2863,f2675]) ).

thf(f5832,plain,
    spl225_289,
    inference(avatar_split_clause,[],[f1586,f5830]) ).

thf(f5830,plain,
    ( spl225_289
  <=> ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK108,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_289])]) ).

thf(f1586,plain,
    ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK108,X0))) ) ),
    inference(cnf_transformation,[],[f1259]) ).

thf(f1259,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
      | ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK108,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)) )
        & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK103,sK104,sK105,sK106,sK107,sK108,sK109])],[f1256,f1258,f1257]) ).

thf(f1257,plain,
    ! [X0: late_freeRes > late_residual > $o] :
      ( ? [X3: late_freeRes,X4: pi,X5: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
     => ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1258,plain,
    ! [X0: late_freeRes > late_residual > $o] :
      ( ? [X6: late_subject,X7: name,X8: pi,X9: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X9) ) )
     => ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK108,X0))) )
        & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)) )
        & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1256,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X3: late_freeRes,X4: pi,X5: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) )
      | ? [X6: late_subject,X7: name,X8: pi,X9: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X6),X7),X8)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X7),X6) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X7),X9) ) ) ),
    inference(rectify,[],[f974]) ).

thf(f974,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6) ) ) ),
    inference(flattening,[],[f973]) ).

thf(f973,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ? [X7: late_freeRes,X8: pi,X9: late_freeRes] : ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
      | ? [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
          & ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
          & ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6) ) ) ),
    inference(ennf_transformation,[],[f508]) ).

thf(f508,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6) )
         => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3) )
           => ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_freeRes] : ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8)) )
       => ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f507]) ).

thf(f507,plain,
    ! [X0: late_freeRes > late_residual > $o,X1: late_freeRes,X2: late_residual] :
      ( ! [X3: late_subject,X4: name,X5: pi,X6: late_freeRes] :
          ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X4),X6)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X3)
           => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X6),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) )
     => ( ! [X7: late_freeRes,X8: pi,X9: late_freeRes] : vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X9),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X7),X8))
       => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f219]) ).

thf(f219,axiom,
    ! [X19: late_freeRes > late_residual > $o,X68: late_freeRes,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi,X69: late_freeRes] :
          ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X57),X69)
         => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X57),X56)
           => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58)) ) )
     => ( ! [X59: late_freeRes,X58: pi,X69: late_freeRes] : vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X19,X69),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X19,X68),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_residual_Ostrong__induct) ).

thf(f5823,plain,
    spl225_288,
    inference(avatar_split_clause,[],[f1795,f5821]) ).

thf(f5821,plain,
    ( spl225_288
  <=> ! [X5: pi,X4: name,X2: pi,X0: name,X6: late_subject > name > pi > $o,X3: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
        | ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2) = X5 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
        | ( X1 = X4 )
        | ( X0 = X4 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_288])]) ).

thf(f1795,plain,
    ! [X2: pi,X3: late_subject,X0: name,X1: name,X6: late_subject > name > pi > $o,X4: name,X5: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
      | ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X4)),nil_Pr743626285e_name)),X2) = X5 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
      | ( X1 = X4 )
      | ( X0 = X4 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(cnf_transformation,[],[f1141]) ).

thf(f5819,plain,
    spl225_287,
    inference(avatar_split_clause,[],[f1383,f5817]) ).

thf(f5817,plain,
    ( spl225_287
  <=> ! [X0: produc1872410278e_name] :
        ( ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK30,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK31,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK32,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK33,X0)))) = X0 )
        | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK34,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK35,X0)),nil_Pr743626285e_name)) = X0 )
        | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK36,X0)),nil_Pr743626285e_name) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_287])]) ).

thf(f1383,plain,
    ! [X0: produc1872410278e_name] :
      ( ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK30,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK31,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK32,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK33,X0)))) = X0 )
      | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK34,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK35,X0)),nil_Pr743626285e_name)) = X0 )
      | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK36,X0)),nil_Pr743626285e_name) = X0 ) ),
    inference(cnf_transformation,[],[f1183]) ).

thf(f1183,plain,
    ! [X0: produc1872410278e_name] :
      ( ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK30,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK31,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK32,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK33,X0)))) = X0 )
      | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK34,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK35,X0)),nil_Pr743626285e_name)) = X0 )
      | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK36,X0)),nil_Pr743626285e_name) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33,sK34,sK35,sK36])],[f1179,f1182,f1181,f1180]) ).

thf(f1180,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X1: produc367475239e_name > produc367475239e_name > $o,X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4))) = X0 )
     => ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK30,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK31,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK32,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK33,X0)))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1181,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X5: produc367475239e_name > produc367475239e_name > $o,X6: produc367475239e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X5),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X6),nil_Pr743626285e_name)) = X0 )
     => ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK34,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK35,X0)),nil_Pr743626285e_name)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1182,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X7: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X7),nil_Pr743626285e_name) = X0 )
     => ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK36,X0)),nil_Pr743626285e_name) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1179,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X1: produc367475239e_name > produc367475239e_name > $o,X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4))) = X0 )
      | ? [X5: produc367475239e_name > produc367475239e_name > $o,X6: produc367475239e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X5),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X6),nil_Pr743626285e_name)) = X0 )
      | ? [X7: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X7),nil_Pr743626285e_name) = X0 ) ),
    inference(rectify,[],[f927]) ).

thf(f927,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: produc367475239e_name,X7: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X6),X7))) = X0 )
      | ? [X2: produc367475239e_name > produc367475239e_name > $o,X3: produc367475239e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),nil_Pr743626285e_name)) = X0 )
      | ? [X1: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),nil_Pr743626285e_name) = X0 ) ),
    inference(flattening,[],[f926]) ).

thf(f926,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: produc367475239e_name,X7: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X6),X7))) = X0 )
      | ? [X2: produc367475239e_name > produc367475239e_name > $o,X3: produc367475239e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),nil_Pr743626285e_name)) = X0 )
      | ? [X1: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),nil_Pr743626285e_name) = X0 ) ),
    inference(ennf_transformation,[],[f783]) ).

thf(f783,plain,
    ! [X0: produc1872410278e_name] :
      ( ! [X1: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),nil_Pr743626285e_name) != X0 )
     => ( ! [X2: produc367475239e_name > produc367475239e_name > $o,X3: produc367475239e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),nil_Pr743626285e_name)) != X0 )
       => ~ ! [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: produc367475239e_name,X7: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X6),X7))) != X0 ) ) ),
    inference(rectify,[],[f207]) ).

thf(f207,axiom,
    ! [X2: produc1872410278e_name] :
      ( ! [X48: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X48),nil_Pr743626285e_name) != X2 )
     => ( ! [X48: produc367475239e_name > produc367475239e_name > $o,X63: produc367475239e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X48),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),nil_Pr743626285e_name)) != X2 )
       => ~ ! [X48: produc367475239e_name > produc367475239e_name > $o,X63: produc367475239e_name,X50: produc367475239e_name,X65: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X48),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X65))) != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_successively_Ocases) ).

thf(f5808,plain,
    spl225_286,
    inference(avatar_split_clause,[],[f1572,f5806]) ).

thf(f5806,plain,
    ( spl225_286
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_286])]) ).

thf(f1572,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ),
    inference(cnf_transformation,[],[f1236]) ).

thf(f1236,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0)) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80,sK81,sK82,sK83,sK84])],[f1232,f1235,f1234,f1233]) ).

thf(f1233,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),X6) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) ) )
     => ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0)) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1234,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X7: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X7),nil_Pr743626285e_name) )
     => ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) ) ),
    introduced(choice_axiom,[]) ).

thf(f1235,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X8: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X8) )
     => ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1232,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),X6) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) ) )
      | ? [X7: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X7),nil_Pr743626285e_name) )
      | ? [X8: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X8) ) ),
    inference(rectify,[],[f964]) ).

thf(f964,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X5: produc367475239e_name,X6: list_P227219501e_name,X7: produc367475239e_name,X8: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),X8) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) ) )
      | ? [X4: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),nil_Pr743626285e_name) )
      | ? [X3: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3) ) ),
    inference(flattening,[],[f963]) ).

thf(f963,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X5: produc367475239e_name,X6: list_P227219501e_name,X7: produc367475239e_name,X8: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),X8) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) ) )
      | ? [X4: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),nil_Pr743626285e_name) )
      | ? [X3: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3) ) ),
    inference(ennf_transformation,[],[f498]) ).

thf(f498,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ! [X3: list_P227219501e_name] : ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3) )
     => ( ! [X4: list_P227219501e_name] : ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),nil_Pr743626285e_name) )
       => ( ! [X5: produc367475239e_name,X6: list_P227219501e_name,X7: produc367475239e_name,X8: list_P227219501e_name] :
              ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) )
             => ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),X8) )
               => ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) ) ) )
         => ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f497]) ).

thf(f497,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ! [X3: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3)
     => ( ! [X4: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X4),nil_Pr743626285e_name)
       => ( ! [X5: produc367475239e_name,X6: list_P227219501e_name,X7: produc367475239e_name,X8: list_P227219501e_name] :
              ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8))
             => ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),X8)
               => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X7),X8)) ) )
         => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ) ),
    inference(rectify,[],[f271]) ).

thf(f271,axiom,
    ! [X19: list_P227219501e_name > list_P227219501e_name > $o,X84: list_P227219501e_name,X85: list_P227219501e_name] :
      ( ! [X73: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,nil_Pr743626285e_name),X73)
     => ( ! [X65: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X65),nil_Pr743626285e_name)
       => ( ! [X63: produc367475239e_name,X65: list_P227219501e_name,X50: produc367475239e_name,X64: list_P227219501e_name] :
              ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X65),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X64))
             => ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),X64)
               => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X64)) ) )
         => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X84),X85) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_shuffles_Oinduct) ).

thf(f5802,plain,
    spl225_285,
    inference(avatar_split_clause,[],[f1576,f5800]) ).

thf(f5800,plain,
    ( spl225_285
  <=> ! [X2: list_P227219501e_name,X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK90,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK92,X0)),nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_285])]) ).

thf(f1576,plain,
    ! [X2: list_P227219501e_name,X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK90,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK92,X0)),nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1244]) ).

thf(f1244,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK90,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0)) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK92,X0)),nil_Pr743626285e_name) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90,sK91,sK92])],[f1241,f1243,f1242]) ).

thf(f1242,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o] :
      ( ? [X3: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,X5: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),X5) ) )
     => ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK90,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1243,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o] :
      ( ? [X6: produc367475239e_name > produc367475239e_name > $o] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X6),nil_Pr743626285e_name) )
     => ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK92,X0)),nil_Pr743626285e_name) ) ),
    introduced(choice_axiom,[]) ).

thf(f1241,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X3: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,X5: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),X5) ) )
      | ? [X6: produc367475239e_name > produc367475239e_name > $o] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X6),nil_Pr743626285e_name) ) ),
    inference(rectify,[],[f968]) ).

thf(f968,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),X6) ) )
      | ? [X3: produc367475239e_name > produc367475239e_name > $o] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),nil_Pr743626285e_name) ) ),
    inference(flattening,[],[f967]) ).

thf(f967,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),X6) ) )
      | ? [X3: produc367475239e_name > produc367475239e_name > $o] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),nil_Pr743626285e_name) ) ),
    inference(ennf_transformation,[],[f502]) ).

thf(f502,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o,X2: list_P227219501e_name] :
      ( ! [X3: produc367475239e_name > produc367475239e_name > $o] : ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),nil_Pr743626285e_name) )
     => ( ! [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: list_P227219501e_name] :
            ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),X6) )
           => ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) ) )
       => ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f501]) ).

thf(f501,plain,
    ! [X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o,X2: list_P227219501e_name] :
      ( ! [X3: produc367475239e_name > produc367475239e_name > $o] : vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X3),nil_Pr743626285e_name)
     => ( ! [X4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,X6: list_P227219501e_name] :
            ( vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),X6)
           => vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X4),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) )
       => vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f274]) ).

thf(f274,axiom,
    ! [X19: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X84: produc367475239e_name > produc367475239e_name > $o,X85: list_P227219501e_name] :
      ( ! [X48: produc367475239e_name > produc367475239e_name > $o] : vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X19,X48),nil_Pr743626285e_name)
     => ( ! [X48: produc367475239e_name > produc367475239e_name > $o,X63: produc367475239e_name,X64: list_P227219501e_name] :
            ( vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X19,X48),X64)
           => vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X19,X48),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X64)) )
       => vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X19,X84),X85) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_sorted__wrt_Oinduct) ).

thf(f5789,plain,
    spl225_284,
    inference(avatar_split_clause,[],[f1772,f5787]) ).

thf(f5787,plain,
    ( spl225_284
  <=> ! [X4: pi,X0: name,X3: late_subject,X2: late_subject > pi > $o,X1: name] :
        ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)) = X3 )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_284])]) ).

thf(f1772,plain,
    ! [X2: late_subject > pi > $o,X3: late_subject,X0: name,X1: name,X4: pi] :
      ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0)) = X3 )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1340]) ).

thf(f5785,plain,
    spl225_283,
    inference(avatar_split_clause,[],[f1654,f5783]) ).

thf(f5783,plain,
    ( spl225_283
  <=> ! [X2: late_residual,X0: name,X1: pi] :
        ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_283])]) ).

thf(f1654,plain,
    ! [X2: late_residual,X0: name,X1: pi] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_residual,sTfun(pi,sTfun(name,name)),sK179,X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_residual,sTfun(pi,sTfun(name,late_freeRes)),sK177,X2),X1),X0)) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X0),X1),X2) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X0),X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1304]) ).

thf(f5775,plain,
    spl225_282,
    inference(avatar_split_clause,[],[f1722,f5773]) ).

thf(f5773,plain,
    ( spl225_282
  <=> ! [X0: name,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_282])]) ).

thf(f1722,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK194,X3),X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1315]) ).

thf(f5769,plain,
    spl225_281,
    inference(avatar_split_clause,[],[f1771,f5767]) ).

thf(f5767,plain,
    ( spl225_281
  <=> ! [X4: pi,X0: name,X3: late_subject,X2: late_subject > pi > $o,X1: name] :
        ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0) != X0 )
        | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_281])]) ).

thf(f1771,plain,
    ! [X2: late_subject > pi > $o,X3: late_subject,X0: name,X1: name,X4: pi] :
      ( ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,name)))),sK220,X4),X3),X2),X1),X0) != X0 )
      | ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)),vAPP(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o))),vAPP(pi,sTfun(late_subject,sTfun(sTfun(late_subject,sTfun(pi,$o)),sTfun(name,sTfun(name,$o)))),sP7,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1340]) ).

thf(f5763,plain,
    spl225_280,
    inference(avatar_split_clause,[],[f1579,f5761]) ).

thf(f5761,plain,
    ( spl225_280
  <=> ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0))) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_280])]) ).

thf(f1579,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X2),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(set_Pr1834926343_pi_pi,late_subject,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,late_subject),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,late_subject)),sK98,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),vAPP(set_Pr1834926343_pi_pi,pi,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,pi),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,pi)),sK100,X2),X1),X0))) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1252]) ).

thf(f5753,plain,
    ( spl225_279
    | ~ spl225_268 ),
    inference(avatar_split_clause,[],[f5699,f5624,f5751]) ).

thf(f5751,plain,
    ( spl225_279
  <=> ! [X0: name] : ( vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_279])]) ).

thf(f5624,plain,
    ( spl225_268
  <=> ! [X0: name,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_InputS,X1) )
        | ( vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_268])]) ).

thf(f5699,plain,
    ( ! [X0: name] : ( vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0)) = X0 )
    | ~ spl225_268 ),
    inference(equality_resolution,[],[f5625]) ).

thf(f5625,plain,
    ( ! [X0: name,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_InputS,X1) )
        | ( vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0)) = X1 ) )
    | ~ spl225_268 ),
    inference(avatar_component_clause,[],[f5624]) ).

thf(f5735,plain,
    spl225_278,
    inference(avatar_split_clause,[],[f1725,f5733]) ).

thf(f5733,plain,
    ( spl225_278
  <=> ! [X0: name,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_278])]) ).

thf(f1725,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(name,name,vAPP(pi,sTfun(name,name),vAPP(late_freeRes,sTfun(pi,sTfun(name,name)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,name))),sK197,X3),X2),X1),X0)),vAPP(name,late_freeRes,vAPP(pi,sTfun(name,late_freeRes),vAPP(late_freeRes,sTfun(pi,sTfun(name,late_freeRes)),vAPP(pi,sTfun(late_freeRes,sTfun(pi,sTfun(name,late_freeRes))),sK195,X3),X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1315]) ).

thf(f5731,plain,
    spl225_277,
    inference(avatar_split_clause,[],[f1571,f5729]) ).

thf(f5729,plain,
    ( spl225_277
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_277])]) ).

thf(f1571,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK79,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ),
    inference(cnf_transformation,[],[f1236]) ).

thf(f5727,plain,
    spl225_276,
    inference(avatar_split_clause,[],[f1570,f5725]) ).

thf(f5725,plain,
    ( spl225_276
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_276])]) ).

thf(f1570,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK80,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK81,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK82,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK83,X0)),nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK84,X0)) ) ),
    inference(cnf_transformation,[],[f1236]) ).

thf(f5721,plain,
    spl225_275,
    inference(avatar_split_clause,[],[f1641,f5719]) ).

thf(f5719,plain,
    ( spl225_275
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0))),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0)) = X0 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_275])]) ).

thf(f1641,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0))),vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK170,X2),X1),X0)) = X0 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f5708,plain,
    spl225_274,
    inference(avatar_split_clause,[],[f1733,f5706]) ).

thf(f5706,plain,
    ( spl225_274
  <=> ! [X4: name,X0: pi,X3: pi,X2: name,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3))) )
        | ( X2 = X4 )
        | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_274])]) ).

thf(f1733,plain,
    ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3))) )
      | ( X2 = X4 )
      | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1094]) ).

thf(f1094,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3))) )
      | ( X2 = X4 )
      | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(flattening,[],[f1093]) ).

thf(f1093,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3))) )
      | ( X2 = X4 )
      | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(ennf_transformation,[],[f678]) ).

thf(f678,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
     => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
       => ( ( X2 != X4 )
         => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3))) ) ) ) ),
    inference(fool_elimination,[],[f677]) ).

thf(f677,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3))
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1)
       => ( ( X2 != X4 )
         => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X4),X3))) ) ) ),
    inference(rectify,[],[f196]) ).

thf(f196,axiom,
    ! [X19: pi,X0: late_subject,X2: name,X31: pi,X22: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X31))
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X22),X0)
       => ( ( X2 != X22 )
         => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X31))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Late__Semantics_OResB) ).

thf(f5672,plain,
    spl225_273,
    inference(avatar_split_clause,[],[f1794,f5670]) ).

thf(f5670,plain,
    ( spl225_273
  <=> ! [X5: pi,X4: name,X2: pi,X0: name,X6: late_subject > name > pi > $o,X3: late_subject,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
        | ( vAPP(name,late_subject,late_InputS,X0) = X3 )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
        | ( X1 = X4 )
        | ( X0 = X4 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_273])]) ).

thf(f1794,plain,
    ! [X2: pi,X3: late_subject,X0: name,X1: name,X6: late_subject > name > pi > $o,X4: name,X5: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),vAPP(late_subject,sTfun(name,sTfun(pi,$o)),X6,X3),X4),X5) )
      | ( vAPP(name,late_subject,late_InputS,X0) = X3 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X2) )
      | ( X1 = X4 )
      | ( X0 = X4 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(cnf_transformation,[],[f1141]) ).

thf(f5668,plain,
    spl225_272,
    inference(avatar_split_clause,[],[f1715,f5666]) ).

thf(f5666,plain,
    ( spl225_272
  <=> ! [X0: name,X3: pi,X2: name,X1: pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X3)))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3))))),rel) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_272])]) ).

thf(f1715,plain,
    ! [X2: name,X3: pi,X0: name,X1: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X3)))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3))))),rel) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1076]) ).

thf(f1076,plain,
    ! [X0: name,X1: pi,X2: name,X3: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X3)))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3))))),rel) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f656]) ).

thf(f656,plain,
    ! [X0: name,X1: pi,X2: name,X3: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X3)))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3))))),rel) ) ),
    inference(fool_elimination,[],[f655]) ).

thf(f655,plain,
    ! [X0: name,X1: pi,X2: name,X3: pi] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X3)))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3))))),rel) ),
    inference(rectify,[],[f285]) ).

thf(f285,axiom,
    ! [X22: name,X88: pi,X68: name,X89: pi] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X88)
     => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X68),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X88),X89)))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X68),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X88),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X89))))),rel) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_ScopeExt) ).

thf(f5644,plain,
    spl225_271,
    inference(avatar_split_clause,[],[f1739,f5642]) ).

thf(f5642,plain,
    ( spl225_271
  <=> ! [X4: pi,X0: pi,X3: pi,X2: name,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_271])]) ).

thf(f1739,plain,
    ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1106]) ).

thf(f1106,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(flattening,[],[f1105]) ).

thf(f1105,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(ennf_transformation,[],[f690]) ).

thf(f690,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4))) ) ) ),
    inference(fool_elimination,[],[f689]) ).

thf(f689,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4)
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X4)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4))) ) ),
    inference(rectify,[],[f303]) ).

thf(f303,axiom,
    ! [X19: pi,X0: late_subject,X2: name,X31: pi,X93: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X31))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X93)
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X31),X93))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_Late__Semantics_OPar1B) ).

thf(f5640,plain,
    spl225_270,
    inference(avatar_split_clause,[],[f1738,f5638]) ).

thf(f5638,plain,
    ( spl225_270
  <=> ! [X4: pi,X0: pi,X3: pi,X2: name,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_270])]) ).

thf(f1738,plain,
    ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1104]) ).

thf(f1104,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(flattening,[],[f1103]) ).

thf(f1103,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(ennf_transformation,[],[f688]) ).

thf(f688,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))) ) ) ),
    inference(fool_elimination,[],[f687]) ).

thf(f687,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X4)
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3))) ) ),
    inference(rectify,[],[f304]) ).

thf(f304,axiom,
    ! [X93: pi,X0: late_subject,X2: name,X94: pi,X19: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X94))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X19)
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X94))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_Late__Semantics_OPar2B) ).

thf(f5636,plain,
    spl225_269,
    inference(avatar_split_clause,[],[f1575,f5634]) ).

thf(f5634,plain,
    ( spl225_269
  <=> ! [X2: list_P227219501e_name,X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK92,X0)),nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_269])]) ).

thf(f1575,plain,
    ! [X2: list_P227219501e_name,X0: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,X1: produc367475239e_name > produc367475239e_name > $o] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true = vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK89,X0)),vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK91,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,$o)),sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK92,X0)),nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1244]) ).

thf(f5626,plain,
    ( spl225_268
    | ~ spl225_53
    | ~ spl225_127 ),
    inference(avatar_split_clause,[],[f3367,f3312,f2534,f5624]) ).

thf(f2534,plain,
    ( spl225_53
  <=> ! [X0: name,X1: name] :
        ( ( X0 = X1 )
        | ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_InputS,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_53])]) ).

thf(f3312,plain,
    ( spl225_127
  <=> ! [X0: name] : ( vAPP(name,late_subject,late_InputS,X0) = vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_127])]) ).

thf(f3367,plain,
    ( ! [X0: name,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_InputS,X1) )
        | ( vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0)) = X1 ) )
    | ~ spl225_53
    | ~ spl225_127 ),
    inference(superposition,[],[f2535,f3313]) ).

thf(f3313,plain,
    ( ! [X0: name] : ( vAPP(name,late_subject,late_InputS,X0) = vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0))) )
    | ~ spl225_127 ),
    inference(avatar_component_clause,[],[f3312]) ).

thf(f2535,plain,
    ( ! [X0: name,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_InputS,X1) )
        | ( X0 = X1 ) )
    | ~ spl225_53 ),
    inference(avatar_component_clause,[],[f2534]) ).

thf(f5622,plain,
    spl225_267,
    inference(avatar_split_clause,[],[f1740,f5620]) ).

thf(f5620,plain,
    ( spl225_267
  <=> ! [X2: late_freeRes,X4: pi > $o,X0: name,X3: pi,X1: pi] :
        ( ( $true = vAPP(pi,$o,X4,X3) )
        | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_267])]) ).

thf(f1740,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi,X4: pi > $o] :
      ( ( $true = vAPP(pi,$o,X4,X3) )
      | ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1319]) ).

thf(f1319,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi,X4: pi > $o] :
      ( ( $true = vAPP(pi,$o,X4,X3) )
      | ( ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
        & ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK199])],[f1108,f1318]) ).

thf(f1318,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X4: pi > $o] :
      ( ? [X5: pi] :
          ( ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X5)) )
          & ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X5)) ) )
     => ( ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
        & ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1108,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi,X4: pi > $o] :
      ( ( $true = vAPP(pi,$o,X4,X3) )
      | ? [X5: pi] :
          ( ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X5)) )
          & ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X5)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(flattening,[],[f1107]) ).

thf(f1107,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi,X4: pi > $o] :
      ( ( $true = vAPP(pi,$o,X4,X3) )
      | ? [X5: pi] :
          ( ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X5)) )
          & ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
          & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X5)) ) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(ennf_transformation,[],[f692]) ).

thf(f692,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi,X4: pi > $o] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
     => ( ! [X5: pi] :
            ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X5)) )
           => ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
             => ( $true = vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X5)) ) ) )
       => ( $true = vAPP(pi,$o,X4,X3) ) ) ),
    inference(fool_elimination,[],[f691]) ).

thf(f691,plain,
    ! [X0: name,X1: pi,X2: late_freeRes,X3: pi,X4: pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3))
     => ( ! [X5: pi] :
            ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X1),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X5))
           => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2)
             => vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X5)) ) )
       => vAPP(pi,$o,X4,X3) ) ),
    inference(rectify,[],[f198]) ).

thf(f198,axiom,
    ! [X2: name,X19: pi,X30: late_freeRes,X45: pi,X46: pi > $o] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X45))
     => ( ! [X47: pi] :
            ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X47))
           => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X30)
             => vAPP(pi,$o,X46,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X47)) ) )
       => vAPP(pi,$o,X46,X45) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_resCasesF) ).

thf(f5616,plain,
    spl225_266,
    inference(avatar_split_clause,[],[f1699,f5614]) ).

thf(f5614,plain,
    ( spl225_266
  <=> ! [X0: name,X3: name,X2: name > noption_pi,X1: name] :
        ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
        | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
        | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_266])]) ).

thf(f1699,plain,
    ! [X2: name > noption_pi,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1065]) ).

thf(f1065,plain,
    ! [X0: name,X1: name,X2: name > noption_pi,X3: name] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1064]) ).

thf(f1064,plain,
    ! [X0: name,X1: name,X2: name > noption_pi,X3: name] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f642]) ).

thf(f642,plain,
    ! [X0: name,X1: name,X2: name > noption_pi,X3: name] :
      ( ( X0 != X1 )
     => ( ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2) = $true )
       => ( ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) = $true )
         => ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ) ),
    inference(fool_elimination,[],[f641]) ).

thf(f641,plain,
    ! [X0: name,X1: name,X2: name > noption_pi,X3: name] :
      ( ( X0 != X1 )
     => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2)
       => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2)
         => vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ),
    inference(rectify,[],[f115]) ).

thf(f115,axiom,
    ! [X32: name,X0: name,X2: name > noption_pi,X1: name] :
      ( ( X0 != X32 )
     => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2)
       => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X32),X2)
         => vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X32),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_fresh__aux) ).

thf(f5604,plain,
    spl225_265,
    inference(avatar_split_clause,[],[f1878,f5602]) ).

thf(f5602,plain,
    ( spl225_265
  <=> ! [X2: name,X0: name,X1: name] :
        ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X1) )
        | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_265])]) ).

thf(f1878,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X1) )
      | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ),
    inference(definition_unfolding,[],[f1639,f1361]) ).

thf(f1639,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) )
      | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1039]) ).

thf(f1039,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) )
      | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ),
    inference(ennf_transformation,[],[f584]) ).

thf(f584,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( $true = vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) )
     => ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) ) ),
    inference(fool_elimination,[],[f583]) ).

thf(f583,plain,
    ! [X0: name,X1: name,X2: name] :
      ( vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2))
     => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X1) ),
    inference(rectify,[],[f181]) ).

thf(f181,axiom,
    ! [X0: name,X2: name,X22: name] :
      ( vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X22))
     => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_fresh__prodD_I1_J) ).

thf(f5600,plain,
    spl225_264,
    inference(avatar_split_clause,[],[f1877,f5598]) ).

thf(f5598,plain,
    ( spl225_264
  <=> ! [X2: name,X0: name,X1: name] :
        ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
        | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_264])]) ).

thf(f1877,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),X0),X2) )
      | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ),
    inference(definition_unfolding,[],[f1638,f1361]) ).

thf(f1638,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) = $true )
      | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1038]) ).

thf(f1038,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) = $true )
      | ( $true != vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) ) ),
    inference(ennf_transformation,[],[f582]) ).

thf(f582,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( $true = vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)) )
     => ( vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) = $true ) ),
    inference(fool_elimination,[],[f581]) ).

thf(f581,plain,
    ! [X0: name,X1: name,X2: name] :
      ( vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2))
     => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X2) ),
    inference(rectify,[],[f179]) ).

thf(f179,axiom,
    ! [X0: name,X2: name,X22: name] :
      ( vAPP(produc367475239e_name,$o,vAPP(name,sTfun(produc367475239e_name,$o),fresh_441084397e_name,X0),vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X22))
     => vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X0),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_fresh__prodD_I2_J) ).

thf(f5569,plain,
    ( spl225_263
    | ~ spl225_63 ),
    inference(avatar_split_clause,[],[f2603,f2588,f5567]) ).

thf(f5567,plain,
    ( spl225_263
  <=> ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != X0 )
        | ( vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)) = X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_263])]) ).

thf(f2603,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != X0 )
        | ( vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)) = X0 )
        | ( X0 = X1 ) )
    | ~ spl225_63 ),
    inference(equality_proxy_clausification,[],[f2602]) ).

thf(f2602,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != X0 )
        | ( vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)) = X0 )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) ) )
    | ~ spl225_63 ),
    inference(equality_proxy_clausification,[],[f2601]) ).

thf(f2601,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name != X0 )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) ) )
    | ~ spl225_63 ),
    inference(equality_proxy_clausification,[],[f2598]) ).

thf(f2598,plain,
    ( ! [X0: list_P227219501e_name,X1: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),nil_Pr743626285e_name) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),X1) ) )
    | ~ spl225_63 ),
    inference(primitive_instantiation,[],[f2589]) ).

thf(f5563,plain,
    spl225_262,
    inference(avatar_split_clause,[],[f1606,f5561]) ).

thf(f5561,plain,
    ( spl225_262
  <=> ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_262])]) ).

thf(f1606,plain,
    ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK155,X0)) ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f5559,plain,
    spl225_261,
    inference(avatar_split_clause,[],[f1605,f5557]) ).

thf(f5557,plain,
    ( spl225_261
  <=> ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_261])]) ).

thf(f1605,plain,
    ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK154,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK152,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK153,X0))) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK156,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK158,X0)) ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f5555,plain,
    spl225_260,
    inference(avatar_split_clause,[],[f1603,f5553]) ).

thf(f5553,plain,
    ( spl225_260
  <=> ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_260])]) ).

thf(f1603,plain,
    ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),late_subject,sK148,X0)) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f5551,plain,
    spl225_259,
    inference(avatar_split_clause,[],[f1602,f5549]) ).

thf(f5549,plain,
    ( spl225_259
  <=> ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
        | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_259])]) ).

thf(f1602,plain,
    ! [X2: late_residual,X0: pi > late_residual > $o,X1: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),X0,vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK147,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(pi,sTfun(late_residual,$o)),late_freeRes,sK145,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK146,X0))) )
      | ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(sTfun(pi,sTfun(late_residual,$o)),name,sK149,X0)),vAPP(sTfun(pi,sTfun(late_residual,$o)),pi,sK151,X0)) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f5547,plain,
    spl225_258,
    inference(avatar_split_clause,[],[f1600,f5545]) ).

thf(f5545,plain,
    ( spl225_258
  <=> ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_258])]) ).

thf(f1600,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK140,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK138,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK139,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK142,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK141,X0)) ) ),
    inference(cnf_transformation,[],[f1279]) ).

thf(f5543,plain,
    spl225_257,
    inference(avatar_split_clause,[],[f1597,f5541]) ).

thf(f5541,plain,
    ( spl225_257
  <=> ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_257])]) ).

thf(f1597,plain,
    ! [X2: late_residual,X0: name > late_residual > $o,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),X0,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK133,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(name,sTfun(late_residual,$o)),late_freeRes,sK131,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),pi,sK132,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(name,sTfun(late_residual,$o)),name,sK135,X0)),vAPP(sTfun(name,sTfun(late_residual,$o)),late_subject,sK134,X0)) ) ),
    inference(cnf_transformation,[],[f1275]) ).

thf(f5539,plain,
    spl225_256,
    inference(avatar_split_clause,[],[f1594,f5537]) ).

thf(f5537,plain,
    ( spl225_256
  <=> ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_256])]) ).

thf(f1594,plain,
    ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK127,X0)) ) ),
    inference(cnf_transformation,[],[f1271]) ).

thf(f5535,plain,
    spl225_255,
    inference(avatar_split_clause,[],[f1593,f5533]) ).

thf(f5533,plain,
    ( spl225_255
  <=> ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_255])]) ).

thf(f1593,plain,
    ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK126,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK124,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK125,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK128,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK130,X0)) ) ),
    inference(cnf_transformation,[],[f1271]) ).

thf(f5531,plain,
    spl225_254,
    inference(avatar_split_clause,[],[f1591,f5529]) ).

thf(f5529,plain,
    ( spl225_254
  <=> ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_254])]) ).

thf(f1591,plain,
    ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK120,X0)) ) ),
    inference(cnf_transformation,[],[f1267]) ).

thf(f5523,plain,
    spl225_253,
    inference(avatar_split_clause,[],[f1590,f5521]) ).

thf(f5521,plain,
    ( spl225_253
  <=> ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_253])]) ).

thf(f1590,plain,
    ! [X2: late_residual,X0: late_subject > late_residual > $o,X1: late_subject] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_subject,sTfun(late_residual,$o),X0,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK119,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_freeRes,sK117,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),pi,sK118,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_subject,sTfun(late_residual,$o)),name,sK121,X0)),vAPP(sTfun(late_subject,sTfun(late_residual,$o)),late_subject,sK123,X0)) ) ),
    inference(cnf_transformation,[],[f1267]) ).

thf(f5519,plain,
    spl225_252,
    inference(avatar_split_clause,[],[f1588,f5517]) ).

thf(f5517,plain,
    ( spl225_252
  <=> ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_252])]) ).

thf(f1588,plain,
    ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK113,X0)) ) ),
    inference(cnf_transformation,[],[f1263]) ).

thf(f5515,plain,
    spl225_251,
    inference(avatar_split_clause,[],[f1587,f5513]) ).

thf(f5513,plain,
    ( spl225_251
  <=> ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_251])]) ).

thf(f1587,plain,
    ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK112,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK110,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK111,X0))) )
      | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK114,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK116,X0)) ) ),
    inference(cnf_transformation,[],[f1263]) ).

thf(f5511,plain,
    spl225_250,
    inference(avatar_split_clause,[],[f1585,f5509]) ).

thf(f5509,plain,
    ( spl225_250
  <=> ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
        | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_250])]) ).

thf(f1585,plain,
    ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
      | ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_subject,sK106,X0)) ) ),
    inference(cnf_transformation,[],[f1259]) ).

thf(f5507,plain,
    spl225_249,
    inference(avatar_split_clause,[],[f1584,f5505]) ).

thf(f5505,plain,
    ( spl225_249
  <=> ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
        | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
        | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_249])]) ).

thf(f1584,plain,
    ! [X2: late_residual,X0: late_freeRes > late_residual > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,X1),X2) )
      | ( $true != vAPP(late_residual,$o,vAPP(late_freeRes,sTfun(late_residual,$o),X0,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK105,X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK103,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),pi,sK104,X0))) )
      | ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),name,sK107,X0)),vAPP(sTfun(late_freeRes,sTfun(late_residual,$o)),late_freeRes,sK109,X0)) ) ),
    inference(cnf_transformation,[],[f1259]) ).

thf(f5493,plain,
    spl225_248,
    inference(avatar_split_clause,[],[f1742,f5491]) ).

thf(f1742,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi,X4: pi > $o] :
      ( ( $true = vAPP(pi,$o,X4,X3) )
      | ( $true != vAPP(pi,$o,X4,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(pi,sTfun(name,pi),vAPP(late_freeRes,sTfun(pi,sTfun(name,pi)),vAPP(sTfun(pi,$o),sTfun(late_freeRes,sTfun(pi,sTfun(name,pi))),sK199,X4),X2),X1),X0))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1319]) ).

thf(f5489,plain,
    spl225_247,
    inference(avatar_split_clause,[],[f1381,f5487]) ).

thf(f5487,plain,
    ( spl225_247
  <=> ! [X0: produc890461031e_name] :
        ( ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK20,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK21,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK22,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK23,X0))) = X0 )
        | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(produc890461031e_name,list_P227219501e_name,sK24,X0)),nil_Pr743626285e_name) = X0 )
        | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK25,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_247])]) ).

thf(f1381,plain,
    ! [X0: produc890461031e_name] :
      ( ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK20,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK21,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK22,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK23,X0))) = X0 )
      | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(produc890461031e_name,list_P227219501e_name,sK24,X0)),nil_Pr743626285e_name) = X0 )
      | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK25,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1174]) ).

thf(f1174,plain,
    ! [X0: produc890461031e_name] :
      ( ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK20,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK21,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK22,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK23,X0))) = X0 )
      | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(produc890461031e_name,list_P227219501e_name,sK24,X0)),nil_Pr743626285e_name) = X0 )
      | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK25,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25])],[f1170,f1173,f1172,f1171]) ).

thf(f1171,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) = X0 )
     => ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK20,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK21,X0))),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK22,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK23,X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1172,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X5: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,X5),nil_Pr743626285e_name) = X0 )
     => ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(produc890461031e_name,list_P227219501e_name,sK24,X0)),nil_Pr743626285e_name) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1173,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X6: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X6) = X0 )
     => ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK25,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1170,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) = X0 )
      | ? [X5: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,X5),nil_Pr743626285e_name) = X0 )
      | ? [X6: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X6) = X0 ) ),
    inference(rectify,[],[f924]) ).

thf(f924,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) = X0 )
      | ? [X2: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,X2),nil_Pr743626285e_name) = X0 )
      | ? [X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X1) = X0 ) ),
    inference(flattening,[],[f923]) ).

thf(f923,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) = X0 )
      | ? [X2: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,X2),nil_Pr743626285e_name) = X0 )
      | ? [X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X1) = X0 ) ),
    inference(ennf_transformation,[],[f781]) ).

thf(f781,plain,
    ! [X0: produc890461031e_name] :
      ( ! [X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X1) != X0 )
     => ( ! [X2: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,X2),nil_Pr743626285e_name) != X0 )
       => ~ ! [X3: produc367475239e_name,X4: list_P227219501e_name,X5: produc367475239e_name,X6: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),X6)) != X0 ) ) ),
    inference(rectify,[],[f209]) ).

thf(f209,axiom,
    ! [X2: produc890461031e_name] :
      ( ! [X64: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X64) != X2 )
     => ( ! [X65: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,X65),nil_Pr743626285e_name) != X2 )
       => ~ ! [X63: produc367475239e_name,X65: list_P227219501e_name,X50: produc367475239e_name,X64: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X64)) != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_shuffles_Ocases) ).

thf(f5379,plain,
    spl225_246,
    inference(avatar_split_clause,[],[f1713,f5377]) ).

thf(f5377,plain,
    ( spl225_246
  <=> ! [X0: name,X3: name,X2: name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X3),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_246])]) ).

thf(f1713,plain,
    ! [X2: name,X3: name,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X3),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1073]) ).

thf(f1073,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X3),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f652]) ).

thf(f652,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X3),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) ) ),
    inference(fool_elimination,[],[f651]) ).

thf(f651,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X3),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) ) ),
    inference(rectify,[],[f276]) ).

thf(f276,axiom,
    ! [X32: name,X19: pi,X0: name,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X32),X19)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X2),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X32),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X32)),nil_Pr743626285e_name)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_alphaInput) ).

thf(f5375,plain,
    spl225_245,
    inference(avatar_split_clause,[],[f1712,f5373]) ).

thf(f5373,plain,
    ( spl225_245
  <=> ! [X0: name,X3: name,X2: late_subject,X1: pi] :
        ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X1) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_245])]) ).

thf(f1712,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: pi] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X1) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1072]) ).

thf(f1072,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name] :
      ( ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X1) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f650]) ).

thf(f650,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X1) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) ) ),
    inference(fool_elimination,[],[f649]) ).

thf(f649,plain,
    ! [X0: name,X1: pi,X2: late_subject,X3: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X1) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X3),X0)),nil_Pr743626285e_name)),X1)) ) ),
    inference(rectify,[],[f252]) ).

thf(f252,axiom,
    ! [X66: name,X19: pi,X0: late_subject,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X66),X19)
     => ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X19) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X66),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X66)),nil_Pr743626285e_name)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_alphaBoundResidual) ).

thf(f5371,plain,
    spl225_244,
    inference(avatar_split_clause,[],[f1711,f5369]) ).

thf(f5369,plain,
    ( spl225_244
  <=> ! [X0: name,X3: name,X2: name,X1: pi] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1)),X0),X3) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_244])]) ).

thf(f1711,plain,
    ! [X2: name,X3: name,X0: name,X1: pi] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1)),X0),X3) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1071]) ).

thf(f1071,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1)),X0),X3) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f648]) ).

thf(f648,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1)),X0),X3) ) ),
    inference(fool_elimination,[],[f647]) ).

thf(f647,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1)),X0),X3) ) ),
    inference(rectify,[],[f328]) ).

thf(f328,axiom,
    ! [X32: name,X19: pi,X0: name,X1: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X32),X19)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X32),X0)),nil_Pr743626285e_name)),X19)),X32),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_renaming) ).

thf(f5367,plain,
    spl225_243,
    inference(avatar_split_clause,[],[f1437,f5365]) ).

thf(f5365,plain,
    ( spl225_243
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK73,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)))) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_243])]) ).

thf(f1437,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK73,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)))) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1229]) ).

thf(f1229,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK73,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)))) )
        & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74,sK75,sK76])],[f1226,f1228,f1227]) ).

thf(f1227,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ? [X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4))) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X4) ) )
     => ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK73,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)))) )
        & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1228,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ? [X5: produc367475239e_name] : ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),nil_Pr743626285e_name)) )
     => ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1226,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ? [X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4))) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X4) ) )
      | ? [X5: produc367475239e_name] : ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X5),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(rectify,[],[f948]) ).

thf(f948,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ? [X3: produc367475239e_name,X4: produc367475239e_name,X5: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5))) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X5) ) )
      | ? [X2: produc367475239e_name] : ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(flattening,[],[f947]) ).

thf(f947,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ? [X3: produc367475239e_name,X4: produc367475239e_name,X5: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5))) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X5) ) )
      | ? [X2: produc367475239e_name] : ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(ennf_transformation,[],[f430]) ).

thf(f430,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
     => ( ! [X2: produc367475239e_name] : ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),nil_Pr743626285e_name)) )
       => ( ! [X3: produc367475239e_name,X4: produc367475239e_name,X5: list_P227219501e_name] :
              ( ( $true = vAPP(list_P227219501e_name,$o,X0,X5) )
             => ( ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)) )
               => ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5))) ) ) )
         => ( $true = vAPP(list_P227219501e_name,$o,X0,X1) ) ) ) ),
    inference(fool_elimination,[],[f429]) ).

thf(f429,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name)
     => ( ! [X2: produc367475239e_name] : vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),nil_Pr743626285e_name))
       => ( ! [X3: produc367475239e_name,X4: produc367475239e_name,X5: list_P227219501e_name] :
              ( vAPP(list_P227219501e_name,$o,X0,X5)
             => ( vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5))
               => vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5))) ) )
         => vAPP(list_P227219501e_name,$o,X0,X1) ) ) ),
    inference(rectify,[],[f270]) ).

thf(f270,axiom,
    ! [X19: list_P227219501e_name > $o,X43: list_P227219501e_name] :
      ( vAPP(list_P227219501e_name,$o,X19,nil_Pr743626285e_name)
     => ( ! [X63: produc367475239e_name] : vAPP(list_P227219501e_name,$o,X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),nil_Pr743626285e_name))
       => ( ! [X63: produc367475239e_name,X50: produc367475239e_name,X86: list_P227219501e_name] :
              ( vAPP(list_P227219501e_name,$o,X19,X86)
             => ( vAPP(list_P227219501e_name,$o,X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X86))
               => vAPP(list_P227219501e_name,$o,X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X86))) ) )
         => vAPP(list_P227219501e_name,$o,X19,X43) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_induct__list012) ).

thf(f5351,plain,
    spl225_242,
    inference(avatar_split_clause,[],[f1721,f5349]) ).

thf(f5349,plain,
    ( spl225_242
  <=> ! [X0: pi,X3: pi,X2: name,X1: name] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) )
        | ( X1 = X2 )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_242])]) ).

thf(f1721,plain,
    ! [X2: name,X3: pi,X0: pi,X1: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) )
      | ( X1 = X2 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ),
    inference(cnf_transformation,[],[f1086]) ).

thf(f1086,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) )
      | ( X1 = X2 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ),
    inference(flattening,[],[f1085]) ).

thf(f1085,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) )
      | ( X1 = X2 )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) ) ),
    inference(ennf_transformation,[],[f668]) ).

thf(f668,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3)) )
     => ( ( X1 != X2 )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f667]) ).

thf(f667,plain,
    ! [X0: pi,X1: name,X2: name,X3: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)),X3))
     => ( ( X1 != X2 )
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X0)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X2),X3)) ) ),
    inference(rectify,[],[f211]) ).

thf(f211,axiom,
    ! [X19: pi,X0: name,X1: name,X31: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1)),X31))
     => ( ( X0 != X1 )
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X0)),X1),X31)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Open) ).

thf(f5343,plain,
    spl225_241,
    inference(avatar_split_clause,[],[f1574,f5341]) ).

thf(f5341,plain,
    ( spl225_241
  <=> ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK85,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_241])]) ).

thf(f1574,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK85,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) ) ),
    inference(cnf_transformation,[],[f1240]) ).

thf(f1240,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK85,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0)) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86,sK87,sK88])],[f1237,f1239,f1238]) ).

thf(f1238,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),X5) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X5),X4) ) )
     => ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),produc367475239e_name,sK85,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0))),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)) )
        & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1239,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o] :
      ( ? [X6: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X6) )
     => ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1237,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X3: produc367475239e_name,X4: list_P227219501e_name,X5: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)),X5) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X5),X4) ) )
      | ? [X6: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X6) ) ),
    inference(rectify,[],[f966]) ).

thf(f966,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X4: produc367475239e_name,X5: list_P227219501e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)),X6) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),X5) ) )
      | ? [X3: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3) ) ),
    inference(flattening,[],[f965]) ).

thf(f965,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ? [X4: produc367475239e_name,X5: list_P227219501e_name,X6: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)),X6) )
          & ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),X5) ) )
      | ? [X3: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3) ) ),
    inference(ennf_transformation,[],[f500]) ).

thf(f500,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ! [X3: list_P227219501e_name] : ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3) )
     => ( ! [X4: produc367475239e_name,X5: list_P227219501e_name,X6: list_P227219501e_name] :
            ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),X5) )
           => ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)),X6) ) )
       => ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f499]) ).

thf(f499,plain,
    ! [X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name,X2: list_P227219501e_name] :
      ( ! [X3: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),X3)
     => ( ! [X4: produc367475239e_name,X5: list_P227219501e_name,X6: list_P227219501e_name] :
            ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X6),X5)
           => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),X5)),X6) )
       => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f269]) ).

thf(f269,axiom,
    ! [X19: list_P227219501e_name > list_P227219501e_name > $o,X84: list_P227219501e_name,X85: list_P227219501e_name] :
      ( ! [X73: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,nil_Pr743626285e_name),X73)
     => ( ! [X63: produc367475239e_name,X65: list_P227219501e_name,X64: list_P227219501e_name] :
            ( vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X64),X65)
           => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),X64) )
       => vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X19,X84),X85) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_splice_Oinduct) ).

thf(f5335,plain,
    spl225_240,
    inference(avatar_split_clause,[],[f1644,f5333]) ).

thf(f5333,plain,
    ( spl225_240
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_240])]) ).

thf(f1644,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f5331,plain,
    spl225_239,
    inference(avatar_split_clause,[],[f1640,f5329]) ).

thf(f5329,plain,
    ( spl225_239
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_239])]) ).

thf(f1640,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK167,X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f5089,plain,
    spl225_238,
    inference(avatar_split_clause,[],[f1882,f5087]) ).

thf(f1882,plain,
    ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ),
    inference(definition_unfolding,[],[f1661,f1358,f1358]) ).

thf(f1661,plain,
    ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ),
    inference(cnf_transformation,[],[f891]) ).

thf(f891,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: name,X3: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ),
    inference(rectify,[],[f282]) ).

thf(f282,axiom,
    ! [X5: list_P227219501e_name,X44: name,X3: name,X4: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X44),X3),X4)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X44)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_pi_Operm_I4_J) ).

thf(f5085,plain,
    spl225_237,
    inference(avatar_split_clause,[],[f1881,f5083]) ).

thf(f5083,plain,
    ( spl225_237
  <=> ! [X0: list_P227219501e_name,X3: name,X2: name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_237])]) ).

thf(f1881,plain,
    ! [X2: name,X3: name,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X3)) ),
    inference(definition_unfolding,[],[f1660,f1358,f1358]) ).

thf(f1660,plain,
    ! [X2: name,X3: name,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3)) ),
    inference(cnf_transformation,[],[f890]) ).

thf(f890,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: name,X3: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3)) ),
    inference(rectify,[],[f326]) ).

thf(f326,axiom,
    ! [X71: list_P227219501e_name,X19: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X71),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X71),X19)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X71),X0)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X71),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_eqvt__subs) ).

thf(f5081,plain,
    spl225_236,
    inference(avatar_split_clause,[],[f1880,f5079]) ).

thf(f1880,plain,
    ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ),
    inference(definition_unfolding,[],[f1659,f1358]) ).

thf(f1659,plain,
    ! [X2: name,X3: pi,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ),
    inference(cnf_transformation,[],[f889]) ).

thf(f889,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: name,X3: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3)) ),
    inference(rectify,[],[f194]) ).

thf(f194,axiom,
    ! [X5: list_P227219501e_name,X44: late_subject,X3: name,X4: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X5),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X44),X3),X4)) = vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X44)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_residual_Operm_I1_J) ).

thf(f5077,plain,
    spl225_235,
    inference(avatar_split_clause,[],[f1716,f5075]) ).

thf(f5075,plain,
    ( spl225_235
  <=> ! [X0: pi,X3: name,X2: pi,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))) )
        | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_235])]) ).

thf(f1716,plain,
    ! [X2: pi,X3: name,X0: pi,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))) )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1078]) ).

thf(f1078,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))) )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(flattening,[],[f1077]) ).

thf(f1077,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))) )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(ennf_transformation,[],[f658]) ).

thf(f658,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
     => ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
       => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))) ) ) ),
    inference(fool_elimination,[],[f657]) ).

thf(f657,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2))
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1)
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))) ) ),
    inference(rectify,[],[f200]) ).

thf(f200,axiom,
    ! [X19: pi,X30: late_freeRes,X31: pi,X22: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31))
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X22),X30)
       => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X19)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X31))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_ResF) ).

thf(f5073,plain,
    spl225_234,
    inference(avatar_split_clause,[],[f1434,f5071]) ).

thf(f5071,plain,
    ( spl225_234
  <=> ! [X0: late_residual > $o,X1: late_residual] :
        ( ( $true = vAPP(late_residual,$o,X0,X1) )
        | ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_residual,$o),late_freeRes,sK68,X0)),vAPP(sTfun(late_residual,$o),pi,sK69,X0))) )
        | ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_residual,$o),late_subject,sK70,X0)),vAPP(sTfun(late_residual,$o),name,sK71,X0)),vAPP(sTfun(late_residual,$o),pi,sK72,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_234])]) ).

thf(f1434,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,X0,X1) )
      | ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_residual,$o),late_freeRes,sK68,X0)),vAPP(sTfun(late_residual,$o),pi,sK69,X0))) )
      | ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_residual,$o),late_subject,sK70,X0)),vAPP(sTfun(late_residual,$o),name,sK71,X0)),vAPP(sTfun(late_residual,$o),pi,sK72,X0))) ) ),
    inference(cnf_transformation,[],[f1225]) ).

thf(f1225,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,X0,X1) )
      | ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_residual,$o),late_freeRes,sK68,X0)),vAPP(sTfun(late_residual,$o),pi,sK69,X0))) )
      | ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_residual,$o),late_subject,sK70,X0)),vAPP(sTfun(late_residual,$o),name,sK71,X0)),vAPP(sTfun(late_residual,$o),pi,sK72,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69,sK70,sK71,sK72])],[f1222,f1224,f1223]) ).

thf(f1223,plain,
    ! [X0: late_residual > $o] :
      ( ? [X2: late_freeRes,X3: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
     => ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(sTfun(late_residual,$o),late_freeRes,sK68,X0)),vAPP(sTfun(late_residual,$o),pi,sK69,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1224,plain,
    ! [X0: late_residual > $o] :
      ( ? [X4: late_subject,X5: name,X6: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X4),X5),X6)) )
     => ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(sTfun(late_residual,$o),late_subject,sK70,X0)),vAPP(sTfun(late_residual,$o),name,sK71,X0)),vAPP(sTfun(late_residual,$o),pi,sK72,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1222,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,X0,X1) )
      | ? [X2: late_freeRes,X3: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) )
      | ? [X4: late_subject,X5: name,X6: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X4),X5),X6)) ) ),
    inference(rectify,[],[f946]) ).

thf(f946,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,X0,X1) )
      | ? [X5: late_freeRes,X6: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
      | ? [X2: late_subject,X3: name,X4: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(flattening,[],[f945]) ).

thf(f945,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,X0,X1) )
      | ? [X5: late_freeRes,X6: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
      | ? [X2: late_subject,X3: name,X4: pi] : ( $true != vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) ) ),
    inference(ennf_transformation,[],[f428]) ).

thf(f428,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ! [X2: late_subject,X3: name,X4: pi] : ( $true = vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4)) )
     => ( ! [X5: late_freeRes,X6: pi] : ( $true = vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6)) )
       => ( $true = vAPP(late_residual,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f427]) ).

thf(f427,plain,
    ! [X0: late_residual > $o,X1: late_residual] :
      ( ! [X2: late_subject,X3: name,X4: pi] : vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X2),X3),X4))
     => ( ! [X5: late_freeRes,X6: pi] : vAPP(late_residual,$o,X0,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X5),X6))
       => vAPP(late_residual,$o,X0,X1) ) ),
    inference(rectify,[],[f204]) ).

thf(f204,axiom,
    ! [X19: late_residual > $o,X55: late_residual] :
      ( ! [X56: late_subject,X57: name,X58: pi] : vAPP(late_residual,$o,X19,vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X56),X57),X58))
     => ( ! [X59: late_freeRes,X58: pi] : vAPP(late_residual,$o,X19,vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X59),X58))
       => vAPP(late_residual,$o,X19,X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_residual_Oinducts) ).

thf(f5055,plain,
    spl225_233,
    inference(avatar_split_clause,[],[f1658,f5053]) ).

thf(f1658,plain,
    ! [X2: name,X3: name,X0: pi,X1: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),X2),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X3)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) ),
    inference(cnf_transformation,[],[f888]) ).

thf(f888,plain,
    ! [X0: pi,X1: pi,X2: name,X3: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1)),X2),X3) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X2),X3)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3)) ),
    inference(rectify,[],[f319]) ).

thf(f319,axiom,
    ! [X19: pi,X93: pi,X32: name,X99: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),X32),X99) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X32),X99)),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X93),X32),X99)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_simps_I8_J) ).

thf(f5051,plain,
    spl225_232,
    inference(avatar_split_clause,[],[f1634,f5049]) ).

thf(f5049,plain,
    ( spl225_232
  <=> ! [X2: name,X0: name,X1: name > noption_pi] :
        ( ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X2),X1) )
        | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_232])]) ).

thf(f1634,plain,
    ! [X2: name,X0: name,X1: name > noption_pi] :
      ( ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X2),X1) )
      | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1033]) ).

thf(f1033,plain,
    ! [X0: name,X1: name > noption_pi,X2: name] :
      ( ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X2),X1) )
      | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X1) ) ),
    inference(flattening,[],[f1032]) ).

thf(f1032,plain,
    ! [X0: name,X1: name > noption_pi,X2: name] :
      ( ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X2),X1) )
      | ( $true != vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f574]) ).

thf(f574,plain,
    ! [X0: name,X1: name > noption_pi,X2: name] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X1) )
     => ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X2),X1) )
       => ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(fool_elimination,[],[f573]) ).

thf(f573,plain,
    ! [X0: name,X1: name > noption_pi,X2: name] :
      ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X1)
     => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X2),X1)
       => ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f68]) ).

thf(f68,axiom,
    ! [X0: name,X2: name > noption_pi,X1: name] :
      ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2)
     => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X1),X2)
       => ( vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_perm__fresh__fresh) ).

thf(f5021,plain,
    spl225_231,
    inference(avatar_split_clause,[],[f1633,f5019]) ).

thf(f5019,plain,
    ( spl225_231
  <=> ! [X2: pi,X0: name,X1: pi] :
        ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)))),rel) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_231])]) ).

thf(f1633,plain,
    ! [X2: pi,X0: name,X1: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)))),rel) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1031]) ).

thf(f1031,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)))),rel) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f572]) ).

thf(f572,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)))),rel) ) ),
    inference(fool_elimination,[],[f571]) ).

thf(f571,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X2)))),rel) ),
    inference(rectify,[],[f286]) ).

thf(f286,axiom,
    ! [X22: name,X88: pi,X89: pi] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X88)
     => vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X88),X89))),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X88),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X22),X89)))),rel) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_Res) ).

thf(f4977,plain,
    spl225_230,
    inference(avatar_split_clause,[],[f1819,f4975]) ).

thf(f4975,plain,
    ( spl225_230
  <=> ! [X0: name] : ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),vAPP(name,name,sK46,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_230])]) ).

thf(f1819,plain,
    ! [X0: name] : ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),vAPP(name,name,sK46,X0)),X0) ),
    inference(definition_unfolding,[],[f1389,f1361]) ).

thf(f1389,plain,
    ! [X0: name] : ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(name,name,sK46,X0)),X0) ),
    inference(cnf_transformation,[],[f1197]) ).

thf(f1197,plain,
    ! [X0: name] : ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(name,name,sK46,X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f933,f1196]) ).

thf(f1196,plain,
    ! [X0: name] :
      ( ? [X1: name] : ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X0) )
     => ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,vAPP(name,name,sK46,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f933,plain,
    ! [X0: name] :
    ? [X1: name] : ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X0) ),
    inference(ennf_transformation,[],[f788]) ).

thf(f788,plain,
    ! [X0: name] :
      ~ ! [X1: name] : ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X0) ),
    inference(flattening,[],[f384]) ).

thf(f384,plain,
    ! [X0: name] :
      ~ ! [X1: name] : ( $true != vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X0) ),
    inference(fool_elimination,[],[f383]) ).

thf(f383,plain,
    ! [X0: name] :
      ~ ! [X1: name] : ~ vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X1),X0),
    inference(rectify,[],[f85]) ).

thf(f85,axiom,
    ! [X2: name] :
      ~ ! [X18: name] : ~ vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,X18),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_name__exists__fresh) ).

thf(f4973,plain,
    spl225_229,
    inference(avatar_split_clause,[],[f1698,f4971]) ).

thf(f4971,plain,
    ( spl225_229
  <=> ! [X0: name,X3: name,X2: pi,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
        | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
        | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_229])]) ).

thf(f1698,plain,
    ! [X2: pi,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1063]) ).

thf(f1063,plain,
    ! [X0: name,X1: name,X2: pi,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1062]) ).

thf(f1062,plain,
    ! [X0: name,X1: name,X2: pi,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f640]) ).

thf(f640,plain,
    ! [X0: name,X1: name,X2: pi,X3: name] :
      ( ( X0 != X1 )
     => ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2) = $true )
       => ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
         => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ) ),
    inference(fool_elimination,[],[f639]) ).

thf(f639,plain,
    ! [X0: name,X1: name,X2: pi,X3: name] :
      ( ( X0 != X1 )
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2)
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2)
         => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ),
    inference(rectify,[],[f114]) ).

thf(f114,axiom,
    ! [X32: name,X0: name,X2: pi,X1: name] :
      ( ( X0 != X32 )
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2)
       => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X32),X2)
         => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X32),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_fresh__aux) ).

thf(f4969,plain,
    spl225_228,
    inference(avatar_split_clause,[],[f1696,f4967]) ).

thf(f4967,plain,
    ( spl225_228
  <=> ! [X0: name,X3: name,X2: late_subject,X1: name] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
        | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
        | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_228])]) ).

thf(f1696,plain,
    ! [X2: late_subject,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1059]) ).

thf(f1059,plain,
    ! [X0: name,X1: name,X2: late_subject,X3: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1058]) ).

thf(f1058,plain,
    ! [X0: name,X1: name,X2: late_subject,X3: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f636]) ).

thf(f636,plain,
    ! [X0: name,X1: name,X2: late_subject,X3: name] :
      ( ( X0 != X1 )
     => ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2) = $true )
       => ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
         => ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ) ),
    inference(fool_elimination,[],[f635]) ).

thf(f635,plain,
    ! [X0: name,X1: name,X2: late_subject,X3: name] :
      ( ( X0 != X1 )
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2)
       => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2)
         => vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ),
    inference(rectify,[],[f111]) ).

thf(f111,axiom,
    ! [X32: name,X0: name,X2: late_subject,X1: name] :
      ( ( X0 != X32 )
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2)
       => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X32),X2)
         => vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X32),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_fresh__aux) ).

thf(f4965,plain,
    spl225_227,
    inference(avatar_split_clause,[],[f1695,f4963]) ).

thf(f4963,plain,
    ( spl225_227
  <=> ! [X0: name,X3: name,X2: late_freeRes,X1: name] :
        ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
        | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
        | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_227])]) ).

thf(f1695,plain,
    ! [X2: late_freeRes,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1057]) ).

thf(f1057,plain,
    ! [X0: name,X1: name,X2: late_freeRes,X3: name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1056]) ).

thf(f1056,plain,
    ! [X0: name,X1: name,X2: late_freeRes,X3: name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f634]) ).

thf(f634,plain,
    ! [X0: name,X1: name,X2: late_freeRes,X3: name] :
      ( ( X0 != X1 )
     => ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2) = $true )
       => ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
         => ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ) ),
    inference(fool_elimination,[],[f633]) ).

thf(f633,plain,
    ! [X0: name,X1: name,X2: late_freeRes,X3: name] :
      ( ( X0 != X1 )
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2)
       => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2)
         => vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ),
    inference(rectify,[],[f112]) ).

thf(f112,axiom,
    ! [X32: name,X0: name,X2: late_freeRes,X1: name] :
      ( ( X0 != X32 )
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2)
       => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X32),X2)
         => vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X32),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_fresh__aux) ).

thf(f4959,plain,
    spl225_226,
    inference(avatar_split_clause,[],[f1694,f4957]) ).

thf(f4957,plain,
    ( spl225_226
  <=> ! [X0: name,X3: name,X2: pi_Rep,X1: name] :
        ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
        | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
        | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_226])]) ).

thf(f1694,plain,
    ! [X2: pi_Rep,X3: name,X0: name,X1: name] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1055]) ).

thf(f1055,plain,
    ! [X0: name,X1: name,X2: pi_Rep,X3: name] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1054]) ).

thf(f1054,plain,
    ! [X0: name,X1: name,X2: pi_Rep,X3: name] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f632]) ).

thf(f632,plain,
    ! [X0: name,X1: name,X2: pi_Rep,X3: name] :
      ( ( X0 != X1 )
     => ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2) = $true )
       => ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) = $true )
         => ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ) ),
    inference(fool_elimination,[],[f631]) ).

thf(f631,plain,
    ! [X0: name,X1: name,X2: pi_Rep,X3: name] :
      ( ( X0 != X1 )
     => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2)
       => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2)
         => vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X3)),nil_Pr743626285e_name)),X2)) ) ) ),
    inference(rectify,[],[f110]) ).

thf(f110,axiom,
    ! [X32: name,X0: name,X2: pi_Rep,X1: name] :
      ( ( X0 != X32 )
     => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2)
       => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X32),X2)
         => vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X32),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_fresh__aux) ).

thf(f4954,plain,
    spl225_225,
    inference(avatar_split_clause,[],[f1630,f4952]) ).

thf(f4952,plain,
    ( spl225_225
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1)),X2),X0) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_225])]) ).

thf(f1630,plain,
    ! [X2: name,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1)),X2),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1026]) ).

thf(f1026,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1)),X2),X0) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f566]) ).

thf(f566,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1)),X2),X0) ) ),
    inference(fool_elimination,[],[f565]) ).

thf(f565,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1)),X2),X0) ) ),
    inference(rectify,[],[f324]) ).

thf(f324,axiom,
    ! [X1: name,X19: pi,X0: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X19)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X19)),X0),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_Agent_OsubstRes3) ).

thf(f4933,plain,
    spl225_224,
    inference(avatar_split_clause,[],[f1525,f4931]) ).

thf(f1525,plain,
    ! [X2: name,X0: name,X1: pi] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2),X0) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) ),
    inference(cnf_transformation,[],[f875]) ).

thf(f875,plain,
    ! [X0: name,X1: pi,X2: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),X2),X0) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) ),
    inference(rectify,[],[f327]) ).

thf(f327,axiom,
    ! [X0: name,X19: pi,X2: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X19)),X2),X0) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3) ).

thf(f4899,plain,
    spl225_223,
    inference(avatar_split_clause,[],[f1710,f4897]) ).

thf(f4897,plain,
    ( spl225_223
  <=> ! [X0: name,X3: name,X2: name,X1: pi] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)),X0),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_223])]) ).

thf(f1710,plain,
    ! [X2: name,X3: name,X0: name,X1: pi] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)),X0),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1070]) ).

thf(f1070,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)),X0),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f646]) ).

thf(f646,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)),X0),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) ) ),
    inference(fool_elimination,[],[f645]) ).

thf(f645,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)),X0),X3) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X3) ) ),
    inference(rectify,[],[f320]) ).

thf(f320,axiom,
    ! [X1: name,X19: pi,X0: name,X32: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X19)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1)),X1),X32) = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X32) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_substTrans) ).

thf(f4895,plain,
    spl225_222,
    inference(avatar_split_clause,[],[f1650,f4893]) ).

thf(f4893,plain,
    ( spl225_222
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_222])]) ).

thf(f1650,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f4888,plain,
    spl225_221,
    inference(avatar_split_clause,[],[f1649,f4886]) ).

thf(f4886,plain,
    ( spl225_221
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_221])]) ).

thf(f1649,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0)),vAPP(late_residual,pi,vAPP(pi,sTfun(late_residual,pi),vAPP(name,sTfun(pi,sTfun(late_residual,pi)),sK171,X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f4884,plain,
    spl225_220,
    inference(avatar_split_clause,[],[f1647,f4882]) ).

thf(f4882,plain,
    ( spl225_220
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_220])]) ).

thf(f1647,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0)),vAPP(late_residual,late_subject,vAPP(pi,sTfun(late_residual,late_subject),vAPP(name,sTfun(pi,sTfun(late_residual,late_subject)),sK172,X2),X1),X0)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f4880,plain,
    spl225_219,
    inference(avatar_split_clause,[],[f1900,f4877]) ).

thf(f4877,plain,
    ( spl225_219
  <=> ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),z),x) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_219])]) ).

thf(f1900,plain,
    $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),z),x),
    inference(definition_unfolding,[],[f1800,f1361]) ).

thf(f1800,plain,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,z),x) = $true,
    inference(cnf_transformation,[],[f740]) ).

thf(f740,plain,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,z),x) = $true,
    inference(fool_elimination,[],[f739]) ).

thf(f739,plain,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,z),x),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,z),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_cClose1_Ohyps_I13_J) ).

thf(f4875,plain,
    spl225_218,
    inference(avatar_split_clause,[],[f1899,f4872]) ).

thf(f4872,plain,
    ( spl225_218
  <=> ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),y),x) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_218])]) ).

thf(f1899,plain,
    $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vAPP(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o)),vAPP(sTfun(sTfun(name,$o),sTfun(name,$o)),sTfun(sTfun(name,sTfun(name,$o)),sTfun(name,sTfun(name,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(name,$o),sTfun(name,$o)),bCOMB,vNOT)),vEQ(name)),y),x),
    inference(definition_unfolding,[],[f1799,f1361]) ).

thf(f1799,plain,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,y),x) = $true,
    inference(cnf_transformation,[],[f738]) ).

thf(f738,plain,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,y),x) = $true,
    inference(fool_elimination,[],[f737]) ).

thf(f737,plain,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,y),x),
    inference(rectify,[],[f48]) ).

thf(f48,axiom,
    vAPP(name,$o,vAPP(name,sTfun(name,$o),fresh_name_name,y),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_cClose1_Ohyps_I12_J) ).

thf(f4870,plain,
    spl225_217,
    inference(avatar_split_clause,[],[f1384,f4868]) ).

thf(f4868,plain,
    ( spl225_217
  <=> ! [X0: produc1872410278e_name] :
        ( ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK37,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK38,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK39,X0))) = X0 )
        | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK40,X0)),nil_Pr743626285e_name) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_217])]) ).

thf(f1384,plain,
    ! [X0: produc1872410278e_name] :
      ( ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK37,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK38,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK39,X0))) = X0 )
      | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK40,X0)),nil_Pr743626285e_name) = X0 ) ),
    inference(cnf_transformation,[],[f1187]) ).

thf(f1187,plain,
    ! [X0: produc1872410278e_name] :
      ( ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK37,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK38,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK39,X0))) = X0 )
      | ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK40,X0)),nil_Pr743626285e_name) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40])],[f1184,f1186,f1185]) ).

thf(f1185,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X1: produc367475239e_name > produc367475239e_name > $o,X2: produc367475239e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) = X0 )
     => ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK37,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc1872410278e_name,produc367475239e_name,sK38,X0)),vAPP(produc1872410278e_name,list_P227219501e_name,sK39,X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1186,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X4: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X4),nil_Pr743626285e_name) = X0 )
     => ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,vAPP(produc1872410278e_name,sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sK40,X0)),nil_Pr743626285e_name) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1184,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X1: produc367475239e_name > produc367475239e_name > $o,X2: produc367475239e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) = X0 )
      | ? [X4: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X4),nil_Pr743626285e_name) = X0 ) ),
    inference(rectify,[],[f928]) ).

thf(f928,plain,
    ! [X0: produc1872410278e_name] :
      ( ? [X2: produc367475239e_name > produc367475239e_name > $o,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) = X0 )
      | ? [X1: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),nil_Pr743626285e_name) = X0 ) ),
    inference(ennf_transformation,[],[f784]) ).

thf(f784,plain,
    ! [X0: produc1872410278e_name] :
      ( ! [X1: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X1),nil_Pr743626285e_name) != X0 )
     => ~ ! [X2: produc367475239e_name > produc367475239e_name > $o,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) != X0 ) ),
    inference(rectify,[],[f206]) ).

thf(f206,axiom,
    ! [X2: produc1872410278e_name] :
      ( ! [X48: produc367475239e_name > produc367475239e_name > $o] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X48),nil_Pr743626285e_name) != X2 )
     => ~ ! [X48: produc367475239e_name > produc367475239e_name > $o,X63: produc367475239e_name,X64: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc1872410278e_name,vAPP(sTfun(produc367475239e_name,sTfun(produc367475239e_name,$o)),sTfun(list_P227219501e_name,produc1872410278e_name),produc1069608854e_name,X48),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X64)) != X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sorted__wrt_Ocases) ).

thf(f4804,plain,
    spl225_216,
    inference(avatar_split_clause,[],[f1720,f4802]) ).

thf(f4802,plain,
    ( spl225_216
  <=> ! [X0: pi,X3: pi,X2: pi,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_216])]) ).

thf(f1720,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1084]) ).

thf(f1084,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(ennf_transformation,[],[f666]) ).

thf(f666,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
     => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) ) ),
    inference(fool_elimination,[],[f665]) ).

thf(f665,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2))
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) ),
    inference(rectify,[],[f298]) ).

thf(f298,axiom,
    ! [X19: pi,X30: late_freeRes,X31: pi,X93: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31))
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X31),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Par1F) ).

thf(f4800,plain,
    spl225_215,
    inference(avatar_split_clause,[],[f1719,f4798]) ).

thf(f4798,plain,
    ( spl225_215
  <=> ! [X0: pi,X3: pi,X2: pi,X1: late_freeRes] :
        ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X2))) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_215])]) ).

thf(f1719,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X2))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1083]) ).

thf(f1083,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X2))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(ennf_transformation,[],[f664]) ).

thf(f664,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
     => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X2))) ) ),
    inference(fool_elimination,[],[f663]) ).

thf(f663,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2))
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X0)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X2))) ),
    inference(rectify,[],[f297]) ).

thf(f297,axiom,
    ! [X93: pi,X30: late_freeRes,X94: pi,X19: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X93),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X94))
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X93)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X19),X94))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Par2F) ).

thf(f4796,plain,
    spl225_214,
    inference(avatar_split_clause,[],[f1705,f4794]) ).

thf(f4794,plain,
    ( spl225_214
  <=> ! [X0: set_Pr1834926343_pi_pi] :
        ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0)))),X0) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_214])]) ).

thf(f1705,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0)))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ),
    inference(cnf_transformation,[],[f1308]) ).

thf(f1308,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0)))),X0) )
        & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK180,sK181,sK182])],[f1306,f1307]) ).

thf(f1307,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X1: pi,X2: pi,X3: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X1)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)),X0) ) )
     => ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0))),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(set_Pr1834926343_pi_pi,name,sK182,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0)))),X0) )
        & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1306,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X1: pi,X2: pi,X3: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X1)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X2))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)),X0) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ),
    inference(rectify,[],[f1305]) ).

thf(f1305,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ? [X7: pi,X8: pi,X9: name] :
          ( ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X7)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X9),X8))),X0) )
          & ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X7),X8)),X0) ) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ),
    inference(nnf_transformation,[],[f1147]) ).

thf(f4792,plain,
    spl225_213,
    inference(avatar_split_clause,[],[f1629,f4790]) ).

thf(f4790,plain,
    ( spl225_213
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_213])]) ).

thf(f1629,plain,
    ! [X2: name,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1025]) ).

thf(f1025,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f564]) ).

thf(f564,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) ) ),
    inference(fool_elimination,[],[f563]) ).

thf(f563,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1)) ) ),
    inference(rectify,[],[f251]) ).

thf(f251,axiom,
    ! [X32: name,X19: pi,X0: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X32),X19)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X32),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X32)),nil_Pr743626285e_name)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_alphaRes) ).

thf(f4788,plain,
    spl225_212,
    inference(avatar_split_clause,[],[f1436,f4786]) ).

thf(f4786,plain,
    ( spl225_212
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0))) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_212])]) ).

thf(f1436,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK74,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1229]) ).

thf(f4771,plain,
    spl225_211,
    inference(avatar_split_clause,[],[f1693,f4769]) ).

thf(f4769,plain,
    ( spl225_211
  <=> ! [X0: name,X3: pi,X2: name,X1: name] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3)),X1),X2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X1),X2)) )
        | ( X0 = X2 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_211])]) ).

thf(f1693,plain,
    ! [X2: name,X3: pi,X0: name,X1: name] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3)),X1),X2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X1),X2)) )
      | ( X0 = X2 )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1053]) ).

thf(f1053,plain,
    ! [X0: name,X1: name,X2: name,X3: pi] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3)),X1),X2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X1),X2)) )
      | ( X0 = X2 )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f1052]) ).

thf(f1052,plain,
    ! [X0: name,X1: name,X2: name,X3: pi] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3)),X1),X2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X1),X2)) )
      | ( X0 = X2 )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f902]) ).

thf(f902,plain,
    ! [X0: name,X1: name,X2: name,X3: pi] :
      ( ( X0 != X1 )
     => ( ( X0 != X2 )
       => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X3)),X1),X2) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X3),X1),X2)) ) ) ),
    inference(rectify,[],[f318]) ).

thf(f318,axiom,
    ! [X2: name,X32: name,X99: name,X19: pi] :
      ( ( X2 != X32 )
     => ( ( X2 != X99 )
       => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X19)),X32),X99) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X32),X99)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_simps_I9_J) ).

thf(f4767,plain,
    spl225_210,
    inference(avatar_split_clause,[],[f1623,f4765]) ).

thf(f4765,plain,
    ( spl225_210
  <=> ! [X2: name > noption_pi,X0: name,X1: list_P227219501e_name] :
        ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X1),X2)) )
        | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_210])]) ).

thf(f1623,plain,
    ! [X2: name > noption_pi,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X1),X2)) )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1017]) ).

thf(f1017,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name > noption_pi] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X1),X2)) )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(flattening,[],[f1016]) ).

thf(f1016,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name > noption_pi] :
      ( ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X1),X2)) )
      | ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f552]) ).

thf(f552,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name > noption_pi] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) )
     => ( ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2) = $true )
       => ( $true = vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X1),X2)) ) ) ),
    inference(fool_elimination,[],[f551]) ).

thf(f551,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: name > noption_pi] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1)
     => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2)
       => vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X1),X2)) ) ),
    inference(rectify,[],[f82]) ).

thf(f82,axiom,
    ! [X0: name,X5: list_P227219501e_name,X2: name > noption_pi] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X5)
     => ( vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),X2)
       => vAPP(sTfun(name,noption_pi),$o,vAPP(name,sTfun(sTfun(name,noption_pi),$o),fresh_543891186ion_pi,X0),vAPP(sTfun(name,noption_pi),sTfun(name,noption_pi),vAPP(list_P227219501e_name,sTfun(sTfun(name,noption_pi),sTfun(name,noption_pi)),perm_n1667196784ion_pi,X5),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_fresh__perm__app) ).

thf(f4739,plain,
    spl225_209,
    inference(avatar_split_clause,[],[f1628,f4737]) ).

thf(f4737,plain,
    ( spl225_209
  <=> ! [X2: name,X0: name,X1: pi] :
        ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1) )
        | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_209])]) ).

thf(f1628,plain,
    ! [X2: name,X0: name,X1: pi] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1024]) ).

thf(f1024,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f562]) ).

thf(f562,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1) ) ),
    inference(fool_elimination,[],[f561]) ).

thf(f561,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X0)),nil_Pr743626285e_name)),X1) ) ),
    inference(rectify,[],[f329]) ).

thf(f329,axiom,
    ! [X1: name,X19: pi,X0: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X19)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_injPermSubst) ).

thf(f4600,plain,
    ( spl225_208
    | ~ spl225_8
    | ~ spl225_193 ),
    inference(avatar_split_clause,[],[f4382,f4337,f2296,f4598]) ).

thf(f4598,plain,
    ( spl225_208
  <=> ! [X0: name] : ( $false = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_208])]) ).

thf(f4337,plain,
    ( spl225_193
  <=> ! [X0: name] : ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_193])]) ).

thf(f4382,plain,
    ( ! [X0: name] : ( $false = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) )
    | ~ spl225_8
    | ~ spl225_193 ),
    inference(trivial_inequality_removal,[],[f4381]) ).

thf(f4381,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $false = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) ) )
    | ~ spl225_8
    | ~ spl225_193 ),
    inference(superposition,[],[f4338,f2297]) ).

thf(f4338,plain,
    ( ! [X0: name] : ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) )
    | ~ spl225_193 ),
    inference(avatar_component_clause,[],[f4337]) ).

thf(f4398,plain,
    spl225_207,
    inference(avatar_split_clause,[],[f1797,f4396]) ).

thf(f4396,plain,
    ( spl225_207
  <=> ! [X5: name,X4: name,X2: name,X0: name,X6: pi,X3: pi,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_207])]) ).

thf(f1797,plain,
    ! [X2: name,X3: pi,X0: name,X1: name,X6: pi,X4: name,X5: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6)) ),
    inference(cnf_transformation,[],[f916]) ).

thf(f916,plain,
    ! [X0: name,X1: name,X2: name,X3: pi,X4: name,X5: name,X6: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6)) ),
    inference(flattening,[],[f734]) ).

thf(f734,plain,
    ! [X0: name,X1: name,X2: name,X3: pi,X4: name,X5: name,X6: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6)) ),
    inference(fool_elimination,[],[f733]) ).

thf(f733,plain,
    ! [X0: name,X1: name,X2: name,X3: pi,X4: name,X5: name,X6: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X4)),X5),X6)),
    inference(rectify,[],[f312]) ).

thf(f312,axiom,
    ! [X2: name,X0: name,X22: name,X19: pi,X1: name,X68: name,X31: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X22),X19))),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X68),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_resInputBoundOutputTrans) ).

thf(f4394,plain,
    spl225_206,
    inference(avatar_split_clause,[],[f1573,f4392]) ).

thf(f1573,plain,
    ! [X2: list_P227219501e_name,X0: list_P227219501e_name > list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,X1),X2) )
      | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK87,X0)),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK86,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),X0,nil_Pr743626285e_name),vAPP(sTfun(list_P227219501e_name,sTfun(list_P227219501e_name,$o)),list_P227219501e_name,sK88,X0)) ) ),
    inference(cnf_transformation,[],[f1240]) ).

thf(f4390,plain,
    spl225_205,
    inference(avatar_split_clause,[],[f1522,f4388]) ).

thf(f4388,plain,
    ( spl225_205
  <=> ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_205])]) ).

thf(f1522,plain,
    ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f41]) ).

thf(f41,axiom,
    ! [X0: name,X1: name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_perm__swap_I2_J) ).

thf(f4386,plain,
    spl225_204,
    inference(avatar_split_clause,[],[f1521,f4384]) ).

thf(f1521,plain,
    ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,axiom,
    ! [X0: name,X1: name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_perm__swap_I1_J) ).

thf(f4379,plain,
    spl225_203,
    inference(avatar_split_clause,[],[f1516,f4377]) ).

thf(f4377,plain,
    ( spl225_203
  <=> ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_203])]) ).

thf(f1516,plain,
    ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f37]) ).

thf(f37,axiom,
    ! [X0: name,X1: name,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_perm__swap_I2_J) ).

thf(f4375,plain,
    spl225_202,
    inference(avatar_split_clause,[],[f1515,f4373]) ).

thf(f1515,plain,
    ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f26]) ).

thf(f26,axiom,
    ! [X0: name,X1: name,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_name__swap__bij) ).

thf(f4371,plain,
    spl225_201,
    inference(avatar_split_clause,[],[f1513,f4369]) ).

thf(f4369,plain,
    ( spl225_201
  <=> ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_201])]) ).

thf(f1513,plain,
    ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f27]) ).

thf(f27,axiom,
    ! [X0: name,X1: name,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_name__swap__bij) ).

thf(f4367,plain,
    spl225_200,
    inference(avatar_split_clause,[],[f1512,f4365]) ).

thf(f1512,plain,
    ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f38]) ).

thf(f38,axiom,
    ! [X0: name,X1: name,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_perm__swap_I2_J) ).

thf(f4363,plain,
    spl225_199,
    inference(avatar_split_clause,[],[f1510,f4361]) ).

thf(f4361,plain,
    ( spl225_199
  <=> ! [X2: pi_Rep,X0: name,X1: name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_199])]) ).

thf(f1510,plain,
    ! [X2: pi_Rep,X0: name,X1: name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f28]) ).

thf(f28,axiom,
    ! [X0: name,X1: name,X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_name__swap__bij) ).

thf(f4359,plain,
    spl225_198,
    inference(avatar_split_clause,[],[f1509,f4357]) ).

thf(f4357,plain,
    ( spl225_198
  <=> ! [X2: pi_Rep,X0: name,X1: name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_198])]) ).

thf(f1509,plain,
    ! [X2: pi_Rep,X0: name,X1: name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f39]) ).

thf(f39,axiom,
    ! [X0: name,X1: name,X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_perm__swap_I2_J) ).

thf(f4355,plain,
    spl225_197,
    inference(avatar_split_clause,[],[f1508,f4353]) ).

thf(f4353,plain,
    ( spl225_197
  <=> ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_197])]) ).

thf(f1508,plain,
    ! [X2: pi,X0: name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    inference(cnf_transformation,[],[f25]) ).

thf(f25,axiom,
    ! [X0: name,X1: name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_name__swap) ).

thf(f4351,plain,
    spl225_196,
    inference(avatar_split_clause,[],[f1506,f4349]) ).

thf(f4349,plain,
    ( spl225_196
  <=> ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_196])]) ).

thf(f1506,plain,
    ! [X2: late_subject,X0: name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    inference(cnf_transformation,[],[f21]) ).

thf(f21,axiom,
    ! [X0: name,X1: name,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_name__swap) ).

thf(f4347,plain,
    spl225_195,
    inference(avatar_split_clause,[],[f1505,f4345]) ).

thf(f1505,plain,
    ! [X2: late_freeRes,X0: name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    inference(cnf_transformation,[],[f22]) ).

thf(f22,axiom,
    ! [X0: name,X1: name,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_name__swap) ).

thf(f4343,plain,
    spl225_194,
    inference(avatar_split_clause,[],[f1504,f4341]) ).

thf(f4341,plain,
    ( spl225_194
  <=> ! [X2: pi_Rep,X0: name,X1: name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_194])]) ).

thf(f1504,plain,
    ! [X2: pi_Rep,X0: name,X1: name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    inference(cnf_transformation,[],[f23]) ).

thf(f23,axiom,
    ! [X0: name,X1: name,X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_name__swap) ).

thf(f4339,plain,
    ( spl225_193
    | ~ spl225_151
    | ~ spl225_192 ),
    inference(avatar_split_clause,[],[f4335,f4329,f3488,f4337]) ).

thf(f3488,plain,
    ( spl225_151
  <=> ! [X2: pi,X0: name,X1: name] : ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_151])]) ).

thf(f4329,plain,
    ( spl225_192
  <=> ! [X2: pi,X4: name,X0: name,X5: pi,X3: late_subject,X1: name] :
        ( ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_192])]) ).

thf(f4335,plain,
    ( ! [X0: name] : ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) )
    | ~ spl225_151
    | ~ spl225_192 ),
    inference(trivial_inequality_removal,[],[f4332]) ).

thf(f4332,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(name,late_subject,late_InputS,X0)) ) )
    | ~ spl225_151
    | ~ spl225_192 ),
    inference(superposition,[],[f4330,f3489]) ).

thf(f3489,plain,
    ( ! [X2: pi,X0: name,X1: name] : ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X1),X2)) )
    | ~ spl225_151 ),
    inference(avatar_component_clause,[],[f3488]) ).

thf(f4330,plain,
    ( ! [X2: pi,X3: late_subject,X0: name,X1: name,X4: name,X5: pi] :
        ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
        | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) ) )
    | ~ spl225_192 ),
    inference(avatar_component_clause,[],[f4329]) ).

thf(f4331,plain,
    spl225_192,
    inference(avatar_split_clause,[],[f1783,f4329]) ).

thf(f1783,plain,
    ! [X2: pi,X3: late_subject,X0: name,X1: name,X4: name,X5: pi] :
      ( ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(cnf_transformation,[],[f1123]) ).

thf(f1123,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) ) ),
    inference(ennf_transformation,[],[f913]) ).

thf(f913,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
     => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) ) ),
    inference(flattening,[],[f710]) ).

thf(f710,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5)) )
     => ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) ) ),
    inference(fool_elimination,[],[f709]) ).

thf(f709,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_subject,X4: name,X5: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X3),X4),X5))
     => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X3) ),
    inference(rectify,[],[f301]) ).

thf(f301,axiom,
    ! [X0: name,X2: name,X19: pi,X1: late_subject,X22: name,X31: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X2),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X22),X31))
     => ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_inputIneqTrans) ).

thf(f4319,plain,
    spl225_191,
    inference(avatar_split_clause,[],[f1734,f4317]) ).

thf(f1734,plain,
    ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) )
      | ( X2 = X4 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1096]) ).

thf(f1096,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) )
      | ( X2 = X4 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(flattening,[],[f1095]) ).

thf(f1095,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) )
      | ( X2 = X4 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(ennf_transformation,[],[f680]) ).

thf(f680,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
       => ( ( X2 != X4 )
         => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) ) ) ) ),
    inference(fool_elimination,[],[f679]) ).

thf(f679,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0)
       => ( ( X2 != X4 )
         => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X3) ) ) ),
    inference(rectify,[],[f213]) ).

thf(f213,axiom,
    ! [X19: pi,X0: late_subject,X2: name,X31: pi,X22: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X31))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X19)
       => ( ( X2 != X22 )
         => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X31) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_freshBoundDerivative_I2_J) ).

thf(f4315,plain,
    spl225_190,
    inference(avatar_split_clause,[],[f1648,f4313]) ).

thf(f4313,plain,
    ( spl225_190
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_190])]) ).

thf(f1648,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK173,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK175,X2),X1),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f4311,plain,
    spl225_189,
    inference(avatar_split_clause,[],[f1643,f4309]) ).

thf(f4309,plain,
    ( spl225_189
  <=> ! [X2: name,X0: late_residual,X1: pi] :
        ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0) )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_189])]) ).

thf(f1643,plain,
    ! [X2: name,X0: late_residual,X1: pi] :
      ( ( vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK168,X2),X1),X0) != vAPP(late_residual,name,vAPP(pi,sTfun(late_residual,name),vAPP(name,sTfun(pi,sTfun(late_residual,name)),sK169,X2),X1),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),vAPP(name,sTfun(pi,sTfun(late_residual,$o)),sP2,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f4279,plain,
    ( spl225_188
    | ~ spl225_29
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2724,f2699,f2414,f4277]) ).

thf(f4277,plain,
    ( spl225_188
  <=> ! [X0: name] : ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),x),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_188])]) ).

thf(f2724,plain,
    ( ! [X0: name] : ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),x),X0) )
    | ~ spl225_29
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2705]) ).

thf(f2705,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),x),X0) ) )
    | ~ spl225_29
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2416]) ).

thf(f4267,plain,
    spl225_187,
    inference(avatar_split_clause,[],[f1631,f4265]) ).

thf(f1631,plain,
    ! [X2: name,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1028]) ).

thf(f1028,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(flattening,[],[f1027]) ).

thf(f1027,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f568]) ).

thf(f568,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1) )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(fool_elimination,[],[f567]) ).

thf(f567,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X1)
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f67]) ).

thf(f67,axiom,
    ! [X0: name,X2: pi,X1: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2)
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X2)
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_perm__fresh__fresh) ).

thf(f4263,plain,
    spl225_186,
    inference(avatar_split_clause,[],[f1616,f4261]) ).

thf(f4261,plain,
    ( spl225_186
  <=> ! [X2: name,X0: name,X1: late_subject] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X2),X1) )
        | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_186])]) ).

thf(f1616,plain,
    ! [X2: name,X0: name,X1: late_subject] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X2),X1) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1003]) ).

thf(f1003,plain,
    ! [X0: name,X1: late_subject,X2: name] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X2),X1) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1) != $true ) ),
    inference(flattening,[],[f1002]) ).

thf(f1002,plain,
    ! [X0: name,X1: late_subject,X2: name] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X2),X1) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f538]) ).

thf(f538,plain,
    ! [X0: name,X1: late_subject,X2: name] :
      ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1) = $true )
     => ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X2),X1) )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(fool_elimination,[],[f537]) ).

thf(f537,plain,
    ! [X0: name,X1: late_subject,X2: name] :
      ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X1)
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X2),X1)
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f64]) ).

thf(f64,axiom,
    ! [X0: name,X2: late_subject,X1: name] :
      ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2)
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X2)
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_perm__fresh__fresh) ).

thf(f4259,plain,
    spl225_185,
    inference(avatar_split_clause,[],[f1612,f4257]) ).

thf(f4257,plain,
    ( spl225_185
  <=> ! [X2: name,X0: name,X1: late_freeRes] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X1) )
        | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_185])]) ).

thf(f1612,plain,
    ! [X2: name,X0: name,X1: late_freeRes] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X1) )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X1) ) ),
    inference(cnf_transformation,[],[f996]) ).

thf(f996,plain,
    ! [X0: name,X1: late_freeRes,X2: name] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X1) )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X1) ) ),
    inference(flattening,[],[f995]) ).

thf(f995,plain,
    ! [X0: name,X1: late_freeRes,X2: name] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X1) )
      | ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X1) ) ),
    inference(ennf_transformation,[],[f530]) ).

thf(f530,plain,
    ! [X0: name,X1: late_freeRes,X2: name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X1) )
     => ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X1) )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(fool_elimination,[],[f529]) ).

thf(f529,plain,
    ! [X0: name,X1: late_freeRes,X2: name] :
      ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X1)
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X2),X1)
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f65]) ).

thf(f65,axiom,
    ! [X0: name,X2: late_freeRes,X1: name] :
      ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2)
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X2)
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_perm__fresh__fresh) ).

thf(f4255,plain,
    spl225_184,
    inference(avatar_split_clause,[],[f1610,f4253]) ).

thf(f4253,plain,
    ( spl225_184
  <=> ! [X2: name,X0: name,X1: pi_Rep] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
        | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X2),X1) )
        | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_184])]) ).

thf(f1610,plain,
    ! [X2: name,X0: name,X1: pi_Rep] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X2),X1) )
      | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X1) ) ),
    inference(cnf_transformation,[],[f992]) ).

thf(f992,plain,
    ! [X0: name,X1: pi_Rep,X2: name] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X2),X1) )
      | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X1) ) ),
    inference(flattening,[],[f991]) ).

thf(f991,plain,
    ! [X0: name,X1: pi_Rep,X2: name] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X2),X1) )
      | ( $true != vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X1) ) ),
    inference(ennf_transformation,[],[f526]) ).

thf(f526,plain,
    ! [X0: name,X1: pi_Rep,X2: name] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X1) )
     => ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X2),X1) )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(fool_elimination,[],[f525]) ).

thf(f525,plain,
    ! [X0: name,X1: pi_Rep,X2: name] :
      ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X1)
     => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X2),X1)
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f63]) ).

thf(f63,axiom,
    ! [X0: name,X2: pi_Rep,X1: name] :
      ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2)
     => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X1),X2)
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_perm__fresh__fresh) ).

thf(f4243,plain,
    spl225_183,
    inference(avatar_split_clause,[],[f1737,f4241]) ).

thf(f1737,plain,
    ! [X2: name,X3: pi,X0: pi,X1: late_subject,X4: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(cnf_transformation,[],[f1102]) ).

thf(f1102,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(flattening,[],[f1101]) ).

thf(f1101,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) ) ),
    inference(ennf_transformation,[],[f686]) ).

thf(f686,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0) )
       => ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) ) ) ),
    inference(fool_elimination,[],[f685]) ).

thf(f685,plain,
    ! [X0: pi,X1: late_subject,X2: name,X3: pi,X4: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X1),X2),X3))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X4),X0)
       => vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X4),X1) ) ),
    inference(rectify,[],[f201]) ).

thf(f201,axiom,
    ! [X19: pi,X0: late_subject,X2: name,X31: pi,X22: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X2),X31))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X19)
       => vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X22),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_freshBoundDerivative_I1_J) ).

thf(f4235,plain,
    ( spl225_182
    | ~ spl225_24
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2723,f2699,f2389,f4233]) ).

thf(f4233,plain,
    ( spl225_182
  <=> ! [X0: name] : ( q2 = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),y),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_182])]) ).

thf(f2723,plain,
    ( ! [X0: name] : ( q2 = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),y),X0) )
    | ~ spl225_24
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2706]) ).

thf(f2706,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( q2 = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),y),X0) ) )
    | ~ spl225_24
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2391]) ).

thf(f4231,plain,
    spl225_181,
    inference(avatar_split_clause,[],[f1378,f4229]) ).

thf(f1378,plain,
    ! [X0: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK12,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0))) = X0 )
      | ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(cnf_transformation,[],[f1163]) ).

thf(f1163,plain,
    ! [X0: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK12,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0))) = X0 )
      | ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f1160,f1162,f1161]) ).

thf(f1161,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X1: produc367475239e_name,X2: produc367475239e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) = X0 )
     => ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK12,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK13,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK14,X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1162,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X4: produc367475239e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),nil_Pr743626285e_name) = X0 )
     => ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK15,X0)),nil_Pr743626285e_name) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1160,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X1: produc367475239e_name,X2: produc367475239e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) = X0 )
      | ? [X4: produc367475239e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X4),nil_Pr743626285e_name) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(rectify,[],[f920]) ).

thf(f920,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) = X0 )
      | ? [X1: produc367475239e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),nil_Pr743626285e_name) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(flattening,[],[f919]) ).

thf(f919,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) = X0 )
      | ? [X1: produc367475239e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),nil_Pr743626285e_name) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(ennf_transformation,[],[f778]) ).

thf(f778,plain,
    ! [X0: list_P227219501e_name] :
      ( ( nil_Pr743626285e_name != X0 )
     => ( ! [X1: produc367475239e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),nil_Pr743626285e_name) != X0 )
       => ~ ! [X2: produc367475239e_name,X3: produc367475239e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X3),X4)) != X0 ) ) ),
    inference(rectify,[],[f273]) ).

thf(f273,axiom,
    ! [X2: list_P227219501e_name] :
      ( ( nil_Pr743626285e_name != X2 )
     => ( ! [X63: produc367475239e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),nil_Pr743626285e_name) != X2 )
       => ~ ! [X63: produc367475239e_name,X50: produc367475239e_name,X65: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X50),X65)) != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_remdups__adj_Ocases) ).

thf(f4227,plain,
    spl225_180,
    inference(avatar_split_clause,[],[f1377,f4225]) ).

thf(f4225,plain,
    ( spl225_180
  <=> ! [X0: list_l1406151091e_name] :
        ( ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_l1406151091e_name,produc367475239e_name,sK8,X0)),vAPP(list_l1406151091e_name,list_P227219501e_name,sK9,X0))),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK10,X0)) = X0 )
        | ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK11,X0)) = X0 )
        | ( nil_li29751603e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_180])]) ).

thf(f1377,plain,
    ! [X0: list_l1406151091e_name] :
      ( ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_l1406151091e_name,produc367475239e_name,sK8,X0)),vAPP(list_l1406151091e_name,list_P227219501e_name,sK9,X0))),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK10,X0)) = X0 )
      | ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK11,X0)) = X0 )
      | ( nil_li29751603e_name = X0 ) ),
    inference(cnf_transformation,[],[f1159]) ).

thf(f1159,plain,
    ! [X0: list_l1406151091e_name] :
      ( ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_l1406151091e_name,produc367475239e_name,sK8,X0)),vAPP(list_l1406151091e_name,list_P227219501e_name,sK9,X0))),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK10,X0)) = X0 )
      | ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK11,X0)) = X0 )
      | ( nil_li29751603e_name = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f1156,f1158,f1157]) ).

thf(f1157,plain,
    ! [X0: list_l1406151091e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name,X3: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2)),X3) = X0 )
     => ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_l1406151091e_name,produc367475239e_name,sK8,X0)),vAPP(list_l1406151091e_name,list_P227219501e_name,sK9,X0))),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK10,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1158,plain,
    ! [X0: list_l1406151091e_name] :
      ( ? [X4: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),X4) = X0 )
     => ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),vAPP(list_l1406151091e_name,list_l1406151091e_name,sK11,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1156,plain,
    ! [X0: list_l1406151091e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name,X3: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2)),X3) = X0 )
      | ? [X4: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),X4) = X0 )
      | ( nil_li29751603e_name = X0 ) ),
    inference(rectify,[],[f918]) ).

thf(f918,plain,
    ! [X0: list_l1406151091e_name] :
      ( ? [X2: produc367475239e_name,X3: list_P227219501e_name,X4: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),X4) = X0 )
      | ? [X1: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),X1) = X0 )
      | ( nil_li29751603e_name = X0 ) ),
    inference(flattening,[],[f917]) ).

thf(f917,plain,
    ! [X0: list_l1406151091e_name] :
      ( ? [X2: produc367475239e_name,X3: list_P227219501e_name,X4: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),X4) = X0 )
      | ? [X1: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),X1) = X0 )
      | ( nil_li29751603e_name = X0 ) ),
    inference(ennf_transformation,[],[f777]) ).

thf(f777,plain,
    ! [X0: list_l1406151091e_name] :
      ( ( nil_li29751603e_name != X0 )
     => ( ! [X1: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),X1) != X0 )
       => ~ ! [X2: produc367475239e_name,X3: list_P227219501e_name,X4: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),X4) != X0 ) ) ),
    inference(rectify,[],[f272]) ).

thf(f272,axiom,
    ! [X2: list_l1406151091e_name] :
      ( ( nil_li29751603e_name != X2 )
     => ( ! [X87: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,nil_Pr743626285e_name),X87) != X2 )
       => ~ ! [X63: produc367475239e_name,X65: list_P227219501e_name,X87: list_l1406151091e_name] : ( vAPP(list_l1406151091e_name,list_l1406151091e_name,vAPP(list_P227219501e_name,sTfun(list_l1406151091e_name,list_l1406151091e_name),cons_l798145763e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),X87) != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_transpose_Ocases) ).

thf(f4081,plain,
    ( spl225_179
    | ~ spl225_25
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2722,f2699,f2394,f4079]) ).

thf(f4079,plain,
    ( spl225_179
  <=> ! [X0: name] : ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),y),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_179])]) ).

thf(f2722,plain,
    ( ! [X0: name] : ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),y),X0) )
    | ~ spl225_25
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2707]) ).

thf(f2707,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),y),X0) ) )
    | ~ spl225_25
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2396]) ).

thf(f4030,plain,
    spl225_178,
    inference(avatar_split_clause,[],[f1887,f4028]) ).

thf(f4028,plain,
    ( spl225_178
  <=> ! [X0: list_P227219501e_name,X3: name,X2: name,X1: $o] :
        ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_178])]) ).

thf(f1887,plain,
    ! [X2: name,X3: name,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
      | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(definition_unfolding,[],[f1689,f1358,f1358]) ).

thf(f1689,plain,
    ! [X2: name,X3: name,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
      | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1050]) ).

thf(f1050,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: name,X3: name] :
      ( ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
      & ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f900]) ).

thf(f900,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: name,X3: name] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) ) ) ),
    inference(flattening,[],[f628]) ).

thf(f628,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: name,X3: name] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f627]) ).

thf(f627,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: name,X3: name] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) ) ) ),
    inference(rectify,[],[f239]) ).

thf(f239,axiom,
    ! [X5: list_P227219501e_name,X1: $o,X74: name,X75: name] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X74),X75)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X75) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X74),X75)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X74) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_if__eqvt) ).

thf(f4026,plain,
    spl225_177,
    inference(avatar_split_clause,[],[f1886,f4024]) ).

thf(f1886,plain,
    ! [X2: name,X3: name,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(definition_unfolding,[],[f1690,f1358,f1358]) ).

thf(f1690,plain,
    ! [X2: name,X3: name,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X1),X2),X3)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X3) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1050]) ).

thf(f4022,plain,
    spl225_176,
    inference(avatar_split_clause,[],[f1692,f4020]) ).

thf(f1692,plain,
    ! [X2: pi,X3: pi,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1051]) ).

thf(f1051,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi,X3: pi] :
      ( ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
      & ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f901]) ).

thf(f901,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi,X3: pi] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) ) ) ),
    inference(flattening,[],[f630]) ).

thf(f630,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi,X3: pi] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f629]) ).

thf(f629,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi,X3: pi] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X3) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) ) ) ),
    inference(rectify,[],[f240]) ).

thf(f240,axiom,
    ! [X5: list_P227219501e_name,X1: $o,X74: pi,X75: pi] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X74),X75)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X75) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X74),X75)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X74) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_if__eqvt) ).

thf(f4018,plain,
    spl225_175,
    inference(avatar_split_clause,[],[f1691,f4016]) ).

thf(f4016,plain,
    ( spl225_175
  <=> ! [X0: list_P227219501e_name,X3: pi,X2: pi,X1: $o] :
        ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_175])]) ).

thf(f1691,plain,
    ! [X2: pi,X3: pi,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X1),X2),X3)) )
      | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1051]) ).

thf(f4014,plain,
    spl225_174,
    inference(avatar_split_clause,[],[f1688,f4012]) ).

thf(f1688,plain,
    ! [X2: late_subject,X3: late_subject,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1049]) ).

thf(f1049,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_subject,X3: late_subject] :
      ( ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
      & ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f899]) ).

thf(f899,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_subject,X3: late_subject] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) ) ) ),
    inference(flattening,[],[f626]) ).

thf(f626,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_subject,X3: late_subject] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f625]) ).

thf(f625,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_subject,X3: late_subject] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X3) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) ) ) ),
    inference(rectify,[],[f236]) ).

thf(f236,axiom,
    ! [X5: list_P227219501e_name,X1: $o,X74: late_subject,X75: late_subject] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X74),X75)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X75) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X74),X75)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X74) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_if__eqvt) ).

thf(f4010,plain,
    spl225_173,
    inference(avatar_split_clause,[],[f1687,f4008]) ).

thf(f4008,plain,
    ( spl225_173
  <=> ! [X0: list_P227219501e_name,X3: late_subject,X2: late_subject,X1: $o] :
        ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_173])]) ).

thf(f1687,plain,
    ! [X2: late_subject,X3: late_subject,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X1),X2),X3)) )
      | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1049]) ).

thf(f4006,plain,
    spl225_172,
    inference(avatar_split_clause,[],[f1686,f4004]) ).

thf(f1686,plain,
    ! [X2: late_freeRes,X3: late_freeRes,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1048]) ).

thf(f1048,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_freeRes,X3: late_freeRes] :
      ( ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
      & ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f898]) ).

thf(f898,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_freeRes,X3: late_freeRes] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) ) ) ),
    inference(flattening,[],[f624]) ).

thf(f624,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_freeRes,X3: late_freeRes] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f623]) ).

thf(f623,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: late_freeRes,X3: late_freeRes] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X3) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) ) ) ),
    inference(rectify,[],[f237]) ).

thf(f237,axiom,
    ! [X5: list_P227219501e_name,X1: $o,X74: late_freeRes,X75: late_freeRes] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X74),X75)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X75) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X74),X75)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X74) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_if__eqvt) ).

thf(f4002,plain,
    ( spl225_171
    | ~ spl225_27
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2720,f2699,f2404,f4000]) ).

thf(f4000,plain,
    ( spl225_171
  <=> ! [X0: name] : ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),z),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_171])]) ).

thf(f2720,plain,
    ( ! [X0: name] : ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),z),X0) )
    | ~ spl225_27
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2709]) ).

thf(f2709,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p),z),X0) ) )
    | ~ spl225_27
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2406]) ).

thf(f3998,plain,
    spl225_170,
    inference(avatar_split_clause,[],[f1685,f3996]) ).

thf(f3996,plain,
    ( spl225_170
  <=> ! [X0: list_P227219501e_name,X3: late_freeRes,X2: late_freeRes,X1: $o] :
        ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_170])]) ).

thf(f1685,plain,
    ! [X2: late_freeRes,X3: late_freeRes,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X1),X2),X3)) )
      | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1048]) ).

thf(f3994,plain,
    spl225_169,
    inference(avatar_split_clause,[],[f1684,f3992]) ).

thf(f1684,plain,
    ! [X2: pi_Rep,X3: pi_Rep,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) )
      | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1047]) ).

thf(f1047,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi_Rep,X3: pi_Rep] :
      ( ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) )
        | ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) )
      & ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f897]) ).

thf(f897,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi_Rep,X3: pi_Rep] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) ) ) ),
    inference(flattening,[],[f622]) ).

thf(f622,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi_Rep,X3: pi_Rep] :
      ( ( ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) ) )
      & ( ( $true = vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f621]) ).

thf(f621,plain,
    ! [X0: list_P227219501e_name,X1: $o,X2: pi_Rep,X3: pi_Rep] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X3) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1)
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) ) ) ),
    inference(rectify,[],[f238]) ).

thf(f238,axiom,
    ! [X5: list_P227219501e_name,X1: $o,X74: pi_Rep,X75: pi_Rep] :
      ( ( ~ vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X74),X75)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X75) ) )
      & ( vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X5),X1)
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X74),X75)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X74) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_if__eqvt) ).

thf(f3990,plain,
    spl225_168,
    inference(avatar_split_clause,[],[f1683,f3988]) ).

thf(f3988,plain,
    ( spl225_168
  <=> ! [X0: list_P227219501e_name,X3: pi_Rep,X2: pi_Rep,X1: $o] :
        ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) )
        | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_168])]) ).

thf(f1683,plain,
    ! [X2: pi_Rep,X3: pi_Rep,X0: list_P227219501e_name,X1: $o] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X1),X2),X3)) )
      | ( $true != vAPP($o,$o,vAPP(list_P227219501e_name,sTfun($o,$o),perm_name_o,X0),X1) ) ),
    inference(cnf_transformation,[],[f1047]) ).

thf(f3986,plain,
    spl225_167,
    inference(avatar_split_clause,[],[f1627,f3984]) ).

thf(f1627,plain,
    ! [X2: name,X0: name,X1: pi] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1023]) ).

thf(f1023,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f560]) ).

thf(f560,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) ) ),
    inference(fool_elimination,[],[f559]) ).

thf(f559,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X1) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X2),X0)) ) ),
    inference(rectify,[],[f325]) ).

thf(f325,axiom,
    ! [X1: name,X19: pi,X0: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X19)
     => ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X19) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_substRes2) ).

thf(f3834,plain,
    ( spl225_166
    | ~ spl225_26
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2719,f2699,f2399,f3832]) ).

thf(f3832,plain,
    ( spl225_166
  <=> ! [X0: name] : ( p2 = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),z),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_166])]) ).

thf(f2719,plain,
    ( ! [X0: name] : ( p2 = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),z),X0) )
    | ~ spl225_26
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2710]) ).

thf(f2710,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( p2 = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,p2),z),X0) ) )
    | ~ spl225_26
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2401]) ).

thf(f3691,plain,
    ( spl225_165
    | ~ spl225_28
    | ~ spl225_81 ),
    inference(avatar_split_clause,[],[f2718,f2699,f2409,f3689]) ).

thf(f3689,plain,
    ( spl225_165
  <=> ! [X0: name] : ( q = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),z),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_165])]) ).

thf(f2718,plain,
    ( ! [X0: name] : ( q = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),z),X0) )
    | ~ spl225_28
    | ~ spl225_81 ),
    inference(trivial_inequality_removal,[],[f2711]) ).

thf(f2711,plain,
    ( ! [X0: name] :
        ( ( $true != $true )
        | ( q = vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q),z),X0) ) )
    | ~ spl225_28
    | ~ spl225_81 ),
    inference(superposition,[],[f2700,f2411]) ).

thf(f3583,plain,
    ( spl225_164
    | ~ spl225_37
    | ~ spl225_58 ),
    inference(avatar_split_clause,[],[f2562,f2557,f2455,f3581]) ).

thf(f3581,plain,
    ( spl225_164
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK53,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK52,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_164])]) ).

thf(f2557,plain,
    ( spl225_58
  <=> ! [X2: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)),X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_58])]) ).

thf(f2562,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK53,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK52,X0)) )
    | ~ spl225_37
    | ~ spl225_58 ),
    inference(superposition,[],[f2558,f2456]) ).

thf(f2558,plain,
    ( ! [X2: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)),X1) = X2 )
    | ~ spl225_58 ),
    inference(avatar_component_clause,[],[f2557]) ).

thf(f3538,plain,
    spl225_163,
    inference(avatar_split_clause,[],[f2258,f3536]) ).

thf(f3536,plain,
    ( spl225_163
  <=> ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_163])]) ).

thf(f2258,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X2)) = X2 ),
    inference(forward_demodulation,[],[f1852,f2255]) ).

thf(f1852,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(definition_unfolding,[],[f1520,f1358,f1358]) ).

thf(f1520,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f40]) ).

thf(f40,axiom,
    ! [X0: name,X1: name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_perm__swap_I2_J) ).

thf(f3534,plain,
    spl225_162,
    inference(avatar_split_clause,[],[f2256,f3532]) ).

thf(f2256,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X0)),X2)) = X2 ),
    inference(forward_demodulation,[],[f1850,f2255]) ).

thf(f1850,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(definition_unfolding,[],[f1518,f1358,f1358]) ).

thf(f1518,plain,
    ! [X2: name,X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,axiom,
    ! [X0: name,X1: name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_perm__swap_I1_J) ).

thf(f3530,plain,
    spl225_161,
    inference(avatar_split_clause,[],[f2255,f3528]) ).

thf(f3526,plain,
    spl225_160,
    inference(avatar_split_clause,[],[f1847,f3524]) ).

thf(f1847,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(definition_unfolding,[],[f1501,f1358]) ).

thf(f1501,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f871]) ).

thf(f871,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X1),X2)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f192]) ).

thf(f192,axiom,
    ! [X5: list_P227219501e_name,X3: name,X4: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4)) = vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_pi_Operm_I9_J) ).

thf(f3522,plain,
    spl225_159,
    inference(avatar_split_clause,[],[f1844,f3520]) ).

thf(f1844,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X2)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1495,f1358,f1358,f1358,f1358]) ).

thf(f1495,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(cnf_transformation,[],[f865]) ).

thf(f865,plain,
    ! [X0: list_P227219501e_name,X1: list_P227219501e_name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(rectify,[],[f119]) ).

thf(f119,axiom,
    ! [X33: list_P227219501e_name,X34: list_P227219501e_name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X33),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X34),X2)) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X33),X34)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X33),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_cp__name__name1) ).

thf(f3518,plain,
    spl225_158,
    inference(avatar_split_clause,[],[f1837,f3516]) ).

thf(f1837,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1479,f1358,f1358]) ).

thf(f1479,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(cnf_transformation,[],[f849]) ).

thf(f849,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2)) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(rectify,[],[f56]) ).

thf(f56,axiom,
    ! [X5: list_P227219501e_name,X4: name,X3: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X4),X3)) = vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X4)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_freeRes_Operm_I1_J) ).

thf(f3514,plain,
    spl225_157,
    inference(avatar_split_clause,[],[f1836,f3512]) ).

thf(f1836,plain,
    ! [X2: list_name,X0: list_P227219501e_name,X1: name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X1),X2)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1471,f1358]) ).

thf(f1471,plain,
    ! [X2: list_name,X0: list_P227219501e_name,X1: name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X1),X2)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),X2)) ),
    inference(cnf_transformation,[],[f841]) ).

thf(f841,plain,
    ! [X0: list_P227219501e_name,X1: name,X2: list_name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X1),X2)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X0),X2)) ),
    inference(rectify,[],[f186]) ).

thf(f186,axiom,
    ! [X5: list_P227219501e_name,X2: name,X43: list_name] : ( vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X5),vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,X2),X43)) = vAPP(list_name,list_name,vAPP(name,sTfun(list_name,list_name),cons_name,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2)),vAPP(list_name,list_name,vAPP(list_P227219501e_name,sTfun(list_name,list_name),perm_name_list_name,X5),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_cons__eqvt) ).

thf(f3510,plain,
    ( spl225_156
    | ~ spl225_34
    | ~ spl225_58 ),
    inference(avatar_split_clause,[],[f2561,f2557,f2443,f3508]) ).

thf(f3508,plain,
    ( spl225_156
  <=> ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK49,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK48,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_156])]) ).

thf(f2561,plain,
    ( ! [X0: produc367475239e_name] : ( vAPP(produc367475239e_name,name,sK49,X0) = vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,X0),vAPP(produc367475239e_name,name,sK48,X0)) )
    | ~ spl225_34
    | ~ spl225_58 ),
    inference(superposition,[],[f2558,f2444]) ).

thf(f3506,plain,
    spl225_155,
    inference(avatar_split_clause,[],[f1835,f3504]) ).

thf(f1835,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,X0),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X1),X2)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1465,f1358]) ).

thf(f1465,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,X0),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X1),X2)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(cnf_transformation,[],[f835]) ).

thf(f835,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: name] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,X0),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X1),X2)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(rectify,[],[f256]) ).

thf(f256,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: name] : ( vAPP(produc1998742700t_name,produc1998742700t_name,vAPP(list_P227219501e_name,sTfun(produc1998742700t_name,produc1998742700t_name),perm_n204483300t_name,X5),vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,X2),X22)) = vAPP(name,produc1998742700t_name,vAPP(late_subject,sTfun(name,produc1998742700t_name),produc1647375838t_name,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_perm__prod_Osimps) ).

thf(f3502,plain,
    spl225_154,
    inference(avatar_split_clause,[],[f1834,f3500]) ).

thf(f1834,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X1),X2)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1464,f1358]) ).

thf(f1464,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X1),X2)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(cnf_transformation,[],[f834]) ).

thf(f834,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: name] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X0),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X1),X2)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(rectify,[],[f261]) ).

thf(f261,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X22: name] : ( vAPP(produc2052722628s_name,produc2052722628s_name,vAPP(list_P227219501e_name,sTfun(produc2052722628s_name,produc2052722628s_name),perm_n258463228s_name,X5),vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,X2),X22)) = vAPP(name,produc2052722628s_name,vAPP(late_freeRes,sTfun(name,produc2052722628s_name),produc1701355766s_name,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_perm__prod_Osimps) ).

thf(f3498,plain,
    spl225_153,
    inference(avatar_split_clause,[],[f1785,f3496]) ).

thf(f3496,plain,
    ( spl225_153
  <=> ! [X3: name,X4: name,X0: name,X5: pi,X2: pi,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X3)),X4),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_153])]) ).

thf(f1785,plain,
    ! [X2: pi,X3: name,X0: name,X1: name,X4: name,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X3)),X4),X5)) ),
    inference(cnf_transformation,[],[f915]) ).

thf(f915,plain,
    ! [X0: name,X1: name,X2: pi,X3: name,X4: name,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X3)),X4),X5)) ),
    inference(flattening,[],[f714]) ).

thf(f714,plain,
    ! [X0: name,X1: name,X2: pi,X3: name,X4: name,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X3)),X4),X5)) ),
    inference(fool_elimination,[],[f713]) ).

thf(f713,plain,
    ! [X0: name,X1: name,X2: pi,X3: name,X4: name,X5: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X3)),X4),X5)),
    inference(rectify,[],[f310]) ).

thf(f310,axiom,
    ! [X0: name,X2: name,X19: pi,X1: name,X22: name,X31: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X2),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,X1)),X22),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_inputBoundOutputTrans) ).

thf(f3494,plain,
    spl225_152,
    inference(avatar_split_clause,[],[f1741,f3492]) ).

thf(f3492,plain,
    ( spl225_152
  <=> ! [X4: pi > $o,X0: name,X3: pi,X2: late_freeRes,X1: pi] :
        ( ( $true = vAPP(pi,$o,X4,X3) )
        | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
        | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_152])]) ).

thf(f1741,plain,
    ! [X2: late_freeRes,X3: pi,X0: name,X1: pi,X4: pi > $o] :
      ( ( $true = vAPP(pi,$o,X4,X3) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X2),X3)) ) ),
    inference(cnf_transformation,[],[f1319]) ).

thf(f3490,plain,
    spl225_151,
    inference(avatar_split_clause,[],[f1655,f3488]) ).

thf(f1655,plain,
    ! [X2: pi,X0: name,X1: name] : ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X1),X2)) ),
    inference(cnf_transformation,[],[f588]) ).

thf(f588,plain,
    ! [X0: name,X1: name,X2: pi] : ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X1),X2)) ),
    inference(fool_elimination,[],[f587]) ).

thf(f587,plain,
    ! [X0: name,X1: name,X2: pi] : vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X1),X2)),
    inference(rectify,[],[f291]) ).

thf(f291,axiom,
    ! [X0: name,X2: name,X19: pi] : vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X2),X19)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,X0)),X2),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Late__Semantics_OInput) ).

thf(f3486,plain,
    spl225_150,
    inference(avatar_split_clause,[],[f1502,f3484]) ).

thf(f1502,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f872]) ).

thf(f872,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X1),X2)) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f281]) ).

thf(f281,axiom,
    ! [X5: list_P227219501e_name,X4: pi,X3: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X4),X3)) = vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X4)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_pi_Operm_I8_J) ).

thf(f3482,plain,
    spl225_149,
    inference(avatar_split_clause,[],[f1498,f3480]) ).

thf(f1498,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f868]) ).

thf(f868,plain,
    ! [X0: list_P227219501e_name,X1: list_P227219501e_name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f120]) ).

thf(f120,axiom,
    ! [X33: list_P227219501e_name,X34: list_P227219501e_name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X33),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X34),X2)) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X33),X34)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X33),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_cp__name__name1) ).

thf(f3478,plain,
    spl225_148,
    inference(avatar_split_clause,[],[f1481,f3476]) ).

thf(f1481,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f851]) ).

thf(f851,plain,
    ! [X0: list_P227219501e_name,X1: list_P227219501e_name,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(rectify,[],[f126]) ).

thf(f126,axiom,
    ! [X34: list_P227219501e_name,X33: list_P227219501e_name,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X34),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X33),X2)) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X34),X33)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X34),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_perm__compose) ).

thf(f3474,plain,
    spl225_147,
    inference(avatar_split_clause,[],[f1480,f3472]) ).

thf(f1480,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f850]) ).

thf(f850,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f62]) ).

thf(f62,axiom,
    ! [X5: list_P227219501e_name,X4: late_freeRes,X3: pi] : ( vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X5),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X3)) = vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X4)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_residual_Operm_I2_J) ).

thf(f3470,plain,
    spl225_146,
    inference(avatar_split_clause,[],[f1476,f3468]) ).

thf(f1476,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f846]) ).

thf(f846,plain,
    ! [X0: list_P227219501e_name,X1: list_P227219501e_name,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(rectify,[],[f117]) ).

thf(f117,axiom,
    ! [X33: list_P227219501e_name,X34: list_P227219501e_name,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X33),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X34),X2)) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X33),X34)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X33),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_cp__name__name1) ).

thf(f3452,plain,
    spl225_145,
    inference(avatar_split_clause,[],[f1473,f3450]) ).

thf(f1473,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: list_P227219501e_name] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f843]) ).

thf(f843,plain,
    ! [X0: list_P227219501e_name,X1: list_P227219501e_name,X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(rectify,[],[f118]) ).

thf(f118,axiom,
    ! [X33: list_P227219501e_name,X34: list_P227219501e_name,X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X33),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X34),X2)) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,list_P227219501e_name),perm_n1160739829e_name,X33),X34)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X33),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_cp__name__name1) ).

thf(f3448,plain,
    spl225_144,
    inference(avatar_split_clause,[],[f1472,f3446]) ).

thf(f1472,plain,
    ! [X2: list_pi,X0: list_P227219501e_name,X1: pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X1),X2)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f842]) ).

thf(f842,plain,
    ! [X0: list_P227219501e_name,X1: pi,X2: list_pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X1),X2)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X1)),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X0),X2)) ),
    inference(rectify,[],[f187]) ).

thf(f187,axiom,
    ! [X5: list_P227219501e_name,X2: pi,X43: list_pi] : ( vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X5),vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,X2),X43)) = vAPP(list_pi,list_pi,vAPP(pi,sTfun(list_pi,list_pi),cons_pi,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2)),vAPP(list_pi,list_pi,vAPP(list_P227219501e_name,sTfun(list_pi,list_pi),perm_name_list_pi,X5),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_cons__eqvt) ).

thf(f3444,plain,
    spl225_143,
    inference(avatar_split_clause,[],[f1470,f3442]) ).

thf(f1470,plain,
    ! [X2: list_Late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X1),X2)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f840]) ).

thf(f840,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: list_Late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X1),X2)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X0),X2)) ),
    inference(rectify,[],[f183]) ).

thf(f183,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X43: list_Late_subject] : ( vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X5),vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,X2),X43)) = vAPP(list_Late_subject,list_Late_subject,vAPP(late_subject,sTfun(list_Late_subject,list_Late_subject),cons_Late_subject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(list_Late_subject,list_Late_subject,vAPP(list_P227219501e_name,sTfun(list_Late_subject,list_Late_subject),perm_n1812647369ubject,X5),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_cons__eqvt) ).

thf(f3440,plain,
    spl225_142,
    inference(avatar_split_clause,[],[f1469,f3438]) ).

thf(f1469,plain,
    ! [X2: list_Late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X1),X2)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f839]) ).

thf(f839,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: list_Late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X1),X2)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X0),X2)) ),
    inference(rectify,[],[f184]) ).

thf(f184,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X43: list_Late_freeRes] : ( vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X5),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,X2),X43)) = vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(late_freeRes,sTfun(list_Late_freeRes,list_Late_freeRes),cons_Late_freeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)),vAPP(list_Late_freeRes,list_Late_freeRes,vAPP(list_P227219501e_name,sTfun(list_Late_freeRes,list_Late_freeRes),perm_n808352945reeRes,X5),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_cons__eqvt) ).

thf(f3436,plain,
    spl225_141,
    inference(avatar_split_clause,[],[f1468,f3434]) ).

thf(f3434,plain,
    ( spl225_141
  <=> ! [X2: list_pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] : ( vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X0),vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,X1),X2)) = vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_141])]) ).

thf(f1468,plain,
    ! [X2: list_pi_Rep,X0: list_P227219501e_name,X1: pi_Rep] : ( vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X0),vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,X1),X2)) = vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f838]) ).

thf(f838,plain,
    ! [X0: list_P227219501e_name,X1: pi_Rep,X2: list_pi_Rep] : ( vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X0),vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,X1),X2)) = vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X1)),vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X0),X2)) ),
    inference(rectify,[],[f185]) ).

thf(f185,axiom,
    ! [X5: list_P227219501e_name,X2: pi_Rep,X43: list_pi_Rep] : ( vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X5),vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,X2),X43)) = vAPP(list_pi_Rep,list_pi_Rep,vAPP(pi_Rep,sTfun(list_pi_Rep,list_pi_Rep),cons_pi_Rep,vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2)),vAPP(list_pi_Rep,list_pi_Rep,vAPP(list_P227219501e_name,sTfun(list_pi_Rep,list_pi_Rep),perm_n729617823pi_Rep,X5),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_cons__eqvt) ).

thf(f3432,plain,
    spl225_140,
    inference(avatar_split_clause,[],[f1467,f3430]) ).

thf(f1467,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,X0),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X1),X2)) = vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f837]) ).

thf(f837,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: pi] : ( vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,X0),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X1),X2)) = vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f257]) ).

thf(f257,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: pi] : ( vAPP(produc140253050ect_pi,produc140253050ect_pi,vAPP(list_P227219501e_name,sTfun(produc140253050ect_pi,produc140253050ect_pi),perm_n359102898ect_pi,X5),vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,X2),X22)) = vAPP(pi,produc140253050ect_pi,vAPP(late_subject,sTfun(pi,produc140253050ect_pi),produc324947500ect_pi,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_perm__prod_Osimps) ).

thf(f3428,plain,
    spl225_139,
    inference(avatar_split_clause,[],[f1466,f3426]) ).

thf(f1466,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X0),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X1),X2)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f836]) ).

thf(f836,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: pi] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X0),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X1),X2)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f262]) ).

thf(f262,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X22: pi] : ( vAPP(produc992857746Res_pi,produc992857746Res_pi,vAPP(list_P227219501e_name,sTfun(produc992857746Res_pi,produc992857746Res_pi),perm_n1211707594Res_pi,X5),vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,X2),X22)) = vAPP(pi,produc992857746Res_pi,vAPP(late_freeRes,sTfun(pi,produc992857746Res_pi),produc1177552196Res_pi,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_perm__prod_Osimps) ).

thf(f3424,plain,
    spl225_138,
    inference(avatar_split_clause,[],[f1463,f3422]) ).

thf(f1463,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,X0),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X1),X2)) = vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f833]) ).

thf(f833,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: late_subject] : ( vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,X0),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X1),X2)) = vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(rectify,[],[f253]) ).

thf(f253,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: late_subject] : ( vAPP(produc1359399907ubject,produc1359399907ubject,vAPP(list_P227219501e_name,sTfun(produc1359399907ubject,produc1359399907ubject),perm_n171497387ubject,X5),vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,X2),X22)) = vAPP(late_subject,produc1359399907ubject,vAPP(late_subject,sTfun(late_subject,produc1359399907ubject),produc1465345179ubject,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_perm__prod_Osimps) ).

thf(f3420,plain,
    spl225_137,
    inference(avatar_split_clause,[],[f1462,f3418]) ).

thf(f1462,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X0),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X1),X2)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f832]) ).

thf(f832,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: late_subject] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X0),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X1),X2)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(rectify,[],[f258]) ).

thf(f258,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X22: late_subject] : ( vAPP(produc214645451ubject,produc214645451ubject,vAPP(list_P227219501e_name,sTfun(produc214645451ubject,produc214645451ubject),perm_n1174226579ubject,X5),vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,X2),X22)) = vAPP(late_subject,produc214645451ubject,vAPP(late_freeRes,sTfun(late_subject,produc214645451ubject),produc320590723ubject,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_perm__prod_Osimps) ).

thf(f3416,plain,
    spl225_136,
    inference(avatar_split_clause,[],[f1461,f3414]) ).

thf(f1461,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X0),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X1),X2)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f831]) ).

thf(f831,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: late_freeRes] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X0),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X1),X2)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(rectify,[],[f254]) ).

thf(f254,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: late_freeRes] : ( vAPP(produc355105483reeRes,produc355105483reeRes,vAPP(list_P227219501e_name,sTfun(produc355105483reeRes,produc355105483reeRes),perm_n1314686611reeRes,X5),vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,X2),X22)) = vAPP(late_freeRes,produc355105483reeRes,vAPP(late_subject,sTfun(late_freeRes,produc355105483reeRes),produc242091907reeRes,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_perm__prod_Osimps) ).

thf(f3412,plain,
    ( spl225_135
    | ~ spl225_8
    | ~ spl225_33 ),
    inference(avatar_split_clause,[],[f2439,f2431,f2296,f3410]) ).

thf(f3410,plain,
    ( spl225_135
  <=> ! [X0: list_P227219501e_name > $o] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_135])]) ).

thf(f2439,plain,
    ( ! [X0: list_P227219501e_name > $o] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) )
    | ~ spl225_8
    | ~ spl225_33 ),
    inference(trivial_inequality_removal,[],[f2438]) ).

thf(f2438,plain,
    ( ! [X0: list_P227219501e_name > $o] :
        ( ( $true != $true )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
        | ( $false = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) )
    | ~ spl225_8
    | ~ spl225_33 ),
    inference(superposition,[],[f2432,f2297]) ).

thf(f3408,plain,
    spl225_134,
    inference(avatar_split_clause,[],[f1460,f3406]) ).

thf(f1460,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X1),X2)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f830]) ).

thf(f830,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X0),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X1),X2)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(rectify,[],[f259]) ).

thf(f259,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X22: late_freeRes] : ( vAPP(produc1357834675reeRes,produc1357834675reeRes,vAPP(list_P227219501e_name,sTfun(produc1357834675reeRes,produc1357834675reeRes),perm_n169932155reeRes,X5),vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,X2),X22)) = vAPP(late_freeRes,produc1357834675reeRes,vAPP(late_freeRes,sTfun(late_freeRes,produc1357834675reeRes),produc1244821099reeRes,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_perm__prod_Osimps) ).

thf(f3404,plain,
    spl225_133,
    inference(avatar_split_clause,[],[f1459,f3402]) ).

thf(f1459,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: late_subject] : ( vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,X0),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X1),X2)) = vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f829]) ).

thf(f829,plain,
    ! [X0: list_P227219501e_name,X1: late_subject,X2: pi_Rep] : ( vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,X0),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X1),X2)) = vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(rectify,[],[f255]) ).

thf(f255,axiom,
    ! [X5: list_P227219501e_name,X2: late_subject,X22: pi_Rep] : ( vAPP(produc257012921pi_Rep,produc257012921pi_Rep,vAPP(list_P227219501e_name,sTfun(produc257012921pi_Rep,produc257012921pi_Rep),perm_n1467004033pi_Rep,X5),vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,X2),X22)) = vAPP(pi_Rep,produc257012921pi_Rep,vAPP(late_subject,sTfun(pi_Rep,produc257012921pi_Rep),produc843063281pi_Rep,vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_perm__prod_Osimps) ).

thf(f3400,plain,
    spl225_132,
    inference(avatar_split_clause,[],[f1458,f3398]) ).

thf(f1458,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: late_freeRes] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X0),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X1),X2)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f828]) ).

thf(f828,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes,X2: pi_Rep] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X0),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X1),X2)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X1)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(rectify,[],[f260]) ).

thf(f260,axiom,
    ! [X5: list_P227219501e_name,X2: late_freeRes,X22: pi_Rep] : ( vAPP(produc1777919905pi_Rep,produc1777919905pi_Rep,vAPP(list_P227219501e_name,sTfun(produc1777919905pi_Rep,produc1777919905pi_Rep),perm_n840427369pi_Rep,X5),vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,X2),X22)) = vAPP(pi_Rep,produc1777919905pi_Rep,vAPP(late_freeRes,sTfun(pi_Rep,produc1777919905pi_Rep),produc216486617pi_Rep,vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_perm__prod_Osimps) ).

thf(f3394,plain,
    spl225_131,
    inference(avatar_split_clause,[],[f1580,f3392]) ).

thf(f3392,plain,
    ( spl225_131
  <=> ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X1) )
        | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_131])]) ).

thf(f1580,plain,
    ! [X2: pi,X0: set_Pr1834926343_pi_pi,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(set_Pr1834926343_pi_pi,name,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,name),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,name)),sK99,X2),X1),X0)),X1) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,vAPP(pi,sTfun(set_Pr1834926343_pi_pi,$o),vAPP(pi,sTfun(pi,sTfun(set_Pr1834926343_pi_pi,$o)),sP0,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1252]) ).

thf(f3390,plain,
    spl225_130,
    inference(avatar_split_clause,[],[f1382,f3388]) ).

thf(f3388,plain,
    ( spl225_130
  <=> ! [X0: produc890461031e_name] :
        ( ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK26,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK27,X0))),vAPP(produc890461031e_name,list_P227219501e_name,sK28,X0)) = X0 )
        | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK29,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_130])]) ).

thf(f1382,plain,
    ! [X0: produc890461031e_name] :
      ( ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK26,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK27,X0))),vAPP(produc890461031e_name,list_P227219501e_name,sK28,X0)) = X0 )
      | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK29,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1178]) ).

thf(f1178,plain,
    ! [X0: produc890461031e_name] :
      ( ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK26,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK27,X0))),vAPP(produc890461031e_name,list_P227219501e_name,sK28,X0)) = X0 )
      | ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK29,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29])],[f1175,f1177,f1176]) ).

thf(f1176,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2)),X3) = X0 )
     => ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(produc890461031e_name,produc367475239e_name,sK26,X0)),vAPP(produc890461031e_name,list_P227219501e_name,sK27,X0))),vAPP(produc890461031e_name,list_P227219501e_name,sK28,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1177,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X4) = X0 )
     => ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),vAPP(produc890461031e_name,list_P227219501e_name,sK29,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1175,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name,X3: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2)),X3) = X0 )
      | ? [X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X4) = X0 ) ),
    inference(rectify,[],[f925]) ).

thf(f925,plain,
    ! [X0: produc890461031e_name] :
      ( ? [X2: produc367475239e_name,X3: list_P227219501e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),X4) = X0 )
      | ? [X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X1) = X0 ) ),
    inference(ennf_transformation,[],[f782]) ).

thf(f782,plain,
    ! [X0: produc890461031e_name] :
      ( ! [X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X1) != X0 )
     => ~ ! [X2: produc367475239e_name,X3: list_P227219501e_name,X4: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)),X4) != X0 ) ),
    inference(rectify,[],[f208]) ).

thf(f208,axiom,
    ! [X2: produc890461031e_name] :
      ( ! [X64: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,nil_Pr743626285e_name),X64) != X2 )
     => ~ ! [X63: produc367475239e_name,X65: list_P227219501e_name,X64: list_P227219501e_name] : ( vAPP(list_P227219501e_name,produc890461031e_name,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,produc890461031e_name),produc208131031e_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X63),X65)),X64) != X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_splice_Ocases) ).

thf(f3384,plain,
    spl225_129,
    inference(avatar_split_clause,[],[f1784,f3382]) ).

thf(f3382,plain,
    ( spl225_129
  <=> ! [X3: pi,X4: late_freeRes,X0: name,X5: pi,X2: name,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_129])]) ).

thf(f1784,plain,
    ! [X2: name,X3: pi,X0: name,X1: name,X4: late_freeRes,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)) ),
    inference(cnf_transformation,[],[f914]) ).

thf(f914,plain,
    ! [X0: name,X1: name,X2: name,X3: pi,X4: late_freeRes,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)) ),
    inference(flattening,[],[f712]) ).

thf(f712,plain,
    ! [X0: name,X1: name,X2: name,X3: pi,X4: late_freeRes,X5: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)) ),
    inference(fool_elimination,[],[f711]) ).

thf(f711,plain,
    ! [X0: name,X1: name,X2: name,X3: pi,X4: late_freeRes,X5: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X1),X2),X3))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X4),X5)),
    inference(rectify,[],[f309]) ).

thf(f309,axiom,
    ! [X2: name,X0: name,X22: name,X19: pi,X30: late_freeRes,X31: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X22),X19))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_resInputFreeTrans) ).

thf(f3364,plain,
    spl225_128,
    inference(avatar_split_clause,[],[f1435,f3362]) ).

thf(f3362,plain,
    ( spl225_128
  <=> ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
        | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
        | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_128])]) ).

thf(f1435,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK75,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK76,X0)),nil_Pr743626285e_name)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1229]) ).

thf(f3314,plain,
    ( spl225_127
    | ~ spl225_90 ),
    inference(avatar_split_clause,[],[f2850,f2802,f3312]) ).

thf(f2802,plain,
    ( spl225_90
  <=> ! [X0: late_subject,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X1) != X0 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_90])]) ).

thf(f2850,plain,
    ( ! [X0: name] : ( vAPP(name,late_subject,late_InputS,X0) = vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,vAPP(name,late_subject,late_InputS,X0))) )
    | ~ spl225_90 ),
    inference(equality_resolution,[],[f2803]) ).

thf(f2803,plain,
    ( ! [X0: late_subject,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X1) != X0 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) )
    | ~ spl225_90 ),
    inference(avatar_component_clause,[],[f2802]) ).

thf(f3262,plain,
    spl225_126,
    inference(avatar_split_clause,[],[f1833,f3260]) ).

thf(f1833,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,X1,X2)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1455,f1358]) ).

thf(f1455,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,X1,X2)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(cnf_transformation,[],[f825]) ).

thf(f825,plain,
    ! [X0: list_P227219501e_name,X1: name > late_subject,X2: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,X1,X2)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(rectify,[],[f139]) ).

thf(f139,axiom,
    ! [X5: list_P227219501e_name,X35: name > late_subject,X2: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(name,late_subject,X35,X2)) = vAPP(name,late_subject,vAPP(sTfun(name,late_subject),sTfun(name,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_subject),sTfun(name,late_subject)),perm_n1387060402ubject,X5),X35),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_perm__app) ).

thf(f3258,plain,
    spl225_125,
    inference(avatar_split_clause,[],[f1832,f3256]) ).

thf(f1832,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,X1,X2)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X2)) ),
    inference(definition_unfolding,[],[f1450,f1358]) ).

thf(f1450,plain,
    ! [X2: name,X0: list_P227219501e_name,X1: name > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,X1,X2)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(cnf_transformation,[],[f820]) ).

thf(f820,plain,
    ! [X0: list_P227219501e_name,X1: name > late_freeRes,X2: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(name,late_freeRes,X1,X2)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,X0),X1),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X2)) ),
    inference(rectify,[],[f144]) ).

thf(f144,axiom,
    ! [X5: list_P227219501e_name,X35: name > late_freeRes,X2: name] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(name,late_freeRes,X35,X2)) = vAPP(name,late_freeRes,vAPP(sTfun(name,late_freeRes),sTfun(name,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(name,late_freeRes),sTfun(name,late_freeRes)),perm_n382765978reeRes,X5),X35),vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_perm__app) ).

thf(f3254,plain,
    spl225_124,
    inference(avatar_split_clause,[],[f1718,f3252]) ).

thf(f1718,plain,
    ! [X2: pi,X3: name,X0: pi,X1: late_freeRes] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1082]) ).

thf(f1082,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(flattening,[],[f1081]) ).

thf(f1081,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(ennf_transformation,[],[f662]) ).

thf(f662,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
       => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) ) ) ),
    inference(fool_elimination,[],[f661]) ).

thf(f661,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0)
       => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X2) ) ),
    inference(rectify,[],[f106]) ).

thf(f106,axiom,
    ! [X19: pi,X30: late_freeRes,X31: pi,X22: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X19)
       => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_freshFreeDerivative_I2_J) ).

thf(f3250,plain,
    spl225_123,
    inference(avatar_split_clause,[],[f1717,f3248]) ).

thf(f1717,plain,
    ! [X2: pi,X3: name,X0: pi,X1: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1080]) ).

thf(f1080,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(flattening,[],[f1079]) ).

thf(f1079,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(ennf_transformation,[],[f660]) ).

thf(f660,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0) )
       => ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) ) ) ),
    inference(fool_elimination,[],[f659]) ).

thf(f659,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X3),X0)
       => vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X3),X1) ) ),
    inference(rectify,[],[f223]) ).

thf(f223,axiom,
    ! [X19: pi,X30: late_freeRes,X31: pi,X22: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31))
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X22),X19)
       => vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X22),X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_freshFreeDerivative_I1_J) ).

thf(f3246,plain,
    spl225_122,
    inference(avatar_split_clause,[],[f1622,f3244]) ).

thf(f3244,plain,
    ( spl225_122
  <=> ! [X2: pi,X0: name,X1: list_P227219501e_name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) )
        | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_122])]) ).

thf(f1622,plain,
    ! [X2: pi,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1015]) ).

thf(f1015,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(flattening,[],[f1014]) ).

thf(f1014,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) )
      | ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f550]) ).

thf(f550,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) )
     => ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
       => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) ) ) ),
    inference(fool_elimination,[],[f549]) ).

thf(f549,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1)
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2)
       => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2)) ) ),
    inference(rectify,[],[f81]) ).

thf(f81,axiom,
    ! [X0: name,X5: list_P227219501e_name,X2: pi] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X5)
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2)
       => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_fresh__perm__app) ).

thf(f3242,plain,
    spl225_121,
    inference(avatar_split_clause,[],[f1620,f3240]) ).

thf(f3240,plain,
    ( spl225_121
  <=> ! [X2: late_subject,X0: name,X1: list_P227219501e_name] :
        ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) )
        | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_121])]) ).

thf(f1620,plain,
    ! [X2: late_subject,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1011]) ).

thf(f1011,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_subject] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(flattening,[],[f1010]) ).

thf(f1010,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_subject] :
      ( ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) )
      | ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f546]) ).

thf(f546,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_subject] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) )
     => ( ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2) = $true )
       => ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) ) ) ),
    inference(fool_elimination,[],[f545]) ).

thf(f545,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_subject] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1)
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2)
       => vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2)) ) ),
    inference(rectify,[],[f78]) ).

thf(f78,axiom,
    ! [X0: name,X5: list_P227219501e_name,X2: late_subject] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X5)
     => ( vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),X2)
       => vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X0),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_fresh__perm__app) ).

thf(f3238,plain,
    spl225_120,
    inference(avatar_split_clause,[],[f1619,f3236]) ).

thf(f3236,plain,
    ( spl225_120
  <=> ! [X2: late_freeRes,X0: name,X1: list_P227219501e_name] :
        ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) )
        | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_120])]) ).

thf(f1619,plain,
    ! [X2: late_freeRes,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1009]) ).

thf(f1009,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(flattening,[],[f1008]) ).

thf(f1008,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) )
      | ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f544]) ).

thf(f544,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_freeRes] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) )
     => ( ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2) = $true )
       => ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) ) ) ),
    inference(fool_elimination,[],[f543]) ).

thf(f543,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: late_freeRes] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1)
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2)
       => vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2)) ) ),
    inference(rectify,[],[f79]) ).

thf(f79,axiom,
    ! [X0: name,X5: list_P227219501e_name,X2: late_freeRes] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X5)
     => ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),X2)
       => vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_fresh__perm__app) ).

thf(f3234,plain,
    spl225_119,
    inference(avatar_split_clause,[],[f1618,f3232]) ).

thf(f3232,plain,
    ( spl225_119
  <=> ! [X2: pi_Rep,X0: name,X1: list_P227219501e_name] :
        ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) )
        | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
        | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_119])]) ).

thf(f1618,plain,
    ! [X2: pi_Rep,X0: name,X1: list_P227219501e_name] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(cnf_transformation,[],[f1007]) ).

thf(f1007,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi_Rep] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(flattening,[],[f1006]) ).

thf(f1006,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi_Rep] :
      ( ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) )
      | ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) != $true )
      | ( $true != vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) ) ),
    inference(ennf_transformation,[],[f542]) ).

thf(f542,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi_Rep] :
      ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1) )
     => ( ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2) = $true )
       => ( $true = vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) ) ) ),
    inference(fool_elimination,[],[f541]) ).

thf(f541,plain,
    ! [X0: name,X1: list_P227219501e_name,X2: pi_Rep] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X1)
     => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2)
       => vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2)) ) ),
    inference(rectify,[],[f77]) ).

thf(f77,axiom,
    ! [X0: name,X5: list_P227219501e_name,X2: pi_Rep] :
      ( vAPP(list_P227219501e_name,$o,vAPP(name,sTfun(list_P227219501e_name,$o),fresh_922791155e_name,X0),X5)
     => ( vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),X2)
       => vAPP(pi_Rep,$o,vAPP(name,sTfun(pi_Rep,$o),fresh_name_pi_Rep,X0),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_fresh__perm__app) ).

thf(f3230,plain,
    spl225_118,
    inference(avatar_split_clause,[],[f1456,f3228]) ).

thf(f1456,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi,late_subject,X1,X2)) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f826]) ).

thf(f826,plain,
    ! [X0: list_P227219501e_name,X1: pi > late_subject,X2: pi] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi,late_subject,X1,X2)) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f140]) ).

thf(f140,axiom,
    ! [X5: list_P227219501e_name,X35: pi > late_subject,X2: pi] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(pi,late_subject,X35,X2)) = vAPP(pi,late_subject,vAPP(sTfun(pi,late_subject),sTfun(pi,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_subject),sTfun(pi,late_subject)),perm_n190055296ubject,X5),X35),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_perm__app) ).

thf(f3226,plain,
    spl225_117,
    inference(avatar_split_clause,[],[f1454,f3224]) ).

thf(f1454,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,X1,X2)) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f824]) ).

thf(f824,plain,
    ! [X0: list_P227219501e_name,X1: late_subject > late_subject,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_subject,late_subject,X1,X2)) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(rectify,[],[f136]) ).

thf(f136,axiom,
    ! [X5: list_P227219501e_name,X35: late_subject > late_subject,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(late_subject,late_subject,X35,X2)) = vAPP(late_subject,late_subject,vAPP(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_subject),sTfun(late_subject,late_subject)),perm_n1447856217ubject,X5),X35),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_perm__app) ).

thf(f3222,plain,
    spl225_116,
    inference(avatar_split_clause,[],[f1453,f3220]) ).

thf(f1453,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_freeRes,late_subject,X1,X2)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f823]) ).

thf(f823,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes > late_subject,X2: late_freeRes] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(late_freeRes,late_subject,X1,X2)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(rectify,[],[f137]) ).

thf(f137,axiom,
    ! [X5: list_P227219501e_name,X35: late_freeRes > late_subject,X2: late_freeRes] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(late_freeRes,late_subject,X35,X2)) = vAPP(late_freeRes,late_subject,vAPP(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_subject),sTfun(late_freeRes,late_subject)),perm_n303101761ubject,X5),X35),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_perm__app) ).

thf(f3099,plain,
    ( ~ spl225_22
    | ~ spl225_108 ),
    inference(avatar_contradiction_clause,[],[f3098]) ).

thf(f3098,plain,
    ( $false
    | ~ spl225_22
    | ~ spl225_108 ),
    inference(trivial_inequality_removal,[],[f3084]) ).

thf(f3084,plain,
    ( ( nil_Pr743626285e_name != nil_Pr743626285e_name )
    | ~ spl225_22
    | ~ spl225_108 ),
    inference(superposition,[],[f2382,f2997]) ).

thf(f2997,plain,
    ( ! [X0: list_P227219501e_name] : ( nil_Pr743626285e_name = X0 )
    | ~ spl225_108 ),
    inference(avatar_component_clause,[],[f2996]) ).

thf(f2996,plain,
    ( spl225_108
  <=> ! [X0: list_P227219501e_name] : ( nil_Pr743626285e_name = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_108])]) ).

thf(f2382,plain,
    ( ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( nil_Pr743626285e_name != vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) )
    | ~ spl225_22 ),
    inference(avatar_component_clause,[],[f2381]) ).

thf(f2381,plain,
    ( spl225_22
  <=> ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( nil_Pr743626285e_name != vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_22])]) ).

thf(f3062,plain,
    spl225_115,
    inference(avatar_split_clause,[],[f1452,f3060]) ).

thf(f1452,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep > late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi_Rep,late_subject,X1,X2)) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f822]) ).

thf(f822,plain,
    ! [X0: list_P227219501e_name,X1: pi_Rep > late_subject,X2: pi_Rep] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(pi_Rep,late_subject,X1,X2)) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(rectify,[],[f138]) ).

thf(f138,axiom,
    ! [X5: list_P227219501e_name,X35: pi_Rep > late_subject,X2: pi_Rep] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(pi_Rep,late_subject,X35,X2)) = vAPP(pi_Rep,late_subject,vAPP(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_subject),sTfun(pi_Rep,late_subject)),perm_n698371375ubject,X5),X35),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_perm__app) ).

thf(f3058,plain,
    spl225_114,
    inference(avatar_split_clause,[],[f1451,f3056]) ).

thf(f1451,plain,
    ! [X2: pi,X0: list_P227219501e_name,X1: pi > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi,late_freeRes,X1,X2)) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(cnf_transformation,[],[f821]) ).

thf(f821,plain,
    ! [X0: list_P227219501e_name,X1: pi > late_freeRes,X2: pi] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi,late_freeRes,X1,X2)) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,X0),X1),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X0),X2)) ),
    inference(rectify,[],[f145]) ).

thf(f145,axiom,
    ! [X5: list_P227219501e_name,X35: pi > late_freeRes,X2: pi] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(pi,late_freeRes,X35,X2)) = vAPP(pi,late_freeRes,vAPP(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi,late_freeRes),sTfun(pi,late_freeRes)),perm_n1333244520reeRes,X5),X35),vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_perm__app) ).

thf(f3054,plain,
    spl225_113,
    inference(avatar_split_clause,[],[f1449,f3052]) ).

thf(f1449,plain,
    ! [X2: late_subject,X0: list_P227219501e_name,X1: late_subject > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_subject,late_freeRes,X1,X2)) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(cnf_transformation,[],[f819]) ).

thf(f819,plain,
    ! [X0: list_P227219501e_name,X1: late_subject > late_freeRes,X2: late_subject] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_subject,late_freeRes,X1,X2)) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,X0),X1),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),X2)) ),
    inference(rectify,[],[f141]) ).

thf(f141,axiom,
    ! [X5: list_P227219501e_name,X35: late_subject > late_freeRes,X2: late_subject] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(late_subject,late_freeRes,X35,X2)) = vAPP(late_subject,late_freeRes,vAPP(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_subject,late_freeRes),sTfun(late_subject,late_freeRes)),perm_n443561793reeRes,X5),X35),vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_perm__app) ).

thf(f3050,plain,
    spl225_112,
    inference(avatar_split_clause,[],[f1448,f3048]) ).

thf(f1448,plain,
    ! [X2: late_freeRes,X0: list_P227219501e_name,X1: late_freeRes > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,X1,X2)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(cnf_transformation,[],[f818]) ).

thf(f818,plain,
    ! [X0: list_P227219501e_name,X1: late_freeRes > late_freeRes,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(late_freeRes,late_freeRes,X1,X2)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X0),X1),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),X2)) ),
    inference(rectify,[],[f142]) ).

thf(f142,axiom,
    ! [X5: list_P227219501e_name,X35: late_freeRes > late_freeRes,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(late_freeRes,late_freeRes,X35,X2)) = vAPP(late_freeRes,late_freeRes,vAPP(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(late_freeRes,late_freeRes),sTfun(late_freeRes,late_freeRes)),perm_n1446290985reeRes,X5),X35),vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_perm__app) ).

thf(f3046,plain,
    spl225_111,
    inference(avatar_split_clause,[],[f1447,f3044]) ).

thf(f1447,plain,
    ! [X2: pi_Rep,X0: list_P227219501e_name,X1: pi_Rep > late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi_Rep,late_freeRes,X1,X2)) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(cnf_transformation,[],[f817]) ).

thf(f817,plain,
    ! [X0: list_P227219501e_name,X1: pi_Rep > late_freeRes,X2: pi_Rep] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),vAPP(pi_Rep,late_freeRes,X1,X2)) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,X0),X1),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X0),X2)) ),
    inference(rectify,[],[f143]) ).

thf(f143,axiom,
    ! [X5: list_P227219501e_name,X35: pi_Rep > late_freeRes,X2: pi_Rep] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(pi_Rep,late_freeRes,X35,X2)) = vAPP(pi_Rep,late_freeRes,vAPP(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes),vAPP(list_P227219501e_name,sTfun(sTfun(pi_Rep,late_freeRes),sTfun(pi_Rep,late_freeRes)),perm_n1841560599reeRes,X5),X35),vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_perm__app) ).

thf(f3018,plain,
    spl225_110,
    inference(avatar_split_clause,[],[f1714,f3016]) ).

thf(f1714,plain,
    ! [X2: name,X3: name,X0: name,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) )
      | ( X0 = X2 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1075]) ).

thf(f1075,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) )
      | ( X0 = X2 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(flattening,[],[f1074]) ).

thf(f1074,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) )
      | ( X0 = X2 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f654]) ).

thf(f654,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( ( X0 != X2 )
       => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) ) ) ),
    inference(fool_elimination,[],[f653]) ).

thf(f653,plain,
    ! [X0: name,X1: pi,X2: name,X3: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( ( X0 != X2 )
       => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X3),X2)) ) ),
    inference(rectify,[],[f322]) ).

thf(f322,axiom,
    ! [X0: name,X19: pi,X32: name,X1: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X19)
     => ( ( X0 != X32 )
       => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X1),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_fresh__fact1) ).

thf(f3004,plain,
    spl225_109,
    inference(avatar_split_clause,[],[f1615,f3002]) ).

thf(f1615,plain,
    ! [X2: list_P227219501e_name,X0: pi,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ),
    inference(cnf_transformation,[],[f1001]) ).

thf(f1001,plain,
    ! [X0: pi,X1: late_residual,X2: list_P227219501e_name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ),
    inference(ennf_transformation,[],[f536]) ).

thf(f536,plain,
    ! [X0: pi,X1: late_residual,X2: list_P227219501e_name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) )
     => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) ) ),
    inference(fool_elimination,[],[f535]) ).

thf(f535,plain,
    ! [X0: pi,X1: late_residual,X2: list_P227219501e_name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1)
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X2),X0)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X2),X1)) ),
    inference(rectify,[],[f42]) ).

thf(f42,axiom,
    ! [X3: pi,X4: late_residual,X5: list_P227219501e_name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X3),X4)
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X3)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_eqvt) ).

thf(f2998,plain,
    ( spl225_107
    | spl225_108
    | ~ spl225_63 ),
    inference(avatar_split_clause,[],[f2604,f2588,f2996,f2992]) ).

thf(f2992,plain,
    ( spl225_107
  <=> ( nil_Pr743626285e_name = vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_107])]) ).

thf(f2604,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( nil_Pr743626285e_name = X0 )
        | ( nil_Pr743626285e_name = vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name)) ) )
    | ~ spl225_63 ),
    inference(equality_proxy_clausification,[],[f2595]) ).

thf(f2595,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name),X0) )
        | ( nil_Pr743626285e_name = vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),nil_Pr743626285e_name)) ) )
    | ~ spl225_63 ),
    inference(leibniz_equality_elimination,[],[f2589]) ).

thf(f2990,plain,
    spl225_106,
    inference(avatar_split_clause,[],[f1903,f2987]) ).

thf(f1903,plain,
    $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,b)),z),q2)),
    inference(definition_unfolding,[],[f1812,f1356]) ).

thf(f1356,plain,
    aa = b,
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    aa = b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062) ).

thf(f1812,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,aa)),z),q2)) = $true,
    inference(cnf_transformation,[],[f764]) ).

thf(f764,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,aa)),z),q2)) = $true,
    inference(fool_elimination,[],[f763]) ).

thf(f763,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,aa)),z),q2)),
    inference(rectify,[],[f173]) ).

thf(f173,axiom,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_BoundOutputS,aa)),z),q2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_cClose1_Ohyps_I2_J) ).

thf(f2930,plain,
    spl225_105,
    inference(avatar_split_clause,[],[f1884,f2928]) ).

thf(f1884,plain,
    ! [X2: name,X3: name,X0: $o,X1: list_P227219501e_name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) )
      | ( $true = X0 ) ),
    inference(definition_unfolding,[],[f1680,f1358,f1358]) ).

thf(f1680,plain,
    ! [X2: name,X3: name,X0: $o,X1: list_P227219501e_name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[],[f1045]) ).

thf(f1045,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: name,X3: name] :
      ( ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) )
        | ( $true = X0 ) )
      & ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) )
        | ( $true != X0 ) ) ),
    inference(ennf_transformation,[],[f895]) ).

thf(f895,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: name,X3: name] :
      ( ( ( $true != X0 )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) ) ) ),
    inference(flattening,[],[f618]) ).

thf(f618,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: name,X3: name] :
      ( ( ( $true != X0 )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f617]) ).

thf(f617,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: name,X3: name] :
      ( ( ~ X0
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X3) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) ) )
      & ( X0
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X1),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X0),X2),X3)) ) ) ),
    inference(rectify,[],[f249]) ).

thf(f249,axiom,
    ! [X32: $o,X5: list_P227219501e_name,X2: name,X22: name] :
      ( ( ~ X32
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X22) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X32),X2),X22)) ) )
      & ( X32
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X2) = vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,X32),X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_abs__fun__if) ).

thf(f2926,plain,
    spl225_104,
    inference(avatar_split_clause,[],[f1682,f2924]) ).

thf(f1682,plain,
    ! [X2: pi,X3: pi,X0: $o,X1: list_P227219501e_name] :
      ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[],[f1046]) ).

thf(f1046,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi,X3: pi] :
      ( ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) )
        | ( $true = X0 ) )
      & ( ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) )
        | ( $true != X0 ) ) ),
    inference(ennf_transformation,[],[f896]) ).

thf(f896,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi,X3: pi] :
      ( ( ( $true != X0 )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) ) ) ),
    inference(flattening,[],[f620]) ).

thf(f620,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi,X3: pi] :
      ( ( ( $true != X0 )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f619]) ).

thf(f619,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi,X3: pi] :
      ( ( ~ X0
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X3) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) ) )
      & ( X0
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X0),X2),X3)) ) ) ),
    inference(rectify,[],[f250]) ).

thf(f250,axiom,
    ! [X32: $o,X5: list_P227219501e_name,X2: pi,X22: pi] :
      ( ( ~ X32
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X22) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X32),X2),X22)) ) )
      & ( X32
       => ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),X2) = vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,X5),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,X32),X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_abs__fun__if) ).

thf(f2922,plain,
    spl225_103,
    inference(avatar_split_clause,[],[f1678,f2920]) ).

thf(f1678,plain,
    ! [X2: late_subject,X3: late_subject,X0: $o,X1: list_P227219501e_name] :
      ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[],[f1044]) ).

thf(f1044,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_subject,X3: late_subject] :
      ( ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) )
        | ( $true = X0 ) )
      & ( ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) )
        | ( $true != X0 ) ) ),
    inference(ennf_transformation,[],[f894]) ).

thf(f894,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_subject,X3: late_subject] :
      ( ( ( $true != X0 )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) ) ) ),
    inference(flattening,[],[f616]) ).

thf(f616,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_subject,X3: late_subject] :
      ( ( ( $true != X0 )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f615]) ).

thf(f615,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_subject,X3: late_subject] :
      ( ( ~ X0
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X3) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) ) )
      & ( X0
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X1),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X0),X2),X3)) ) ) ),
    inference(rectify,[],[f246]) ).

thf(f246,axiom,
    ! [X32: $o,X5: list_P227219501e_name,X2: late_subject,X22: late_subject] :
      ( ( ~ X32
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X22) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X32),X2),X22)) ) )
      & ( X32
       => ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),X2) = vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,X32),X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_abs__fun__if) ).

thf(f2918,plain,
    spl225_102,
    inference(avatar_split_clause,[],[f1676,f2916]) ).

thf(f1676,plain,
    ! [X2: late_freeRes,X3: late_freeRes,X0: $o,X1: list_P227219501e_name] :
      ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[],[f1043]) ).

thf(f1043,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_freeRes,X3: late_freeRes] :
      ( ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) )
        | ( $true = X0 ) )
      & ( ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) )
        | ( $true != X0 ) ) ),
    inference(ennf_transformation,[],[f893]) ).

thf(f893,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_freeRes,X3: late_freeRes] :
      ( ( ( $true != X0 )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) ) ) ),
    inference(flattening,[],[f614]) ).

thf(f614,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_freeRes,X3: late_freeRes] :
      ( ( ( $true != X0 )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f613]) ).

thf(f613,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: late_freeRes,X3: late_freeRes] :
      ( ( ~ X0
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X3) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) ) )
      & ( X0
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X1),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X0),X2),X3)) ) ) ),
    inference(rectify,[],[f247]) ).

thf(f247,axiom,
    ! [X32: $o,X5: list_P227219501e_name,X2: late_freeRes,X22: late_freeRes] :
      ( ( ~ X32
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X22) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X32),X2),X22)) ) )
      & ( X32
       => ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),X2) = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,X32),X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_abs__fun__if) ).

thf(f2914,plain,
    ( spl225_101
    | ~ spl225_33 ),
    inference(avatar_split_clause,[],[f2441,f2431,f2912]) ).

thf(f2912,plain,
    ( spl225_101
  <=> ! [X0: list_P227219501e_name] :
        ( ( vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)) != X0 )
        | ( nil_Pr743626285e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_101])]) ).

thf(f2441,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)) != X0 )
        | ( nil_Pr743626285e_name = X0 ) )
    | ~ spl225_33 ),
    inference(equality_proxy_clausification,[],[f2440]) ).

thf(f2440,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0)) != X0 )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),nil_Pr743626285e_name) ) )
    | ~ spl225_33 ),
    inference(equality_proxy_clausification,[],[f2437]) ).

thf(f2437,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( $true != vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0))) )
        | ( $true = vAPP(list_P227219501e_name,$o,vAPP(list_P227219501e_name,sTfun(list_P227219501e_name,$o),vEQ(list_P227219501e_name),X0),nil_Pr743626285e_name) ) )
    | ~ spl225_33 ),
    inference(primitive_instantiation,[],[f2432]) ).

thf(f2910,plain,
    spl225_100,
    inference(avatar_split_clause,[],[f1674,f2908]) ).

thf(f1674,plain,
    ! [X2: pi_Rep,X3: pi_Rep,X0: $o,X1: list_P227219501e_name] :
      ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[],[f1042]) ).

thf(f1042,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi_Rep,X3: pi_Rep] :
      ( ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) )
        | ( $true = X0 ) )
      & ( ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) )
        | ( $true != X0 ) ) ),
    inference(ennf_transformation,[],[f892]) ).

thf(f892,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi_Rep,X3: pi_Rep] :
      ( ( ( $true != X0 )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) ) ) ),
    inference(flattening,[],[f612]) ).

thf(f612,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi_Rep,X3: pi_Rep] :
      ( ( ( $true != X0 )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) ) )
      & ( ( $true = X0 )
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) ) ) ),
    inference(fool_elimination,[],[f611]) ).

thf(f611,plain,
    ! [X0: $o,X1: list_P227219501e_name,X2: pi_Rep,X3: pi_Rep] :
      ( ( ~ X0
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X3) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) ) )
      & ( X0
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X1),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X0),X2),X3)) ) ) ),
    inference(rectify,[],[f248]) ).

thf(f248,axiom,
    ! [X32: $o,X5: list_P227219501e_name,X2: pi_Rep,X22: pi_Rep] :
      ( ( ~ X32
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X22) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X32),X2),X22)) ) )
      & ( X32
       => ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),X2) = vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,X5),vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,X32),X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_abs__fun__if) ).

thf(f2869,plain,
    spl225_99,
    inference(avatar_split_clause,[],[f1902,f2866]) ).

thf(f1902,plain,
    $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),pxQ)),
    inference(definition_unfolding,[],[f1811,f1355]) ).

thf(f1355,plain,
    alpha = late_TauR,
    inference(cnf_transformation,[],[f9]) ).

thf(f9,axiom,
    alpha = late_TauR,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_cClose1_Ohyps_I14_J) ).

thf(f1811,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),pxQ)) = $true,
    inference(cnf_transformation,[],[f762]) ).

thf(f762,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),pxQ)) = $true,
    inference(fool_elimination,[],[f761]) ).

thf(f761,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),pxQ)),
    inference(rectify,[],[f275]) ).

thf(f275,axiom,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q))),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),pxQ)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Free_Ohyps) ).

thf(f2864,plain,
    spl225_98,
    inference(avatar_split_clause,[],[f1446,f2862]) ).

thf(f2860,plain,
    spl225_97,
    inference(avatar_split_clause,[],[f1439,f2858]) ).

thf(f1439,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1231]) ).

thf(f1231,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f950,f1230]) ).

thf(f1230,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ? [X2: produc367475239e_name,X3: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X3) ) )
     => ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(sTfun(list_P227219501e_name,$o),produc367475239e_name,sK77,X0)),vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0))) )
        & ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f950,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ? [X2: produc367475239e_name,X3: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X3) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(flattening,[],[f949]) ).

thf(f949,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ? [X2: produc367475239e_name,X3: list_P227219501e_name] :
          ( ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) )
          & ( $true = vAPP(list_P227219501e_name,$o,X0,X3) ) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(ennf_transformation,[],[f432]) ).

thf(f432,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
     => ( ! [X2: produc367475239e_name,X3: list_P227219501e_name] :
            ( ( $true = vAPP(list_P227219501e_name,$o,X0,X3) )
           => ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) ) )
       => ( $true = vAPP(list_P227219501e_name,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f431]) ).

thf(f431,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name)
     => ( ! [X2: produc367475239e_name,X3: list_P227219501e_name] :
            ( vAPP(list_P227219501e_name,$o,X0,X3)
           => vAPP(list_P227219501e_name,$o,X0,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X3)) )
       => vAPP(list_P227219501e_name,$o,X0,X1) ) ),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    ! [X19: list_P227219501e_name > $o,X76: list_P227219501e_name] :
      ( vAPP(list_P227219501e_name,$o,X19,nil_Pr743626285e_name)
     => ( ! [X79: produc367475239e_name,X80: list_P227219501e_name] :
            ( vAPP(list_P227219501e_name,$o,X19,X80)
           => vAPP(list_P227219501e_name,$o,X19,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X79),X80)) )
       => vAPP(list_P227219501e_name,$o,X19,X76) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_list_Oinducts) ).

thf(f2856,plain,
    spl225_96,
    inference(avatar_split_clause,[],[f1433,f2854]) ).

thf(f1433,plain,
    ! [X0: late_freeRes > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,X0,X1) )
      | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
      | ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) ),
    inference(cnf_transformation,[],[f1221]) ).

thf(f1221,plain,
    ! [X0: late_freeRes > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,X0,X1) )
      | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
      | ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f944,f1220]) ).

thf(f1220,plain,
    ! [X0: late_freeRes > $o] :
      ( ? [X2: name,X3: name] : ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) )
     => ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(sTfun(late_freeRes,$o),name,sK66,X0)),vAPP(sTfun(late_freeRes,$o),name,sK67,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f944,plain,
    ! [X0: late_freeRes > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,X0,X1) )
      | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
      | ? [X2: name,X3: name] : ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) ) ),
    inference(flattening,[],[f943]) ).

thf(f943,plain,
    ! [X0: late_freeRes > $o,X1: late_freeRes] :
      ( ( $true = vAPP(late_freeRes,$o,X0,X1) )
      | ( $true != vAPP(late_freeRes,$o,X0,late_TauR) )
      | ? [X2: name,X3: name] : ( $true != vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) ) ),
    inference(ennf_transformation,[],[f426]) ).

thf(f426,plain,
    ! [X0: late_freeRes > $o,X1: late_freeRes] :
      ( ! [X2: name,X3: name] : ( $true = vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3)) )
     => ( ( $true = vAPP(late_freeRes,$o,X0,late_TauR) )
       => ( $true = vAPP(late_freeRes,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f425]) ).

thf(f425,plain,
    ! [X0: late_freeRes > $o,X1: late_freeRes] :
      ( ! [X2: name,X3: name] : vAPP(late_freeRes,$o,X0,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X2),X3))
     => ( vAPP(late_freeRes,$o,X0,late_TauR)
       => vAPP(late_freeRes,$o,X0,X1) ) ),
    inference(rectify,[],[f103]) ).

thf(f103,axiom,
    ! [X19: late_freeRes > $o,X25: late_freeRes] :
      ( ! [X26: name,X27: name] : vAPP(late_freeRes,$o,X19,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X26),X27))
     => ( vAPP(late_freeRes,$o,X19,late_TauR)
       => vAPP(late_freeRes,$o,X19,X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_freeRes_Oinducts) ).

thf(f2838,plain,
    spl225_95,
    inference(avatar_split_clause,[],[f1767,f2836]) ).

thf(f1767,plain,
    ! [X2: pi,X3: late_freeRes,X0: name,X1: name,X4: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ),
    inference(cnf_transformation,[],[f912]) ).

thf(f912,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_freeRes,X4: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ),
    inference(flattening,[],[f698]) ).

thf(f698,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_freeRes,X4: pi] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)) ),
    inference(fool_elimination,[],[f697]) ).

thf(f697,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_freeRes,X4: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4)),
    inference(rectify,[],[f302]) ).

thf(f302,axiom,
    ! [X0: name,X2: name,X19: pi,X30: late_freeRes,X31: pi] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X2),X19)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X30),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_inputFreeTrans) ).

thf(f2834,plain,
    spl225_94,
    inference(avatar_split_clause,[],[f1726,f2832]) ).

thf(f1726,plain,
    ! [X2: pi,X3: late_residual,X0: name,X1: name] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) ),
    inference(cnf_transformation,[],[f906]) ).

thf(f906,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_residual] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) ),
    inference(flattening,[],[f672]) ).

thf(f672,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_residual] : ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3) ),
    inference(fool_elimination,[],[f671]) ).

thf(f671,plain,
    ! [X0: name,X1: name,X2: pi,X3: late_residual] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2))),X3),
    inference(rectify,[],[f300]) ).

thf(f300,axiom,
    ! [X2: name,X22: name,X19: pi,X60: late_residual] : ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X2),X22),X19))),X60),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_resTrans_I2_J) ).

thf(f2830,plain,
    spl225_93,
    inference(avatar_split_clause,[],[f1428,f2828]) ).

thf(f1428,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,X0,X1) )
      | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
      | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) ),
    inference(cnf_transformation,[],[f1211]) ).

thf(f1211,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,X0,X1) )
      | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) )
      | ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f1208,f1210,f1209]) ).

thf(f1209,plain,
    ! [X0: late_subject > $o] :
      ( ? [X2: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,X2)) )
     => ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,vAPP(sTfun(late_subject,$o),name,sK56,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1210,plain,
    ! [X0: late_subject > $o] :
      ( ? [X3: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,X3)) )
     => ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,vAPP(sTfun(late_subject,$o),name,sK57,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1208,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,X0,X1) )
      | ? [X2: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,X2)) )
      | ? [X3: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,X3)) ) ),
    inference(rectify,[],[f938]) ).

thf(f938,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,X0,X1) )
      | ? [X3: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,X3)) )
      | ? [X2: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,X2)) ) ),
    inference(flattening,[],[f937]) ).

thf(f937,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ( $true = vAPP(late_subject,$o,X0,X1) )
      | ? [X3: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,X3)) )
      | ? [X2: name] : ( $true != vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,X2)) ) ),
    inference(ennf_transformation,[],[f416]) ).

thf(f416,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ! [X2: name] : ( $true = vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,X2)) )
     => ( ! [X3: name] : ( $true = vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,X3)) )
       => ( $true = vAPP(late_subject,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f415]) ).

thf(f415,plain,
    ! [X0: late_subject > $o,X1: late_subject] :
      ( ! [X2: name] : vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_InputS,X2))
     => ( ! [X3: name] : vAPP(late_subject,$o,X0,vAPP(name,late_subject,late_BoundOutputS,X3))
       => vAPP(late_subject,$o,X0,X1) ) ),
    inference(rectify,[],[f295]) ).

thf(f295,axiom,
    ! [X19: late_subject > $o,X51: late_subject] :
      ( ! [X57: name] : vAPP(late_subject,$o,X19,vAPP(name,late_subject,late_InputS,X57))
     => ( ! [X57: name] : vAPP(late_subject,$o,X19,vAPP(name,late_subject,late_BoundOutputS,X57))
       => vAPP(late_subject,$o,X19,X51) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_subject_Oinducts) ).

thf(f2814,plain,
    spl225_92,
    inference(avatar_split_clause,[],[f1866,f2812]) ).

thf(f1866,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( X1 = X2 )
      | ( X0 = X1 ) ),
    inference(definition_unfolding,[],[f1561,f1358]) ).

thf(f1561,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( X1 = X2 )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f954]) ).

thf(f954,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( X1 = X2 )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f953]) ).

thf(f953,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 )
      | ( X1 = X2 )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f878]) ).

thf(f878,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( X0 != X1 )
     => ( ( X1 != X2 )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),nil_Pr743626285e_name)),X1) = X1 ) ) ),
    inference(rectify,[],[f109]) ).

thf(f109,axiom,
    ! [X0: name,X32: name,X1: name] :
      ( ( X0 != X32 )
     => ( ( X1 != X32 )
       => ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X32) = X32 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_swap__simps_I3_J) ).

thf(f2810,plain,
    spl225_91,
    inference(avatar_split_clause,[],[f1614,f2808]) ).

thf(f1614,plain,
    ! [X2: name,X0: pi,X1: late_residual] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ),
    inference(cnf_transformation,[],[f1000]) ).

thf(f1000,plain,
    ! [X0: pi,X1: late_residual,X2: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ),
    inference(flattening,[],[f999]) ).

thf(f999,plain,
    ! [X0: pi,X1: late_residual,X2: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) ) ),
    inference(ennf_transformation,[],[f534]) ).

thf(f534,plain,
    ! [X0: pi,X1: late_residual,X2: name] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1) )
     => ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0) )
       => ( $true = vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) ) ) ),
    inference(fool_elimination,[],[f533]) ).

thf(f533,plain,
    ! [X0: pi,X1: late_residual,X2: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),X1)
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X0)
       => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X1) ) ),
    inference(rectify,[],[f212]) ).

thf(f212,axiom,
    ! [X19: pi,X60: late_residual,X2: name] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X19),X60)
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X2),X19)
       => vAPP(late_residual,$o,vAPP(name,sTfun(late_residual,$o),fresh_81631222sidual,X2),X60) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_freshResidual) ).

thf(f2804,plain,
    ( spl225_90
    | ~ spl225_10
    | ~ spl225_52 ),
    inference(avatar_split_clause,[],[f2537,f2530,f2333,f2802]) ).

thf(f2333,plain,
    ( spl225_10
  <=> ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_10])]) ).

thf(f2537,plain,
    ( ! [X0: late_subject,X1: name] :
        ( ( vAPP(name,late_subject,late_InputS,X1) != X0 )
        | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) )
    | ~ spl225_10
    | ~ spl225_52 ),
    inference(superposition,[],[f2334,f2531]) ).

thf(f2334,plain,
    ( ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) )
    | ~ spl225_10 ),
    inference(avatar_component_clause,[],[f2333]) ).

thf(f2800,plain,
    spl225_89,
    inference(avatar_split_clause,[],[f1704,f2798]) ).

thf(f1704,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( ( $true = vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(set_Pr1834926343_pi_pi,pi,sK180,X0)),vAPP(set_Pr1834926343_pi_pi,pi,sK181,X0))),X0) )
      | ( $true != vAPP(set_Pr1834926343_pi_pi,$o,sP3,X0) ) ),
    inference(cnf_transformation,[],[f1308]) ).

thf(f2756,plain,
    spl225_88,
    inference(avatar_split_clause,[],[f1637,f2754]) ).

thf(f1637,plain,
    ! [X2: pi,X0: name,X1: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
      | ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1037]) ).

thf(f1037,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
      | ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ),
    inference(ennf_transformation,[],[f580]) ).

thf(f580,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) )
     => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(fool_elimination,[],[f579]) ).

thf(f579,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2))
     => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ),
    inference(rectify,[],[f182]) ).

thf(f182,axiom,
    ! [X0: name,X2: pi,X22: pi] :
      ( vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X22))
     => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_fresh__prodD_I1_J) ).

thf(f2752,plain,
    spl225_87,
    inference(avatar_split_clause,[],[f1636,f2750]) ).

thf(f1636,plain,
    ! [X2: pi,X0: name,X1: pi] :
      ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
      | ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1036]) ).

thf(f1036,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true )
      | ( $true != vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) ) ),
    inference(ennf_transformation,[],[f578]) ).

thf(f578,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2)) )
     => ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) = $true ) ),
    inference(fool_elimination,[],[f577]) ).

thf(f577,plain,
    ! [X0: name,X1: pi,X2: pi] :
      ( vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2))
     => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X2) ),
    inference(rectify,[],[f180]) ).

thf(f180,axiom,
    ! [X0: name,X2: pi,X22: pi] :
      ( vAPP(product_prod_pi_pi,$o,vAPP(name,sTfun(product_prod_pi_pi,$o),fresh_1627595501_pi_pi,X0),vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X22))
     => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_fresh__prodD_I2_J) ).

thf(f2748,plain,
    spl225_86,
    inference(avatar_split_clause,[],[f1432,f2746]) ).

thf(f1432,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
      | ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) ),
    inference(cnf_transformation,[],[f1219]) ).

thf(f1219,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
      | ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f942,f1218]) ).

thf(f1218,plain,
    ! [X0: produc367475239e_name > $o] :
      ( ? [X2: name,X3: name] : ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) )
     => ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK64,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK65,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f942,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
      | ? [X2: name,X3: name] : ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) ) ),
    inference(ennf_transformation,[],[f424]) ).

thf(f424,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ! [X2: name,X3: name] : ( $true = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) )
     => ( $true = vAPP(produc367475239e_name,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f423]) ).

thf(f423,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ! [X2: name,X3: name] : vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3))
     => vAPP(produc367475239e_name,$o,X0,X1) ),
    inference(rectify,[],[f232]) ).

thf(f232,axiom,
    ! [X19: produc367475239e_name > $o,X72: produc367475239e_name] :
      ( ! [X61: name,X62: name] : vAPP(produc367475239e_name,$o,X19,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X61),X62))
     => vAPP(produc367475239e_name,$o,X19,X72) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_old_Oprod_Oinducts) ).

thf(f2743,plain,
    spl225_85,
    inference(avatar_split_clause,[],[f1431,f2741]) ).

thf(f1431,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
      | ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) ),
    inference(cnf_transformation,[],[f1217]) ).

thf(f1217,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
      | ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f941,f1216]) ).

thf(f1216,plain,
    ! [X0: produc367475239e_name > $o] :
      ( ? [X2: name,X3: name] : ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) )
     => ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(sTfun(produc367475239e_name,$o),name,sK62,X0)),vAPP(sTfun(produc367475239e_name,$o),name,sK63,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f941,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ( $true = vAPP(produc367475239e_name,$o,X0,X1) )
      | ? [X2: name,X3: name] : ( $true != vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) ) ),
    inference(ennf_transformation,[],[f422]) ).

thf(f422,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ! [X2: name,X3: name] : ( $true = vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3)) )
     => ( $true = vAPP(produc367475239e_name,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f421]) ).

thf(f421,plain,
    ! [X0: produc367475239e_name > $o,X1: produc367475239e_name] :
      ( ! [X2: name,X3: name] : vAPP(produc367475239e_name,$o,X0,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X2),X3))
     => vAPP(produc367475239e_name,$o,X0,X1) ),
    inference(rectify,[],[f226]) ).

thf(f226,axiom,
    ! [X19: produc367475239e_name > $o,X71: produc367475239e_name] :
      ( ! [X61: name,X62: name] : vAPP(produc367475239e_name,$o,X19,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X61),X62))
     => vAPP(produc367475239e_name,$o,X19,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_prod__cases) ).

thf(f2739,plain,
    spl225_84,
    inference(avatar_split_clause,[],[f1430,f2737]) ).

thf(f1430,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
      | ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) ),
    inference(cnf_transformation,[],[f1215]) ).

thf(f1215,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
      | ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61])],[f940,f1214]) ).

thf(f1214,plain,
    ! [X0: product_prod_pi_pi > $o] :
      ( ? [X2: pi,X3: pi] : ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) )
     => ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK60,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK61,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f940,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
      | ? [X2: pi,X3: pi] : ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) ) ),
    inference(ennf_transformation,[],[f420]) ).

thf(f420,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ! [X2: pi,X3: pi] : ( $true = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) )
     => ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f419]) ).

thf(f419,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ! [X2: pi,X3: pi] : vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3))
     => vAPP(product_prod_pi_pi,$o,X0,X1) ),
    inference(rectify,[],[f227]) ).

thf(f227,axiom,
    ! [X19: product_prod_pi_pi > $o,X71: product_prod_pi_pi] :
      ( ! [X61: pi,X62: pi] : vAPP(product_prod_pi_pi,$o,X19,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X61),X62))
     => vAPP(product_prod_pi_pi,$o,X19,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_prod__cases) ).

thf(f2735,plain,
    spl225_83,
    inference(avatar_split_clause,[],[f1429,f2733]) ).

thf(f1429,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
      | ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) ),
    inference(cnf_transformation,[],[f1213]) ).

thf(f1213,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
      | ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f939,f1212]) ).

thf(f1212,plain,
    ! [X0: product_prod_pi_pi > $o] :
      ( ? [X2: pi,X3: pi] : ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) )
     => ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(sTfun(product_prod_pi_pi,$o),pi,sK58,X0)),vAPP(sTfun(product_prod_pi_pi,$o),pi,sK59,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f939,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) )
      | ? [X2: pi,X3: pi] : ( $true != vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) ) ),
    inference(ennf_transformation,[],[f418]) ).

thf(f418,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ! [X2: pi,X3: pi] : ( $true = vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3)) )
     => ( $true = vAPP(product_prod_pi_pi,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f417]) ).

thf(f417,plain,
    ! [X0: product_prod_pi_pi > $o,X1: product_prod_pi_pi] :
      ( ! [X2: pi,X3: pi] : vAPP(product_prod_pi_pi,$o,X0,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X2),X3))
     => vAPP(product_prod_pi_pi,$o,X0,X1) ),
    inference(rectify,[],[f233]) ).

thf(f233,axiom,
    ! [X19: product_prod_pi_pi > $o,X72: product_prod_pi_pi] :
      ( ! [X61: pi,X62: pi] : vAPP(product_prod_pi_pi,$o,X19,vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X61),X62))
     => vAPP(product_prod_pi_pi,$o,X19,X72) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_old_Oprod_Oinducts) ).

thf(f2731,plain,
    spl225_82,
    inference(avatar_split_clause,[],[f1901,f2728]) ).

thf(f1901,plain,
    $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,b)),y),p2)),
    inference(definition_unfolding,[],[f1810,f1356]) ).

thf(f1810,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,aa)),y),p2)) = $true,
    inference(cnf_transformation,[],[f760]) ).

thf(f760,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,aa)),y),p2)) = $true,
    inference(fool_elimination,[],[f759]) ).

thf(f759,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,aa)),y),p2)),
    inference(rectify,[],[f193]) ).

thf(f193,axiom,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,p),vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,vAPP(name,late_subject,late_InputS,aa)),y),p2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_cClose1_Ohyps_I1_J) ).

thf(f2701,plain,
    spl225_81,
    inference(avatar_split_clause,[],[f1626,f2699]) ).

thf(f1626,plain,
    ! [X2: name,X0: name,X1: pi] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(cnf_transformation,[],[f1022]) ).

thf(f1022,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 )
      | ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) ) ),
    inference(ennf_transformation,[],[f558]) ).

thf(f558,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1) )
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 ) ),
    inference(fool_elimination,[],[f557]) ).

thf(f557,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X1)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X1),X0),X2) = X1 ) ),
    inference(rectify,[],[f321]) ).

thf(f321,axiom,
    ! [X0: name,X19: pi,X1: name] :
      ( vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),X19)
     => ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_forget) ).

thf(f2697,plain,
    spl225_80,
    inference(avatar_split_clause,[],[f1562,f2695]) ).

thf(f2695,plain,
    ( spl225_80
  <=> ! [X2: pi,X0: name,X1: name] :
        ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X2),X0),X1)) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_80])]) ).

thf(f1562,plain,
    ! [X2: pi,X0: name,X1: name] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X2),X0),X1)) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f955]) ).

thf(f955,plain,
    ! [X0: name,X1: name,X2: pi] :
      ( ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X2),X0),X1)) )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f494]) ).

thf(f494,plain,
    ! [X0: name,X1: name,X2: pi] :
      ( ( X0 != X1 )
     => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X2),X0),X1)) ) ),
    inference(fool_elimination,[],[f493]) ).

thf(f493,plain,
    ! [X0: name,X1: name,X2: pi] :
      ( ( X0 != X1 )
     => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X2),X0),X1)) ),
    inference(rectify,[],[f323]) ).

thf(f323,axiom,
    ! [X0: name,X1: name,X19: pi] :
      ( ( X0 != X1 )
     => vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_fresh__fact2) ).

thf(f2680,plain,
    spl225_79,
    inference(avatar_split_clause,[],[f1826,f2678]) ).

thf(f1826,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(definition_unfolding,[],[f1413,f1358]) ).

thf(f1413,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(cnf_transformation,[],[f809]) ).

thf(f809,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(rectify,[],[f19]) ).

thf(f19,axiom,
    ! [X0: name,X2: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_name__id) ).

thf(f2676,plain,
    spl225_78,
    inference(avatar_split_clause,[],[f1825,f2674]) ).

thf(f1825,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X1) = X0 ),
    inference(definition_unfolding,[],[f1412,f1358]) ).

thf(f1412,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X1) = X0 ),
    inference(cnf_transformation,[],[f108]) ).

thf(f108,axiom,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_swap__simps_I2_J) ).

thf(f2672,plain,
    spl225_77,
    inference(avatar_split_clause,[],[f1824,f2670]) ).

thf(f1824,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X0) = X1 ),
    inference(definition_unfolding,[],[f1411,f1358]) ).

thf(f1411,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X0) = X1 ),
    inference(cnf_transformation,[],[f107]) ).

thf(f107,axiom,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),nil_Pr743626285e_name)),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_swap__simps_I1_J) ).

thf(f2665,plain,
    spl225_76,
    inference(avatar_split_clause,[],[f1809,f2662]) ).

thf(f1809,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $true,
    inference(cnf_transformation,[],[f758]) ).

thf(f758,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)) = $true,
    inference(fool_elimination,[],[f757]) ).

thf(f757,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,q),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_cOpen_Ohyps_I1_J) ).

thf(f2660,plain,
    spl225_75,
    inference(avatar_split_clause,[],[f1414,f2658]) ).

thf(f2658,plain,
    ( spl225_75
  <=> ! [X0: name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_75])]) ).

thf(f1414,plain,
    ! [X0: name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(cnf_transformation,[],[f810]) ).

thf(f810,plain,
    ! [X0: name,X1: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(rectify,[],[f20]) ).

thf(f20,axiom,
    ! [X0: name,X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_name__id) ).

thf(f2656,plain,
    spl225_74,
    inference(avatar_split_clause,[],[f1410,f2654]) ).

thf(f1410,plain,
    ! [X0: name,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(cnf_transformation,[],[f808]) ).

thf(f808,plain,
    ! [X0: name,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(rectify,[],[f16]) ).

thf(f16,axiom,
    ! [X0: name,X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_name__id) ).

thf(f2652,plain,
    spl225_73,
    inference(avatar_split_clause,[],[f1409,f2650]) ).

thf(f2650,plain,
    ( spl225_73
  <=> ! [X0: name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_73])]) ).

thf(f1409,plain,
    ! [X0: name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(cnf_transformation,[],[f807]) ).

thf(f807,plain,
    ! [X0: name,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(rectify,[],[f17]) ).

thf(f17,axiom,
    ! [X0: name,X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_name__id) ).

thf(f2648,plain,
    spl225_72,
    inference(avatar_split_clause,[],[f1408,f2646]) ).

thf(f2646,plain,
    ( spl225_72
  <=> ! [X0: name,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_72])]) ).

thf(f1408,plain,
    ! [X0: name,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(cnf_transformation,[],[f806]) ).

thf(f806,plain,
    ! [X0: name,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X1) = X1 ),
    inference(rectify,[],[f18]) ).

thf(f18,axiom,
    ! [X0: name,X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X0)),nil_Pr743626285e_name)),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_name__id) ).

thf(f2639,plain,
    spl225_71,
    inference(avatar_split_clause,[],[f1823,f2637]) ).

thf(f1823,plain,
    ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_BoundOutputS,X1)) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) ),
    inference(definition_unfolding,[],[f1407,f1358]) ).

thf(f1407,plain,
    ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_BoundOutputS,X1)) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)) ),
    inference(cnf_transformation,[],[f805]) ).

thf(f805,plain,
    ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_BoundOutputS,X1)) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)) ),
    inference(rectify,[],[f57]) ).

thf(f57,axiom,
    ! [X5: list_P227219501e_name,X3: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(name,late_subject,late_BoundOutputS,X3)) = vAPP(name,late_subject,late_BoundOutputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_subject_Operm_I2_J) ).

thf(f2635,plain,
    spl225_70,
    inference(avatar_split_clause,[],[f1822,f2633]) ).

thf(f1822,plain,
    ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_InputS,X1)) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),name_prm_name,X0),X1)) ),
    inference(definition_unfolding,[],[f1406,f1358]) ).

thf(f1406,plain,
    ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_InputS,X1)) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)) ),
    inference(cnf_transformation,[],[f804]) ).

thf(f804,plain,
    ! [X0: list_P227219501e_name,X1: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X0),vAPP(name,late_subject,late_InputS,X1)) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X0),X1)) ),
    inference(rectify,[],[f284]) ).

thf(f284,axiom,
    ! [X5: list_P227219501e_name,X3: name] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,X5),vAPP(name,late_subject,late_InputS,X3)) = vAPP(name,late_subject,late_InputS,vAPP(name,name,vAPP(list_P227219501e_name,sTfun(name,name),perm_name_name,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_subject_Operm_I1_J) ).

thf(f2631,plain,
    spl225_69,
    inference(avatar_split_clause,[],[f1729,f2629]) ).

thf(f1729,plain,
    ! [X2: pi,X3: pi,X0: name,X1: name,X4: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) ),
    inference(cnf_transformation,[],[f909]) ).

thf(f909,plain,
    ! [X0: name,X1: name,X2: pi,X3: pi,X4: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) ),
    inference(rectify,[],[f287]) ).

thf(f287,axiom,
    ! [X28: name,X29: name,X5: pi,X90: pi,X91: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X28),X29),X5) != vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X90),X91) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_pi_Odistinct_I55_J) ).

thf(f2627,plain,
    spl225_68,
    inference(avatar_split_clause,[],[f1728,f2625]) ).

thf(f1728,plain,
    ! [X2: pi,X3: name,X0: name,X1: name,X4: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) ),
    inference(cnf_transformation,[],[f908]) ).

thf(f908,plain,
    ! [X0: name,X1: name,X2: pi,X3: name,X4: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X3),X4) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X0),X1),X2) ),
    inference(rectify,[],[f292]) ).

thf(f292,axiom,
    ! [X28: name,X29: name,X5: pi,X92: name,X54: pi] : ( vAPP(pi,pi,vAPP(name,sTfun(pi,pi),vAPP(name,sTfun(name,sTfun(pi,pi)),input,X28),X29),X5) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X92),X54) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_pi_Odistinct_I57_J) ).

thf(f2623,plain,
    spl225_67,
    inference(avatar_split_clause,[],[f1727,f2621]) ).

thf(f1727,plain,
    ! [X2: pi,X3: late_freeRes,X0: late_subject,X1: name,X4: pi] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4) != vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X1),X2) ),
    inference(cnf_transformation,[],[f907]) ).

thf(f907,plain,
    ! [X0: late_subject,X1: name,X2: pi,X3: late_freeRes,X4: pi] : ( vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X3),X4) != vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X0),X1),X2) ),
    inference(rectify,[],[f203]) ).

thf(f203,axiom,
    ! [X51: late_subject,X52: name,X5: pi,X53: late_freeRes,X54: pi] : ( vAPP(pi,late_residual,vAPP(name,sTfun(pi,late_residual),vAPP(late_subject,sTfun(name,sTfun(pi,late_residual)),late_BoundR,X51),X52),X5) != vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X53),X54) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_residual_Odistinct_I1_J) ).

thf(f2618,plain,
    spl225_66,
    inference(avatar_split_clause,[],[f1375,f2616]) ).

thf(f2616,plain,
    ( spl225_66
  <=> ! [X0: set_Pr1834926343_pi_pi] : ( vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,vAPP(set_Pr1834926343_pi_pi,sTfun(product_prod_pi_pi,$o),vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(product_prod_pi_pi,$o)),cCOMB,member558706512_pi_pi),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_66])]) ).

thf(f1375,plain,
    ! [X0: set_Pr1834926343_pi_pi] : ( vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,vAPP(set_Pr1834926343_pi_pi,sTfun(product_prod_pi_pi,$o),vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(product_prod_pi_pi,$o)),cCOMB,member558706512_pi_pi),X0)) = X0 ),
    inference(cnf_transformation,[],[f374]) ).

thf(f374,plain,
    ! [X0: set_Pr1834926343_pi_pi] : ( vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,vAPP(set_Pr1834926343_pi_pi,sTfun(product_prod_pi_pi,$o),vAPP(sTfun(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o)),sTfun(set_Pr1834926343_pi_pi,sTfun(product_prod_pi_pi,$o)),cCOMB,member558706512_pi_pi),X0)) = X0 ),
    inference(fool_elimination,[],[f373]) ).

thf(f373,plain,
    ! [X0: set_Pr1834926343_pi_pi] :
      ( vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,
          ^ [X1: product_prod_pi_pi] : vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X1),X0)) = X0 ),
    inference(rectify,[],[f94]) ).

thf(f94,axiom,
    ! [X20: set_Pr1834926343_pi_pi] :
      ( vAPP(sTfun(product_prod_pi_pi,$o),set_Pr1834926343_pi_pi,collec1051790738_pi_pi,
          ^ [X21: product_prod_pi_pi] : vAPP(set_Pr1834926343_pi_pi,$o,vAPP(product_prod_pi_pi,sTfun(set_Pr1834926343_pi_pi,$o),member558706512_pi_pi,X21),X20)) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Collect__mem__eq) ).

thf(f2608,plain,
    spl225_65,
    inference(avatar_split_clause,[],[f1557,f2606]) ).

thf(f1557,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X1 )
      | ( X1 = X2 )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f951]) ).

thf(f951,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( ( ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X1 )
            | ( X1 = X2 ) )
          & ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X0 )
            | ( X1 != X2 ) ) )
        | ( X0 = X1 ) )
      & ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X2 )
        | ( X0 != X1 ) ) ),
    inference(ennf_transformation,[],[f876]) ).

thf(f876,plain,
    ! [X0: name,X1: name,X2: name] :
      ( ( ( X0 != X1 )
       => ( ( ( X1 != X2 )
           => ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X1 ) )
          & ( ( X1 = X2 )
           => ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X0 ) ) ) )
      & ( ( X0 = X1 )
       => ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X2 ) ) ),
    inference(rectify,[],[f336]) ).

thf(f336,axiom,
    ! [X0: name,X32: name,X1: name] :
      ( ( ( X0 != X32 )
       => ( ( ( X1 != X32 )
           => ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X32) = X32 ) )
          & ( ( X1 = X32 )
           => ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X32) = X0 ) ) ) )
      & ( ( X0 = X32 )
       => ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X1)),X32) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_swap__name_Osimps) ).

thf(f2594,plain,
    ( spl225_64
    | ~ spl225_23
    | ~ spl225_60 ),
    inference(avatar_split_clause,[],[f2578,f2571,f2385,f2592]) ).

thf(f2592,plain,
    ( spl225_64
  <=> ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0) != X0 )
        | ( nil_Pr743626285e_name = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_64])]) ).

thf(f2578,plain,
    ( ! [X0: list_P227219501e_name] :
        ( ( vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0) != X0 )
        | ( nil_Pr743626285e_name = X0 ) )
    | ~ spl225_23
    | ~ spl225_60 ),
    inference(superposition,[],[f2386,f2572]) ).

thf(f2590,plain,
    spl225_63,
    inference(avatar_split_clause,[],[f1438,f2588]) ).

thf(f1438,plain,
    ! [X0: list_P227219501e_name > $o,X1: list_P227219501e_name] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
      | ( $true = vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK78,X0)) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(cnf_transformation,[],[f1231]) ).

thf(f2584,plain,
    spl225_62,
    inference(avatar_split_clause,[],[f1904,f2582]) ).

thf(f2582,plain,
    ( spl225_62
  <=> ! [X2: name,X0: name] :
        ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X2) = X0 )
        | ( X0 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_62])]) ).

thf(f1904,plain,
    ! [X2: name,X0: name] :
      ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X2) = X0 )
      | ( X0 = X2 ) ),
    inference(equality_resolution,[],[f1556]) ).

thf(f1556,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X0 )
      | ( X1 != X2 )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f951]) ).

thf(f2577,plain,
    spl225_61,
    inference(avatar_split_clause,[],[f1386,f2575]) ).

thf(f1386,plain,
    ! [X0: late_freeRes] :
      ( ( late_TauR = X0 )
      | ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_freeRes,name,sK42,X0)),vAPP(late_freeRes,name,sK43,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1191]) ).

thf(f1191,plain,
    ! [X0: late_freeRes] :
      ( ( late_TauR = X0 )
      | ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_freeRes,name,sK42,X0)),vAPP(late_freeRes,name,sK43,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f930,f1190]) ).

thf(f1190,plain,
    ! [X0: late_freeRes] :
      ( ? [X1: name,X2: name] : ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2) = X0 )
     => ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,vAPP(late_freeRes,name,sK42,X0)),vAPP(late_freeRes,name,sK43,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f930,plain,
    ! [X0: late_freeRes] :
      ( ( late_TauR = X0 )
      | ? [X1: name,X2: name] : ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2) = X0 ) ),
    inference(ennf_transformation,[],[f785]) ).

thf(f785,plain,
    ! [X0: late_freeRes] :
      ( ! [X1: name,X2: name] : ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X1),X2) != X0 )
     => ( late_TauR = X0 ) ),
    inference(rectify,[],[f102]) ).

thf(f102,axiom,
    ! [X22: late_freeRes] :
      ( ! [X23: name,X24: name] : ( vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X23),X24) != X22 )
     => ( late_TauR = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_freeRes_Oexhaust) ).

thf(f2573,plain,
    spl225_60,
    inference(avatar_split_clause,[],[f1379,f2571]) ).

thf(f1379,plain,
    ! [X0: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(cnf_transformation,[],[f1165]) ).

thf(f1165,plain,
    ! [X0: list_P227219501e_name] :
      ( ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f921,f1164]) ).

thf(f1164,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2) = X0 )
     => ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(list_P227219501e_name,produc367475239e_name,sK16,X0)),vAPP(list_P227219501e_name,list_P227219501e_name,sK17,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f921,plain,
    ! [X0: list_P227219501e_name] :
      ( ? [X1: produc367475239e_name,X2: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2) = X0 )
      | ( nil_Pr743626285e_name = X0 ) ),
    inference(ennf_transformation,[],[f779]) ).

thf(f779,plain,
    ! [X0: list_P227219501e_name] :
      ( ( nil_Pr743626285e_name != X0 )
     => ~ ! [X1: produc367475239e_name,X2: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X1),X2) != X0 ) ),
    inference(rectify,[],[f265]) ).

thf(f265,axiom,
    ! [X22: list_P227219501e_name] :
      ( ( nil_Pr743626285e_name != X22 )
     => ~ ! [X77: produc367475239e_name,X78: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X77),X78) != X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_list_Oexhaust) ).

thf(f2567,plain,
    ~ spl225_59,
    inference(avatar_split_clause,[],[f1813,f2564]) ).

thf(f1813,plain,
    $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,b),x)),q_a))),
    inference(definition_unfolding,[],[f1348,f1356]) ).

thf(f1348,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,aa),x)),q_a))) != $true,
    inference(cnf_transformation,[],[f765]) ).

thf(f765,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,aa),x)),q_a))) != $true,
    inference(flattening,[],[f366]) ).

thf(f366,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,aa),x)),q_a))) != $true,
    inference(fool_elimination,[],[f365]) ).

thf(f365,plain,
    ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,aa),x)),q_a))),
    inference(rectify,[],[f362]) ).

thf(f362,negated_conjecture,
    ~ vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,aa),x)),q_a))),
    inference(negated_conjecture,[],[f361]) ).

thf(f361,conjecture,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),q)),vAPP(late_residual,late_residual,vAPP(list_P227219501e_name,sTfun(late_residual,late_residual),perm_n414416632sidual,vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,z),x)),nil_Pr743626285e_name)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,aa),x)),q_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f2559,plain,
    spl225_58,
    inference(avatar_split_clause,[],[f1905,f2557]) ).

thf(f1905,plain,
    ! [X2: name,X1: name] : ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2)),X1) = X2 ),
    inference(equality_resolution,[],[f1555]) ).

thf(f1555,plain,
    ! [X2: name,X0: name,X1: name] :
      ( ( vAPP(name,name,vAPP(produc367475239e_name,sTfun(name,name),swap_name,vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X0),X2)),X1) = X2 )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f951]) ).

thf(f2555,plain,
    spl225_57,
    inference(avatar_split_clause,[],[f1808,f2552]) ).

thf(f1808,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true,
    inference(cnf_transformation,[],[f756]) ).

thf(f756,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true,
    inference(fool_elimination,[],[f755]) ).

thf(f755,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),
    inference(rectify,[],[f75]) ).

thf(f75,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_cClose1_Ohyps_I9_J) ).

thf(f2550,plain,
    spl225_56,
    inference(avatar_split_clause,[],[f1807,f2547]) ).

thf(f1807,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true,
    inference(cnf_transformation,[],[f754]) ).

thf(f754,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)) = $true,
    inference(fool_elimination,[],[f753]) ).

thf(f753,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),
    inference(rectify,[],[f76]) ).

thf(f76,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,x),q)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_cClose1_Ohyps_I4_J) ).

thf(f2545,plain,
    spl225_55,
    inference(avatar_split_clause,[],[f1656,f2543]) ).

thf(f1656,plain,
    ! [X2: name,X3: pi,X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X3) ),
    inference(cnf_transformation,[],[f886]) ).

thf(f886,plain,
    ! [X0: pi,X1: pi,X2: name,X3: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X1) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X2),X3) ),
    inference(rectify,[],[f289]) ).

thf(f289,axiom,
    ! [X33: pi,X34: pi,X92: name,X54: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X33),X34) != vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X92),X54) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_pi_Odistinct_I85_J) ).

thf(f2541,plain,
    spl225_54,
    inference(avatar_split_clause,[],[f1440,f2539]) ).

thf(f1440,plain,
    ! [X0: name,X1: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)) ),
    inference(cnf_transformation,[],[f434]) ).

thf(f434,plain,
    ! [X0: name,X1: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)) ),
    inference(fool_elimination,[],[f433]) ).

thf(f433,plain,
    ! [X0: name,X1: pi] : vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X1)),
    inference(rectify,[],[f202]) ).

thf(f202,axiom,
    ! [X0: name,X19: pi] : vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,X0),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_freshRes) ).

thf(f2536,plain,
    spl225_53,
    inference(avatar_split_clause,[],[f2239,f2534]) ).

thf(f2239,plain,
    ! [X0: name,X1: name] :
      ( ( X0 = X1 )
      | ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_InputS,X1) ) ),
    inference(equality_proxy_clausification,[],[f2238]) ).

thf(f2238,plain,
    ! [X0: name,X1: name] :
      ( ( X0 = X1 )
      | ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_InputS,X0)),vAPP(name,late_subject,late_InputS,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2234]) ).

thf(f2234,plain,
    ! [X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) )
      | ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_InputS,X0)),vAPP(name,late_subject,late_InputS,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1415]) ).

thf(f1415,plain,
    ! [X0: name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_InputS,X0)),vAPP(name,late_subject,late_InputS,X1)) ),
    inference(cnf_transformation,[],[f390]) ).

thf(f390,plain,
    ! [X0: name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_InputS,X0)),vAPP(name,late_subject,late_InputS,X1)) ),
    inference(fool_elimination,[],[f389]) ).

thf(f389,plain,
    ! [X0: name,X1: name] :
      ( ( vAPP(name,late_subject,late_InputS,X0) = vAPP(name,late_subject,late_InputS,X1) )
      = ( X0 = X1 ) ),
    inference(rectify,[],[f278]) ).

thf(f278,axiom,
    ! [X3: name,X7: name] :
      ( ( vAPP(name,late_subject,late_InputS,X3) = vAPP(name,late_subject,late_InputS,X7) )
      = ( X3 = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Late__Semantics1_Osubject_Oinject_I1_J) ).

thf(f2532,plain,
    spl225_52,
    inference(avatar_split_clause,[],[f1380,f2530]) ).

thf(f1380,plain,
    ! [X0: late_subject] :
      ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(late_subject,name,sK18,X0)) = X0 )
      | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1169]) ).

thf(f1169,plain,
    ! [X0: late_subject] :
      ( ( vAPP(name,late_subject,late_BoundOutputS,vAPP(late_subject,name,sK18,X0)) = X0 )
      | ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f1166,f1168,f1167]) ).

thf(f1167,plain,
    ! [X0: late_subject] :
      ( ? [X1: name] : ( vAPP(name,late_subject,late_BoundOutputS,X1) = X0 )
     => ( vAPP(name,late_subject,late_BoundOutputS,vAPP(late_subject,name,sK18,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1168,plain,
    ! [X0: late_subject] :
      ( ? [X2: name] : ( vAPP(name,late_subject,late_InputS,X2) = X0 )
     => ( vAPP(name,late_subject,late_InputS,vAPP(late_subject,name,sK19,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1166,plain,
    ! [X0: late_subject] :
      ( ? [X1: name] : ( vAPP(name,late_subject,late_BoundOutputS,X1) = X0 )
      | ? [X2: name] : ( vAPP(name,late_subject,late_InputS,X2) = X0 ) ),
    inference(rectify,[],[f922]) ).

thf(f922,plain,
    ! [X0: late_subject] :
      ( ? [X2: name] : ( vAPP(name,late_subject,late_BoundOutputS,X2) = X0 )
      | ? [X1: name] : ( vAPP(name,late_subject,late_InputS,X1) = X0 ) ),
    inference(ennf_transformation,[],[f780]) ).

thf(f780,plain,
    ! [X0: late_subject] :
      ( ! [X1: name] : ( vAPP(name,late_subject,late_InputS,X1) != X0 )
     => ~ ! [X2: name] : ( vAPP(name,late_subject,late_BoundOutputS,X2) != X0 ) ),
    inference(rectify,[],[f296]) ).

thf(f296,axiom,
    ! [X22: late_subject] :
      ( ! [X79: name] : ( vAPP(name,late_subject,late_InputS,X79) != X22 )
     => ~ ! [X80: name] : ( vAPP(name,late_subject,late_BoundOutputS,X80) != X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_subject_Oexhaust) ).

thf(f2513,plain,
    spl225_51,
    inference(avatar_split_clause,[],[f2237,f2511]) ).

thf(f2511,plain,
    ( spl225_51
  <=> ! [X0: name,X1: name] :
        ( ( X0 != X1 )
        | ( vAPP(name,late_subject,late_InputS,X0) = vAPP(name,late_subject,late_InputS,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_51])]) ).

thf(f2237,plain,
    ! [X0: name,X1: name] :
      ( ( X0 != X1 )
      | ( vAPP(name,late_subject,late_InputS,X0) = vAPP(name,late_subject,late_InputS,X1) ) ),
    inference(equality_proxy_clausification,[],[f2236]) ).

thf(f2236,plain,
    ! [X0: name,X1: name] :
      ( ( X0 != X1 )
      | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_InputS,X0)),vAPP(name,late_subject,late_InputS,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2235]) ).

thf(f2235,plain,
    ! [X0: name,X1: name] :
      ( ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) )
      | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_InputS,X0)),vAPP(name,late_subject,late_InputS,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1415]) ).

thf(f2509,plain,
    spl225_50,
    inference(avatar_split_clause,[],[f1427,f2507]) ).

thf(f1427,plain,
    ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$true),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f414]) ).

thf(f414,plain,
    ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$true),X0),X1) = X0 ),
    inference(fool_elimination,[],[f413]) ).

thf(f413,plain,
    ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$true),X0),X1) = X0 ),
    inference(rectify,[],[f351]) ).

thf(f351,axiom,
    ! [X2: pi,X22: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$true),X2),X22) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi_T) ).

thf(f2505,plain,
    spl225_49,
    inference(avatar_split_clause,[],[f1426,f2503]) ).

thf(f2503,plain,
    ( spl225_49
  <=> ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$false),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_49])]) ).

thf(f1426,plain,
    ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$false),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f412]) ).

thf(f412,plain,
    ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$false),X0),X1) = X1 ),
    inference(fool_elimination,[],[f411]) ).

thf(f411,plain,
    ! [X0: pi,X1: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$false),X0),X1) = X1 ),
    inference(rectify,[],[f350]) ).

thf(f350,axiom,
    ! [X2: pi,X22: pi] : ( vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),vAPP($o,sTfun(pi,sTfun(pi,pi)),if_pi,$false),X2),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi_T) ).

thf(f2501,plain,
    spl225_48,
    inference(avatar_split_clause,[],[f1425,f2499]) ).

thf(f1425,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$true),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f410]) ).

thf(f410,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$true),X0),X1) = X0 ),
    inference(fool_elimination,[],[f409]) ).

thf(f409,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$true),X0),X1) = X0 ),
    inference(rectify,[],[f353]) ).

thf(f353,axiom,
    ! [X2: name,X22: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$true),X2),X22) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Oname_T) ).

thf(f2497,plain,
    spl225_47,
    inference(avatar_split_clause,[],[f1424,f2495]) ).

thf(f2495,plain,
    ( spl225_47
  <=> ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$false),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_47])]) ).

thf(f1424,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$false),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f408]) ).

thf(f408,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$false),X0),X1) = X1 ),
    inference(fool_elimination,[],[f407]) ).

thf(f407,plain,
    ! [X0: name,X1: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$false),X0),X1) = X1 ),
    inference(rectify,[],[f352]) ).

thf(f352,axiom,
    ! [X2: name,X22: name] : ( vAPP(name,name,vAPP(name,sTfun(name,name),vAPP($o,sTfun(name,sTfun(name,name)),if_name,$false),X2),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Oname_T) ).

thf(f2493,plain,
    spl225_46,
    inference(avatar_split_clause,[],[f2233,f2491]) ).

thf(f2233,plain,
    ! [X0: name,X1: name] :
      ( ( X0 = X1 )
      | ( vAPP(name,late_subject,late_BoundOutputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) ) ),
    inference(equality_proxy_clausification,[],[f2232]) ).

thf(f2232,plain,
    ! [X0: name,X1: name] :
      ( ( X0 = X1 )
      | ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_BoundOutputS,X0)),vAPP(name,late_subject,late_BoundOutputS,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2228]) ).

thf(f2228,plain,
    ! [X0: name,X1: name] :
      ( ( $true = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) )
      | ( $false = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_BoundOutputS,X0)),vAPP(name,late_subject,late_BoundOutputS,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1416]) ).

thf(f1416,plain,
    ! [X0: name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_BoundOutputS,X0)),vAPP(name,late_subject,late_BoundOutputS,X1)) ),
    inference(cnf_transformation,[],[f392]) ).

thf(f392,plain,
    ! [X0: name,X1: name] : ( vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_BoundOutputS,X0)),vAPP(name,late_subject,late_BoundOutputS,X1)) ),
    inference(fool_elimination,[],[f391]) ).

thf(f391,plain,
    ! [X0: name,X1: name] :
      ( ( vAPP(name,late_subject,late_BoundOutputS,X0) = vAPP(name,late_subject,late_BoundOutputS,X1) )
      = ( X0 = X1 ) ),
    inference(rectify,[],[f59]) ).

thf(f59,axiom,
    ! [X4: name,X6: name] :
      ( ( vAPP(name,late_subject,late_BoundOutputS,X4) = vAPP(name,late_subject,late_BoundOutputS,X6) )
      = ( X4 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Late__Semantics1_Osubject_Oinject_I2_J) ).

thf(f2489,plain,
    spl225_45,
    inference(avatar_split_clause,[],[f1423,f2487]) ).

thf(f1423,plain,
    ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$true),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f406]) ).

thf(f406,plain,
    ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$true),X0),X1) = X0 ),
    inference(fool_elimination,[],[f405]) ).

thf(f405,plain,
    ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$true),X0),X1) = X0 ),
    inference(rectify,[],[f360]) ).

thf(f360,axiom,
    ! [X2: late_subject,X22: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$true),X2),X22) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Late____Semantics__Osubject_T) ).

thf(f2485,plain,
    spl225_44,
    inference(avatar_split_clause,[],[f1422,f2483]) ).

thf(f2483,plain,
    ( spl225_44
  <=> ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$false),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_44])]) ).

thf(f1422,plain,
    ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$false),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f404]) ).

thf(f404,plain,
    ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$false),X0),X1) = X1 ),
    inference(fool_elimination,[],[f403]) ).

thf(f403,plain,
    ! [X0: late_subject,X1: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$false),X0),X1) = X1 ),
    inference(rectify,[],[f359]) ).

thf(f359,axiom,
    ! [X2: late_subject,X22: late_subject] : ( vAPP(late_subject,late_subject,vAPP(late_subject,sTfun(late_subject,late_subject),vAPP($o,sTfun(late_subject,sTfun(late_subject,late_subject)),if_Late_subject,$false),X2),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__Osubject_T) ).

thf(f2481,plain,
    spl225_43,
    inference(avatar_split_clause,[],[f1421,f2479]) ).

thf(f1421,plain,
    ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$true),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f402]) ).

thf(f402,plain,
    ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$true),X0),X1) = X0 ),
    inference(fool_elimination,[],[f401]) ).

thf(f401,plain,
    ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$true),X0),X1) = X0 ),
    inference(rectify,[],[f357]) ).

thf(f357,axiom,
    ! [X2: late_freeRes,X22: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$true),X2),X22) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Late____Semantics__OfreeRes_T) ).

thf(f2477,plain,
    spl225_42,
    inference(avatar_split_clause,[],[f1420,f2475]) ).

thf(f2475,plain,
    ( spl225_42
  <=> ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$false),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_42])]) ).

thf(f1420,plain,
    ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$false),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f400]) ).

thf(f400,plain,
    ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$false),X0),X1) = X1 ),
    inference(fool_elimination,[],[f399]) ).

thf(f399,plain,
    ! [X0: late_freeRes,X1: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$false),X0),X1) = X1 ),
    inference(rectify,[],[f356]) ).

thf(f356,axiom,
    ! [X2: late_freeRes,X22: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(late_freeRes,sTfun(late_freeRes,late_freeRes),vAPP($o,sTfun(late_freeRes,sTfun(late_freeRes,late_freeRes)),if_Late_freeRes,$false),X2),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__OfreeRes_T) ).

thf(f2473,plain,
    spl225_41,
    inference(avatar_split_clause,[],[f1419,f2471]) ).

thf(f1419,plain,
    ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$true),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f398]) ).

thf(f398,plain,
    ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$true),X0),X1) = X0 ),
    inference(fool_elimination,[],[f397]) ).

thf(f397,plain,
    ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$true),X0),X1) = X0 ),
    inference(rectify,[],[f355]) ).

thf(f355,axiom,
    ! [X2: pi_Rep,X22: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$true),X2),X22) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi____Rep_T) ).

thf(f2469,plain,
    spl225_40,
    inference(avatar_split_clause,[],[f1418,f2467]) ).

thf(f2467,plain,
    ( spl225_40
  <=> ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$false),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_40])]) ).

thf(f1418,plain,
    ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$false),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f396]) ).

thf(f396,plain,
    ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$false),X0),X1) = X1 ),
    inference(fool_elimination,[],[f395]) ).

thf(f395,plain,
    ! [X0: pi_Rep,X1: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$false),X0),X1) = X1 ),
    inference(rectify,[],[f354]) ).

thf(f354,axiom,
    ! [X2: pi_Rep,X22: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(pi_Rep,sTfun(pi_Rep,pi_Rep),vAPP($o,sTfun(pi_Rep,sTfun(pi_Rep,pi_Rep)),if_pi_Rep,$false),X2),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi____Rep_T) ).

thf(f2465,plain,
    spl225_39,
    inference(avatar_split_clause,[],[f1402,f2463]) ).

thf(f2463,plain,
    ( spl225_39
  <=> ! [X0: pi,X1: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_39])]) ).

thf(f1402,plain,
    ! [X0: pi,X1: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X1),X1) = X0 ),
    inference(cnf_transformation,[],[f800]) ).

thf(f800,plain,
    ! [X0: pi,X1: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X0),X1),X1) = X0 ),
    inference(rectify,[],[f317]) ).

thf(f317,axiom,
    ! [X19: pi,X0: name] : ( vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,X19),X0),X0) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_subst__identity) ).

thf(f2461,plain,
    spl225_38,
    inference(avatar_split_clause,[],[f1394,f2459]) ).

thf(f1394,plain,
    ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK54,X0)),vAPP(product_prod_pi_pi,pi,sK55,X0)) = X0 ),
    inference(cnf_transformation,[],[f1207]) ).

thf(f1207,plain,
    ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK54,X0)),vAPP(product_prod_pi_pi,pi,sK55,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f793,f1206]) ).

thf(f1206,plain,
    ! [X0: product_prod_pi_pi] :
      ( ? [X1: pi,X2: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2) = X0 )
     => ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK54,X0)),vAPP(product_prod_pi_pi,pi,sK55,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f793,plain,
    ! [X0: product_prod_pi_pi] :
    ? [X1: pi,X2: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2) = X0 ),
    inference(rectify,[],[f225]) ).

thf(f225,axiom,
    ! [X71: product_prod_pi_pi] :
    ? [X63: pi,X50: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X63),X50) = X71 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_surj__pair) ).

thf(f2457,plain,
    spl225_37,
    inference(avatar_split_clause,[],[f1393,f2455]) ).

thf(f1393,plain,
    ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK52,X0)),vAPP(produc367475239e_name,name,sK53,X0)) = X0 ),
    inference(cnf_transformation,[],[f1205]) ).

thf(f1205,plain,
    ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK52,X0)),vAPP(produc367475239e_name,name,sK53,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53])],[f792,f1204]) ).

thf(f1204,plain,
    ! [X0: produc367475239e_name] :
      ( ? [X1: name,X2: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2) = X0 )
     => ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK52,X0)),vAPP(produc367475239e_name,name,sK53,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f792,plain,
    ! [X0: produc367475239e_name] :
    ? [X1: name,X2: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2) = X0 ),
    inference(rectify,[],[f224]) ).

thf(f224,axiom,
    ! [X71: produc367475239e_name] :
    ? [X63: name,X50: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X63),X50) = X71 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_surj__pair) ).

thf(f2453,plain,
    spl225_36,
    inference(avatar_split_clause,[],[f1392,f2451]) ).

thf(f1392,plain,
    ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK50,X0)),vAPP(product_prod_pi_pi,pi,sK51,X0)) = X0 ),
    inference(cnf_transformation,[],[f1203]) ).

thf(f1203,plain,
    ! [X0: product_prod_pi_pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK50,X0)),vAPP(product_prod_pi_pi,pi,sK51,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f936,f1202]) ).

thf(f1202,plain,
    ! [X0: product_prod_pi_pi] :
      ( ? [X1: pi,X2: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2) = X0 )
     => ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,vAPP(product_prod_pi_pi,pi,sK50,X0)),vAPP(product_prod_pi_pi,pi,sK51,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f936,plain,
    ! [X0: product_prod_pi_pi] :
    ? [X1: pi,X2: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2) = X0 ),
    inference(ennf_transformation,[],[f791]) ).

thf(f791,plain,
    ! [X0: product_prod_pi_pi] :
      ~ ! [X1: pi,X2: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X1),X2) != X0 ),
    inference(rectify,[],[f231]) ).

thf(f231,axiom,
    ! [X22: product_prod_pi_pi] :
      ~ ! [X61: pi,X62: pi] : ( vAPP(pi,product_prod_pi_pi,vAPP(pi,sTfun(pi,product_prod_pi_pi),product_Pair_pi_pi,X61),X62) != X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_old_Oprod_Oexhaust) ).

thf(f2449,plain,
    spl225_35,
    inference(avatar_split_clause,[],[f2231,f2447]) ).

thf(f2447,plain,
    ( spl225_35
  <=> ! [X0: name,X1: name] :
        ( ( X0 != X1 )
        | ( vAPP(name,late_subject,late_BoundOutputS,X0) = vAPP(name,late_subject,late_BoundOutputS,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_35])]) ).

thf(f2231,plain,
    ! [X0: name,X1: name] :
      ( ( X0 != X1 )
      | ( vAPP(name,late_subject,late_BoundOutputS,X0) = vAPP(name,late_subject,late_BoundOutputS,X1) ) ),
    inference(equality_proxy_clausification,[],[f2230]) ).

thf(f2230,plain,
    ! [X0: name,X1: name] :
      ( ( X0 != X1 )
      | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_BoundOutputS,X0)),vAPP(name,late_subject,late_BoundOutputS,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2229]) ).

thf(f2229,plain,
    ! [X0: name,X1: name] :
      ( ( $false = vAPP(name,$o,vAPP(name,sTfun(name,$o),vEQ(name),X0),X1) )
      | ( $true = vAPP(late_subject,$o,vAPP(late_subject,sTfun(late_subject,$o),vEQ(late_subject),vAPP(name,late_subject,late_BoundOutputS,X0)),vAPP(name,late_subject,late_BoundOutputS,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1416]) ).

thf(f2445,plain,
    spl225_34,
    inference(avatar_split_clause,[],[f1391,f2443]) ).

thf(f1391,plain,
    ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0)) = X0 ),
    inference(cnf_transformation,[],[f1201]) ).

thf(f1201,plain,
    ! [X0: produc367475239e_name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f935,f1200]) ).

thf(f1200,plain,
    ! [X0: produc367475239e_name] :
      ( ? [X1: name,X2: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2) = X0 )
     => ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,vAPP(produc367475239e_name,name,sK48,X0)),vAPP(produc367475239e_name,name,sK49,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f935,plain,
    ! [X0: produc367475239e_name] :
    ? [X1: name,X2: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2) = X0 ),
    inference(ennf_transformation,[],[f790]) ).

thf(f790,plain,
    ! [X0: produc367475239e_name] :
      ~ ! [X1: name,X2: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X1),X2) != X0 ),
    inference(rectify,[],[f230]) ).

thf(f230,axiom,
    ! [X22: produc367475239e_name] :
      ~ ! [X61: name,X62: name] : ( vAPP(name,produc367475239e_name,vAPP(name,sTfun(name,produc367475239e_name),produc1570949143e_name,X61),X62) != X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_old_Oprod_Oexhaust) ).

thf(f2433,plain,
    spl225_33,
    inference(avatar_split_clause,[],[f1385,f2431]) ).

thf(f1385,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) ),
    inference(cnf_transformation,[],[f1189]) ).

thf(f1189,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
      | ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f929,f1188]) ).

thf(f1188,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ? [X1: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,X0,X1) )
     => ( $true != vAPP(list_P227219501e_name,$o,X0,vAPP(sTfun(list_P227219501e_name,$o),list_P227219501e_name,sK41,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f929,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) )
      | ? [X1: list_P227219501e_name] : ( $true != vAPP(list_P227219501e_name,$o,X0,X1) ) ),
    inference(ennf_transformation,[],[f378]) ).

thf(f378,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ! [X1: list_P227219501e_name] : ( $true = vAPP(list_P227219501e_name,$o,X0,X1) )
     => ( $true = vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ) ),
    inference(fool_elimination,[],[f377]) ).

thf(f377,plain,
    ! [X0: list_P227219501e_name > $o] :
      ( ! [X1: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,X0,X1)
     => vAPP(list_P227219501e_name,$o,X0,nil_Pr743626285e_name) ),
    inference(rectify,[],[f235]) ).

thf(f235,axiom,
    ! [X19: list_P227219501e_name > $o] :
      ( ! [X73: list_P227219501e_name] : vAPP(list_P227219501e_name,$o,X19,X73)
     => vAPP(list_P227219501e_name,$o,X19,nil_Pr743626285e_name) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_allE__Nil) ).

thf(f2429,plain,
    spl225_32,
    inference(avatar_split_clause,[],[f1390,f2427]) ).

thf(f1390,plain,
    ! [X0: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),X0) ),
    inference(cnf_transformation,[],[f1199]) ).

thf(f1199,plain,
    ! [X0: pi] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f934,f1198]) ).

thf(f1198,plain,
    ! [X0: pi] :
      ( ? [X1: name] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X0) )
     => ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,vAPP(pi,name,sK47,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f934,plain,
    ! [X0: pi] :
    ? [X1: name] : ( $true = vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X0) ),
    inference(ennf_transformation,[],[f789]) ).

thf(f789,plain,
    ! [X0: pi] :
      ~ ! [X1: name] : ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X0) ),
    inference(flattening,[],[f386]) ).

thf(f386,plain,
    ! [X0: pi] :
      ~ ! [X1: name] : ( $true != vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X0) ),
    inference(fool_elimination,[],[f385]) ).

thf(f385,plain,
    ! [X0: pi] :
      ~ ! [X1: name] : ~ vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X1),X0),
    inference(rectify,[],[f86]) ).

thf(f86,axiom,
    ! [X2: pi] :
      ~ ! [X18: name] : ~ vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,X18),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_name__exists__fresh) ).

thf(f2425,plain,
    spl225_31,
    inference(avatar_split_clause,[],[f1388,f2423]) ).

thf(f2423,plain,
    ( spl225_31
  <=> ! [X0: late_subject] : ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_subject,name,sK45,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_31])]) ).

thf(f1388,plain,
    ! [X0: late_subject] : ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_subject,name,sK45,X0)),X0) ),
    inference(cnf_transformation,[],[f1195]) ).

thf(f1195,plain,
    ! [X0: late_subject] : ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_subject,name,sK45,X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f932,f1194]) ).

thf(f1194,plain,
    ! [X0: late_subject] :
      ( ? [X1: name] : ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X0) )
     => ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,vAPP(late_subject,name,sK45,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f932,plain,
    ! [X0: late_subject] :
    ? [X1: name] : ( $true = vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X0) ),
    inference(ennf_transformation,[],[f787]) ).

thf(f787,plain,
    ! [X0: late_subject] :
      ~ ! [X1: name] : ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X0) ),
    inference(flattening,[],[f382]) ).

thf(f382,plain,
    ! [X0: late_subject] :
      ~ ! [X1: name] : ( $true != vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X0) ),
    inference(fool_elimination,[],[f381]) ).

thf(f381,plain,
    ! [X0: late_subject] :
      ~ ! [X1: name] : ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X1),X0),
    inference(rectify,[],[f83]) ).

thf(f83,axiom,
    ! [X2: late_subject] :
      ~ ! [X18: name] : ~ vAPP(late_subject,$o,vAPP(name,sTfun(late_subject,$o),fresh_717452603ubject,X18),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_name__exists__fresh) ).

thf(f2421,plain,
    spl225_30,
    inference(avatar_split_clause,[],[f1387,f2419]) ).

thf(f2419,plain,
    ( spl225_30
  <=> ! [X0: late_freeRes] : ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(late_freeRes,name,sK44,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_30])]) ).

thf(f1387,plain,
    ! [X0: late_freeRes] : ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(late_freeRes,name,sK44,X0)),X0) ),
    inference(cnf_transformation,[],[f1193]) ).

thf(f1193,plain,
    ! [X0: late_freeRes] : ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(late_freeRes,name,sK44,X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f931,f1192]) ).

thf(f1192,plain,
    ! [X0: late_freeRes] :
      ( ? [X1: name] : ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X0) )
     => ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,vAPP(late_freeRes,name,sK44,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f931,plain,
    ! [X0: late_freeRes] :
    ? [X1: name] : ( $true = vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X0) ),
    inference(ennf_transformation,[],[f786]) ).

thf(f786,plain,
    ! [X0: late_freeRes] :
      ~ ! [X1: name] : ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X0) ),
    inference(flattening,[],[f380]) ).

thf(f380,plain,
    ! [X0: late_freeRes] :
      ~ ! [X1: name] : ( $true != vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X0) ),
    inference(fool_elimination,[],[f379]) ).

thf(f379,plain,
    ! [X0: late_freeRes] :
      ~ ! [X1: name] : ~ vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X1),X0),
    inference(rectify,[],[f84]) ).

thf(f84,axiom,
    ! [X2: late_freeRes] :
      ~ ! [X18: name] : ~ vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X18),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_name__exists__fresh) ).

thf(f2417,plain,
    spl225_29,
    inference(avatar_split_clause,[],[f1806,f2414]) ).

thf(f1806,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p) = $true,
    inference(cnf_transformation,[],[f752]) ).

thf(f752,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p) = $true,
    inference(fool_elimination,[],[f751]) ).

thf(f751,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p),
    inference(rectify,[],[f49]) ).

thf(f49,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,x),p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_assms_I1_J) ).

thf(f2412,plain,
    spl225_28,
    inference(avatar_split_clause,[],[f1805,f2409]) ).

thf(f1805,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q) = $true,
    inference(cnf_transformation,[],[f750]) ).

thf(f750,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q) = $true,
    inference(fool_elimination,[],[f749]) ).

thf(f749,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q),
    inference(rectify,[],[f43]) ).

thf(f43,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),q),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062) ).

thf(f2407,plain,
    spl225_27,
    inference(avatar_split_clause,[],[f1804,f2404]) ).

thf(f1804,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p) = $true,
    inference(cnf_transformation,[],[f748]) ).

thf(f748,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p) = $true,
    inference(fool_elimination,[],[f747]) ).

thf(f747,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p),
    inference(rectify,[],[f50]) ).

thf(f50,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_cClose1_Ohyps_I8_J) ).

thf(f2402,plain,
    spl225_26,
    inference(avatar_split_clause,[],[f1803,f2399]) ).

thf(f1803,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p2) = $true,
    inference(cnf_transformation,[],[f746]) ).

thf(f746,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p2) = $true,
    inference(fool_elimination,[],[f745]) ).

thf(f745,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p2),
    inference(rectify,[],[f46]) ).

thf(f46,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,z),p2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_cClose1_Ohyps_I11_J) ).

thf(f2397,plain,
    spl225_25,
    inference(avatar_split_clause,[],[f1802,f2394]) ).

thf(f1802,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),p) = $true,
    inference(cnf_transformation,[],[f744]) ).

thf(f744,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),p) = $true,
    inference(fool_elimination,[],[f743]) ).

thf(f743,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),p),
    inference(rectify,[],[f51]) ).

thf(f51,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_cClose1_Ohyps_I3_J) ).

thf(f2392,plain,
    spl225_24,
    inference(avatar_split_clause,[],[f1801,f2389]) ).

thf(f1801,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),q2) = $true,
    inference(cnf_transformation,[],[f742]) ).

thf(f742,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),q2) = $true,
    inference(fool_elimination,[],[f741]) ).

thf(f741,plain,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),q2),
    inference(rectify,[],[f47]) ).

thf(f47,axiom,
    vAPP(pi,$o,vAPP(name,sTfun(pi,$o),fresh_name_pi,y),q2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_cClose1_Ohyps_I7_J) ).

thf(f2387,plain,
    spl225_23,
    inference(avatar_split_clause,[],[f1401,f2385]) ).

thf(f1401,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) != X1 ),
    inference(cnf_transformation,[],[f799]) ).

thf(f799,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) != X1 ),
    inference(rectify,[],[f234]) ).

thf(f234,axiom,
    ! [X2: produc367475239e_name,X43: list_P227219501e_name] : ( vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X2),X43) != X43 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_not__Cons__self2) ).

thf(f2383,plain,
    spl225_22,
    inference(avatar_split_clause,[],[f1400,f2381]) ).

thf(f1400,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( nil_Pr743626285e_name != vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) ),
    inference(cnf_transformation,[],[f798]) ).

thf(f798,plain,
    ! [X0: produc367475239e_name,X1: list_P227219501e_name] : ( nil_Pr743626285e_name != vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X0),X1) ),
    inference(rectify,[],[f263]) ).

thf(f263,axiom,
    ! [X37: produc367475239e_name,X38: list_P227219501e_name] : ( nil_Pr743626285e_name != vAPP(list_P227219501e_name,list_P227219501e_name,vAPP(produc367475239e_name,sTfun(list_P227219501e_name,list_P227219501e_name),cons_P1213805021e_name,X37),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_list_Odistinct_I1_J) ).

thf(f2379,plain,
    spl225_21,
    inference(avatar_split_clause,[],[f1398,f2377]) ).

thf(f1398,plain,
    ! [X0: name,X1: name] : ( late_TauR != vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) ),
    inference(cnf_transformation,[],[f796]) ).

thf(f796,plain,
    ! [X0: name,X1: name] : ( late_TauR != vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X0),X1) ),
    inference(rectify,[],[f105]) ).

thf(f105,axiom,
    ! [X28: name,X29: name] : ( late_TauR != vAPP(name,late_freeRes,vAPP(name,sTfun(name,late_freeRes),late_OutputR,X28),X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Late__Semantics_OfreeRes_Odistinct_I1_J) ).

thf(f2375,plain,
    spl225_20,
    inference(avatar_split_clause,[],[f1395,f2373]) ).

thf(f2373,plain,
    ( spl225_20
  <=> ! [X0: name] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),late_TauR) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_20])]) ).

thf(f1395,plain,
    ! [X0: name] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),late_TauR) = $true ),
    inference(cnf_transformation,[],[f388]) ).

thf(f388,plain,
    ! [X0: name] : ( vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),late_TauR) = $true ),
    inference(fool_elimination,[],[f387]) ).

thf(f387,plain,
    ! [X0: name] : vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),late_TauR),
    inference(rectify,[],[f188]) ).

thf(f188,axiom,
    ! [X0: name] : vAPP(late_freeRes,$o,vAPP(name,sTfun(late_freeRes,$o),fresh_1641682979reeRes,X0),late_TauR),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_freeRes_Ofresh_I2_J) ).

thf(f2371,plain,
    spl225_19,
    inference(avatar_split_clause,[],[f1373,f2369]) ).

thf(f1373,plain,
    ! [X0: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f776]) ).

thf(f776,plain,
    ! [X0: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f35]) ).

thf(f35,axiom,
    ! [X2: pi] : ( vAPP(pi,pi,vAPP(list_P227219501e_name,sTfun(pi,pi),perm_name_pi,nil_Pr743626285e_name),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_pt__name1) ).

thf(f2367,plain,
    spl225_18,
    inference(avatar_split_clause,[],[f1370,f2365]) ).

thf(f2363,plain,
    spl225_17,
    inference(avatar_split_clause,[],[f1369,f2361]) ).

thf(f1369,plain,
    ! [X0: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f773]) ).

thf(f773,plain,
    ! [X0: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f31]) ).

thf(f31,axiom,
    ! [X2: late_subject] : ( vAPP(late_subject,late_subject,vAPP(list_P227219501e_name,sTfun(late_subject,late_subject),perm_n1559866809ubject,nil_Pr743626285e_name),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_pt__name1) ).

thf(f2359,plain,
    spl225_16,
    inference(avatar_split_clause,[],[f1368,f2357]) ).

thf(f1368,plain,
    ! [X0: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f772]) ).

thf(f772,plain,
    ! [X0: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f32]) ).

thf(f32,axiom,
    ! [X2: late_freeRes] : ( vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,nil_Pr743626285e_name),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_pt__name1) ).

thf(f2355,plain,
    spl225_15,
    inference(avatar_split_clause,[],[f1366,f2353]) ).

thf(f1366,plain,
    ! [X0: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f770]) ).

thf(f770,plain,
    ! [X0: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f33]) ).

thf(f33,axiom,
    ! [X2: pi_Rep] : ( vAPP(pi_Rep,pi_Rep,vAPP(list_P227219501e_name,sTfun(pi_Rep,pi_Rep),perm_name_pi_Rep,nil_Pr743626285e_name),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_pt__name1) ).

thf(f2351,plain,
    spl225_14,
    inference(avatar_split_clause,[],[f1365,f2349]) ).

thf(f2349,plain,
    ( spl225_14
  <=> ! [X0: late_residual_Rep] : ( vAPP(late_residual_Rep,late_residual_Rep,vAPP(list_P227219501e_name,sTfun(late_residual_Rep,late_residual_Rep),perm_n890803237al_Rep,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_14])]) ).

thf(f1365,plain,
    ! [X0: late_residual_Rep] : ( vAPP(late_residual_Rep,late_residual_Rep,vAPP(list_P227219501e_name,sTfun(late_residual_Rep,late_residual_Rep),perm_n890803237al_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f769]) ).

thf(f769,plain,
    ! [X0: late_residual_Rep] : ( vAPP(late_residual_Rep,late_residual_Rep,vAPP(list_P227219501e_name,sTfun(late_residual_Rep,late_residual_Rep),perm_n890803237al_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f52]) ).

thf(f52,axiom,
    ! [X12: late_residual_Rep] : ( vAPP(late_residual_Rep,late_residual_Rep,vAPP(list_P227219501e_name,sTfun(late_residual_Rep,late_residual_Rep),perm_n890803237al_Rep,nil_Pr743626285e_name),X12) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_residual__perm__empty) ).

thf(f2347,plain,
    spl225_13,
    inference(avatar_split_clause,[],[f1364,f2345]) ).

thf(f2345,plain,
    ( spl225_13
  <=> ! [X0: late_subject_Rep] : ( vAPP(late_subject_Rep,late_subject_Rep,vAPP(list_P227219501e_name,sTfun(late_subject_Rep,late_subject_Rep),perm_n697952036ct_Rep,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_13])]) ).

thf(f1364,plain,
    ! [X0: late_subject_Rep] : ( vAPP(late_subject_Rep,late_subject_Rep,vAPP(list_P227219501e_name,sTfun(late_subject_Rep,late_subject_Rep),perm_n697952036ct_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f768]) ).

thf(f768,plain,
    ! [X0: late_subject_Rep] : ( vAPP(late_subject_Rep,late_subject_Rep,vAPP(list_P227219501e_name,sTfun(late_subject_Rep,late_subject_Rep),perm_n697952036ct_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f53]) ).

thf(f53,axiom,
    ! [X13: late_subject_Rep] : ( vAPP(late_subject_Rep,late_subject_Rep,vAPP(list_P227219501e_name,sTfun(late_subject_Rep,late_subject_Rep),perm_n697952036ct_Rep,nil_Pr743626285e_name),X13) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_subject__perm__empty) ).

thf(f2343,plain,
    spl225_12,
    inference(avatar_split_clause,[],[f1363,f2341]) ).

thf(f2341,plain,
    ( spl225_12
  <=> ! [X0: late_freeRes_Rep] : ( vAPP(late_freeRes_Rep,late_freeRes_Rep,vAPP(list_P227219501e_name,sTfun(late_freeRes_Rep,late_freeRes_Rep),perm_n1938283068es_Rep,nil_Pr743626285e_name),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_12])]) ).

thf(f1363,plain,
    ! [X0: late_freeRes_Rep] : ( vAPP(late_freeRes_Rep,late_freeRes_Rep,vAPP(list_P227219501e_name,sTfun(late_freeRes_Rep,late_freeRes_Rep),perm_n1938283068es_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(cnf_transformation,[],[f767]) ).

thf(f767,plain,
    ! [X0: late_freeRes_Rep] : ( vAPP(late_freeRes_Rep,late_freeRes_Rep,vAPP(list_P227219501e_name,sTfun(late_freeRes_Rep,late_freeRes_Rep),perm_n1938283068es_Rep,nil_Pr743626285e_name),X0) = X0 ),
    inference(rectify,[],[f54]) ).

thf(f54,axiom,
    ! [X14: late_freeRes_Rep] : ( vAPP(late_freeRes_Rep,late_freeRes_Rep,vAPP(list_P227219501e_name,sTfun(late_freeRes_Rep,late_freeRes_Rep),perm_n1938283068es_Rep,nil_Pr743626285e_name),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_freeRes__perm__empty) ).

thf(f2339,plain,
    spl225_11,
    inference(avatar_split_clause,[],[f1362,f2337]) ).

thf(f1362,plain,
    ! [X0: list_P227219501e_name] : ( late_TauR = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),late_TauR) ),
    inference(cnf_transformation,[],[f766]) ).

thf(f766,plain,
    ! [X0: list_P227219501e_name] : ( late_TauR = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X0),late_TauR) ),
    inference(rectify,[],[f60]) ).

thf(f60,axiom,
    ! [X5: list_P227219501e_name] : ( late_TauR = vAPP(late_freeRes,late_freeRes,vAPP(list_P227219501e_name,sTfun(late_freeRes,late_freeRes),perm_n336613537reeRes,X5),late_TauR) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_freeRes_Operm_I2_J) ).

thf(f2335,plain,
    spl225_10,
    inference(avatar_split_clause,[],[f1396,f2333]) ).

thf(f1396,plain,
    ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) ),
    inference(cnf_transformation,[],[f794]) ).

thf(f794,plain,
    ! [X0: name,X1: name] : ( vAPP(name,late_subject,late_InputS,X0) != vAPP(name,late_subject,late_BoundOutputS,X1) ),
    inference(rectify,[],[f293]) ).

thf(f293,axiom,
    ! [X52: name,X92: name] : ( vAPP(name,late_subject,late_InputS,X52) != vAPP(name,late_subject,late_BoundOutputS,X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Late__Semantics_Osubject_Odistinct_I1_J) ).

thf(f2331,plain,
    spl225_9,
    inference(avatar_split_clause,[],[f1798,f2328]) ).

thf(f2328,plain,
    ( spl225_9
  <=> ( vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,rel) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_9])]) ).

thf(f1798,plain,
    vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,rel) = $true,
    inference(cnf_transformation,[],[f736]) ).

thf(f736,plain,
    vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,rel) = $true,
    inference(fool_elimination,[],[f735]) ).

thf(f735,plain,
    vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,rel),
    inference(rectify,[],[f316]) ).

thf(f316,axiom,
    vAPP(set_Pr1834926343_pi_pi,$o,eqvt_pi,rel),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_EqvtRel) ).

thf(f2298,plain,
    spl225_8,
    inference(avatar_split_clause,[],[f364,f2296]) ).

thf(f364,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f2294,plain,
    ~ spl225_7,
    inference(avatar_split_clause,[],[f1815,f2291]) ).

thf(f2291,plain,
    ( spl225_7
  <=> ( b = z ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_7])]) ).

thf(f1815,plain,
    b != z,
    inference(definition_unfolding,[],[f1351,f1356]) ).

thf(f1351,plain,
    aa != z,
    inference(cnf_transformation,[],[f3]) ).

thf(f3,axiom,
    aa != z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cClose1_Ohyps_I10_J) ).

thf(f2289,plain,
    ~ spl225_6,
    inference(avatar_split_clause,[],[f1814,f2286]) ).

thf(f2286,plain,
    ( spl225_6
  <=> ( b = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_6])]) ).

thf(f1814,plain,
    b != y,
    inference(definition_unfolding,[],[f1350,f1356]) ).

thf(f1350,plain,
    aa != y,
    inference(cnf_transformation,[],[f5]) ).

thf(f5,axiom,
    aa != y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cClose1_Ohyps_I5_J) ).

thf(f2284,plain,
    ~ spl225_5,
    inference(avatar_split_clause,[],[f1354,f2281]) ).

thf(f1354,plain,
    x != z,
    inference(cnf_transformation,[],[f6]) ).

thf(f6,axiom,
    x != z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062) ).

thf(f2279,plain,
    ~ spl225_4,
    inference(avatar_split_clause,[],[f1353,f2276]) ).

thf(f1353,plain,
    x != y,
    inference(cnf_transformation,[],[f36]) ).

thf(f36,axiom,
    x != y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062) ).

thf(f2274,plain,
    ~ spl225_3,
    inference(avatar_split_clause,[],[f1352,f2271]) ).

thf(f2271,plain,
    ( spl225_3
  <=> ( z = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_3])]) ).

thf(f1352,plain,
    z != y,
    inference(cnf_transformation,[],[f4]) ).

thf(f4,axiom,
    z != y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_cClose1_Ohyps_I6_J) ).

thf(f2269,plain,
    ~ spl225_2,
    inference(avatar_split_clause,[],[f1349,f2266]) ).

thf(f2266,plain,
    ( spl225_2
  <=> ( b = x ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_2])]) ).

thf(f1349,plain,
    b != x,
    inference(cnf_transformation,[],[f2]) ).

thf(f2,axiom,
    b != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cOpen_Ohyps_I2_J) ).

thf(f2264,plain,
    ~ spl225_1,
    inference(avatar_split_clause,[],[f363,f2261]) ).

thf(f2261,plain,
    ( spl225_1
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl225_1])]) ).

thf(f363,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ITP190^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n009.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sat May 18 16:32:53 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (16078)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.42  % (16081)WARNING: value z3 for option sas not known
% 0.23/0.42  % (16082)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.42  % (16084)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.23/0.42  % (16079)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.42  % (16083)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.23/0.42  % (16080)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.42  % (16085)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.23/0.42  % (16081)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.23/0.47  % (16085)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.50  % Exception at run slice level
% 0.23/0.50  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.51  % Exception at run slice level
% 0.23/0.51  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.52  % (16086)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.98/0.52  % Exception at run slice level
% 0.98/0.52  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.98/0.52  % (16087)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.98/0.53  % (16088)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 1.04/0.56  % (16087)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.04/0.56  % (16086)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.04/0.57  % Exception at run slice level
% 1.04/0.57  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.04/0.58  % (16089)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 6.77/1.38  % (16083)First to succeed.
% 7.74/1.49  % (16083)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16078"
% 7.74/1.50  % (16083)Refutation found. Thanks to Tanya!
% 7.74/1.50  % SZS status Theorem for theBenchmark
% 7.74/1.50  % SZS output start Proof for theBenchmark
% See solution above
% 7.74/1.52  % (16083)------------------------------
% 7.74/1.52  % (16083)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.74/1.52  % (16083)Termination reason: Refutation
% 7.74/1.52  
% 7.74/1.52  % (16083)Memory used [KB]: 9134
% 7.74/1.52  % (16083)Time elapsed: 1.077 s
% 7.74/1.52  % (16083)Instructions burned: 3941 (million)
% 7.74/1.52  % (16078)Success in time 1.132 s
%------------------------------------------------------------------------------