TSTP Solution File: ITP085^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP085^1 : 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 : n017.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 22:51:14 EDT 2024

% Result   : Theorem 13.44s 2.36s
% Output   : Refutation 13.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      : 1718
% Syntax   : Number of formulae    : 4803 (1014 unt; 483 typ;   0 def)
%            Number of atoms       : 53246 (9081 equ;   0 cnn)
%            Maximal formula atoms :   13 (  12 avg)
%            Number of connectives : 13263 (4591   ~;5449   |;1092   &;   0   @)
%                                         ( 800 <=>;1331  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Number of types       :   20 (  19 usr)
%            Number of type conns  : 4069 (4068   >;   1   *;   0   +;   0  <<)
%            Number of symbols     : 1252 (1249 usr; 810 con; 0-6 aty)
%            Number of variables   : 9379 (  54   ^7955   !;1356   ?;9379   :)
%                                         (  14  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    set_li185139947ession: $tType ).

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

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

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

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

thf(type_def_10,type,
    set_li849033543y_Keys: $tType ).

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

thf(type_def_12,type,
    set_li2007071804ecrets: $tType ).

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

thf(type_def_14,type,
    list_S529945141ession: $tType ).

thf(type_def_15,type,
    set_Se1942955227ession: $tType ).

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

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

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

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

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

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

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

thf(type_def_23,type,
    list_l425507653ession: $tType ).

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

thf(func_def_0,type,
    list_l425507653ession: $tType ).

thf(func_def_1,type,
    set_li185139947ession: $tType ).

thf(func_def_2,type,
    set_li2007071804ecrets: $tType ).

thf(func_def_3,type,
    set_li849033543y_Keys: $tType ).

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

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

thf(func_def_6,type,
    list_S529945141ession: $tType ).

thf(func_def_7,type,
    set_Se1942955227ession: $tType ).

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_19,type,
    bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).

thf(func_def_20,type,
    bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).

thf(func_def_21,type,
    bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).

thf(func_def_22,type,
    bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets ).

thf(func_def_23,type,
    bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession ).

thf(func_def_24,type,
    bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS ).

thf(func_def_25,type,
    bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys ).

thf(func_def_26,type,
    bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets ).

thf(func_def_27,type,
    localSecrets: secrecy_specID > set_Secrecy_KS ).

thf(func_def_28,type,
    knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).

thf(func_def_29,type,
    knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).

thf(func_def_30,type,
    knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).

thf(func_def_31,type,
    knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).

thf(func_def_32,type,
    mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).

thf(func_def_33,type,
    mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).

thf(func_def_34,type,
    append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).

thf(func_def_35,type,
    append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_36,type,
    append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_37,type,
    append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_38,type,
    append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).

thf(func_def_39,type,
    append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).

thf(func_def_40,type,
    bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).

thf(func_def_41,type,
    bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).

thf(func_def_42,type,
    bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).

thf(func_def_43,type,
    bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).

thf(func_def_44,type,
    butlas171474643ession: list_S529945141ession > list_S529945141ession ).

thf(func_def_45,type,
    butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_46,type,
    concat388015140ession: list_l425507653ession > list_S529945141ession ).

thf(func_def_47,type,
    concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_48,type,
    distin1076152135ession: list_S529945141ession > $o ).

thf(func_def_49,type,
    distin1495927511ecy_KS: list_Secrecy_KS > $o ).

thf(func_def_50,type,
    foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_51,type,
    foldr_1711005747ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_52,type,
    insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).

thf(func_def_53,type,
    insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_54,type,
    last_S1532390982ession: list_S529945141ession > secrecy_Expression ).

thf(func_def_55,type,
    last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).

thf(func_def_56,type,
    cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).

thf(func_def_57,type,
    cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_58,type,
    cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).

thf(func_def_59,type,
    cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_60,type,
    cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).

thf(func_def_61,type,
    cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).

thf(func_def_62,type,
    nil_li311616943ession: list_l425507653ession ).

thf(func_def_63,type,
    nil_list_Secrecy_KS: list_list_Secrecy_KS ).

thf(func_def_64,type,
    nil_Se901661471ession: list_S529945141ession ).

thf(func_def_65,type,
    nil_Secrecy_KS: list_Secrecy_KS ).

thf(func_def_66,type,
    nil_Secrecy_Keys: list_Secrecy_Keys ).

thf(func_def_67,type,
    nil_Secrecy_Secrets: list_Secrecy_Secrets ).

thf(func_def_68,type,
    hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).

thf(func_def_69,type,
    hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_70,type,
    hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).

thf(func_def_71,type,
    hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).

thf(func_def_72,type,
    tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).

thf(func_def_73,type,
    tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_74,type,
    list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).

thf(func_def_75,type,
    list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).

thf(func_def_76,type,
    listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).

thf(func_def_77,type,
    listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).

thf(func_def_78,type,
    listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).

thf(func_def_79,type,
    listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).

thf(func_def_80,type,
    map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_81,type,
    map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).

thf(func_def_82,type,
    maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).

thf(func_def_83,type,
    maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).

thf(func_def_84,type,
    maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).

thf(func_def_85,type,
    maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_86,type,
    member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).

thf(func_def_87,type,
    member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).

thf(func_def_88,type,
    lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).

thf(func_def_89,type,
    lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).

thf(func_def_90,type,
    produc1450295286ession: list_l425507653ession > list_l425507653ession ).

thf(func_def_91,type,
    produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_92,type,
    remdup484344169ession: list_S529945141ession > list_S529945141ession ).

thf(func_def_93,type,
    remdup351570169ecy_KS: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_94,type,
    rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).

thf(func_def_95,type,
    rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_96,type,
    rotate1237234450ession: list_S529945141ession > list_S529945141ession ).

thf(func_def_97,type,
    rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_98,type,
    shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).

thf(func_def_99,type,
    shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).

thf(func_def_100,type,
    splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_101,type,
    splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_102,type,
    subseq348280080ession: list_S529945141ession > list_l425507653ession ).

thf(func_def_103,type,
    subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_104,type,
    succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).

thf(func_def_105,type,
    succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).

thf(func_def_106,type,
    decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).

thf(func_def_107,type,
    enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).

thf(func_def_108,type,
    encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).

thf(func_def_109,type,
    ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).

thf(func_def_110,type,
    sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).

thf(func_def_111,type,
    eout: secrecy_specID > secrecy_Expression > $o ).

thf(func_def_112,type,
    ine: secrecy_specID > secrecy_Expression > $o ).

thf(func_def_113,type,
    notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).

thf(func_def_114,type,
    specKeys: secrecy_specID > set_Secrecy_Keys ).

thf(func_def_115,type,
    specKeysSecrets: secrecy_specID > set_Secrecy_KS ).

thf(func_def_116,type,
    specSecrets: secrecy_specID > set_Secrecy_Secrets ).

thf(func_def_117,type,
    secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).

thf(func_def_118,type,
    secrecy_kE: secrecy_Keys > secrecy_Expression ).

thf(func_def_119,type,
    secrecy_sE: secrecy_Secrets > secrecy_Expression ).

thf(func_def_120,type,
    secrec1016742679ession: secrecy_KS > secrecy_Expression ).

thf(func_def_121,type,
    secrecy_kKS: secrecy_Keys > secrecy_KS ).

thf(func_def_122,type,
    secrecy_sKS: secrecy_Secrets > secrecy_KS ).

thf(func_def_123,type,
    collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).

thf(func_def_124,type,
    collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).

thf(func_def_125,type,
    collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).

thf(func_def_126,type,
    member249235532ession: list_S529945141ession > set_li185139947ession > $o ).

thf(func_def_127,type,
    member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).

thf(func_def_128,type,
    member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).

thf(func_def_129,type,
    member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).

thf(func_def_130,type,
    member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).

thf(func_def_131,type,
    member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).

thf(func_def_132,type,
    member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).

thf(func_def_133,type,
    member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).

thf(func_def_134,type,
    a: secrecy_specID ).

thf(func_def_135,type,
    m: secrecy_Secrets ).

thf(func_def_139,type,
    vOR: $o > $o > $o ).

thf(func_def_140,type,
    vAND: $o > $o > $o ).

thf(func_def_141,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_142,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_143,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_144,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_145,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_146,type,
    vIMP: $o > $o > $o ).

thf(func_def_147,type,
    vNOT: $o > $o ).

thf(func_def_148,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_149,type,
    sP0: list_Secrecy_KS > list_Secrecy_KS > $o ).

thf(func_def_150,type,
    sP1: list_S529945141ession > list_S529945141ession > $o ).

thf(func_def_151,type,
    sP2: list_Secrecy_KS > $o > $o ).

thf(func_def_152,type,
    sP3: list_S529945141ession > $o > $o ).

thf(func_def_153,type,
    sP4: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > $o ).

thf(func_def_154,type,
    sP5: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > $o ).

thf(func_def_155,type,
    sP6: list_S529945141ession > list_S529945141ession > list_S529945141ession > $o ).

thf(func_def_156,type,
    sP7: list_S529945141ession > list_S529945141ession > list_S529945141ession > $o ).

thf(func_def_157,type,
    sP8: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > $o ).

thf(func_def_158,type,
    sP9: list_Secrecy_KS > secrecy_KS > secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).

thf(func_def_159,type,
    sP10: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > $o ).

thf(func_def_160,type,
    sP11: list_S529945141ession > list_Secrecy_KS > ( secrecy_Expression > secrecy_KS > $o ) > $o ).

thf(func_def_161,type,
    sP12: list_Secrecy_KS > list_S529945141ession > ( secrecy_KS > secrecy_Expression > $o ) > $o ).

thf(func_def_162,type,
    sP13: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > $o ).

thf(func_def_163,type,
    sP14: list_S529945141ession > secrecy_Expression > secrecy_Expression > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).

thf(func_def_164,type,
    sP15: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > $o ).

thf(func_def_165,type,
    sP16: ( secrecy_KS > secrecy_KS > $o ) > ( list_Secrecy_KS > list_Secrecy_KS > $o ) > $o ).

thf(func_def_166,type,
    sP17: ( secrecy_Expression > secrecy_Expression > $o ) > ( list_S529945141ession > list_S529945141ession > $o ) > $o ).

thf(func_def_167,type,
    sK18: list_list_Secrecy_KS > secrecy_KS ).

thf(func_def_168,type,
    sK19: list_list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_169,type,
    sK20: list_list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_170,type,
    sK21: list_list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_171,type,
    sK22: list_l425507653ession > secrecy_Expression ).

thf(func_def_172,type,
    sK23: list_l425507653ession > list_S529945141ession ).

thf(func_def_173,type,
    sK24: list_l425507653ession > list_l425507653ession ).

thf(func_def_174,type,
    sK25: list_l425507653ession > list_l425507653ession ).

thf(func_def_175,type,
    sK26: list_Secrecy_KS > secrecy_KS ).

thf(func_def_176,type,
    sK27: list_Secrecy_KS > secrecy_KS ).

thf(func_def_177,type,
    sK28: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_178,type,
    sK29: list_Secrecy_KS > secrecy_KS ).

thf(func_def_179,type,
    sK30: list_Secrecy_KS > secrecy_KS ).

thf(func_def_180,type,
    sK31: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_181,type,
    sK32: list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_182,type,
    sK33: list_Secrecy_KS > secrecy_KS ).

thf(func_def_183,type,
    sK34: list_S529945141ession > secrecy_Expression ).

thf(func_def_184,type,
    sK35: list_S529945141ession > secrecy_Expression ).

thf(func_def_185,type,
    sK36: list_S529945141ession > list_S529945141ession ).

thf(func_def_186,type,
    sK37: list_S529945141ession > secrecy_Expression ).

thf(func_def_187,type,
    sK38: list_S529945141ession > secrecy_Expression ).

thf(func_def_188,type,
    sK39: list_S529945141ession > list_S529945141ession ).

thf(func_def_189,type,
    sK40: list_S529945141ession > list_S529945141ession ).

thf(func_def_190,type,
    sK41: list_S529945141ession > secrecy_Expression ).

thf(func_def_191,type,
    sK42: secrecy_KS > secrecy_Secrets ).

thf(func_def_192,type,
    sK43: secrecy_KS > secrecy_Keys ).

thf(func_def_193,type,
    sK44: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_194,type,
    sK45: ( list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_195,type,
    sK46: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_196,type,
    sK47: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_197,type,
    sK48: ( list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_198,type,
    sK49: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_199,type,
    sK50: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_200,type,
    sK51: ( list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_201,type,
    sK52: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_202,type,
    sK53: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_203,type,
    sK54: ( list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_204,type,
    sK55: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_205,type,
    sK56: list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_206,type,
    sK57: list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_207,type,
    sK58: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_208,type,
    sK59: list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_209,type,
    sK60: list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_210,type,
    sK61: list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_211,type,
    sK62: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_212,type,
    sK63: list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_213,type,
    sK64: list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_214,type,
    sK65: list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_215,type,
    sK66: list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_216,type,
    sK67: ( secrecy_KS > $o ) > secrecy_Secrets ).

thf(func_def_217,type,
    sK68: ( secrecy_KS > $o ) > secrecy_Keys ).

thf(func_def_218,type,
    sK69: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_219,type,
    sK70: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_220,type,
    sK71: ( list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_221,type,
    sK72: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_222,type,
    sK73: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_223,type,
    sK74: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_224,type,
    sK75: ( list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_225,type,
    sK76: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_226,type,
    sK77: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_227,type,
    sK78: ( list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_228,type,
    sK79: ( list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_229,type,
    sK80: ( list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_230,type,
    sK81: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_231,type,
    sK82: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_232,type,
    sK83: ( list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_233,type,
    sK84: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_234,type,
    sK85: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_235,type,
    sK86: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_236,type,
    sK87: ( list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_237,type,
    sK88: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_238,type,
    sK89: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_239,type,
    sK90: ( list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_240,type,
    sK91: ( list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_241,type,
    sK92: ( list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_242,type,
    sK93: secrecy_Expression > secrecy_specID > secrecy_Secrets ).

thf(func_def_243,type,
    sK94: secrecy_Expression > secrecy_specID > secrecy_Keys ).

thf(func_def_244,type,
    sK95: list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_245,type,
    sK96: list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_246,type,
    sK97: list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_247,type,
    sK98: list_Secrecy_KS > secrecy_KS ).

thf(func_def_248,type,
    sK99: list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_249,type,
    sK100: list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_250,type,
    sK101: list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_251,type,
    sK102: list_S529945141ession > secrecy_Expression ).

thf(func_def_252,type,
    sK103: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_253,type,
    sK104: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_254,type,
    sK105: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_255,type,
    sK106: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_256,type,
    sK107: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_257,type,
    sK108: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_258,type,
    sK109: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_259,type,
    sK110: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_260,type,
    sK111: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_261,type,
    sK112: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_262,type,
    sK113: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_263,type,
    sK114: list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_264,type,
    sK115: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_265,type,
    sK116: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_266,type,
    sK117: list_S529945141ession > list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_267,type,
    sK118: list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_268,type,
    sK119: list_S529945141ession > list_S529945141ession > list_l425507653ession > list_l425507653ession ).

thf(func_def_269,type,
    sK120: list_S529945141ession > list_S529945141ession > list_l425507653ession > list_S529945141ession ).

thf(func_def_270,type,
    sK121: list_S529945141ession > list_S529945141ession > list_l425507653ession > list_S529945141ession ).

thf(func_def_271,type,
    sK122: list_S529945141ession > list_S529945141ession > list_l425507653ession > list_l425507653ession ).

thf(func_def_272,type,
    sK123: $o > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_273,type,
    sK124: $o > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_274,type,
    sK125: $o > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_275,type,
    sK126: list_Secrecy_KS > secrecy_KS ).

thf(func_def_276,type,
    sK127: $o > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_277,type,
    sK128: $o > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_278,type,
    sK129: $o > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_279,type,
    sK130: list_S529945141ession > secrecy_Expression ).

thf(func_def_280,type,
    sK131: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_281,type,
    sK132: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_282,type,
    sK133: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_283,type,
    sK134: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_284,type,
    sK135: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_285,type,
    sK136: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_286,type,
    sK137: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_287,type,
    sK138: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_288,type,
    sK139: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_289,type,
    sK140: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_290,type,
    sK141: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_291,type,
    sK142: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_292,type,
    sK143: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_293,type,
    sK144: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_294,type,
    sK145: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_295,type,
    sK146: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_296,type,
    sK147: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_297,type,
    sK148: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_298,type,
    sK149: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_299,type,
    sK150: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_300,type,
    sK151: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS > secrecy_KS > $o ).

thf(func_def_301,type,
    sK152: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_302,type,
    sK153: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_303,type,
    sK154: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_304,type,
    sK155: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS > secrecy_KS > $o ).

thf(func_def_305,type,
    sK156: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_306,type,
    sK157: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS > secrecy_KS > $o ).

thf(func_def_307,type,
    sK158: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS > secrecy_KS > $o ).

thf(func_def_308,type,
    sK159: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_309,type,
    sK160: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_310,type,
    sK161: ( ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ) > secrecy_KS > secrecy_KS > $o ).

thf(func_def_311,type,
    sK162: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression > $o ).

thf(func_def_312,type,
    sK163: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_313,type,
    sK164: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_314,type,
    sK165: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_315,type,
    sK166: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression > $o ).

thf(func_def_316,type,
    sK167: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_317,type,
    sK168: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression > $o ).

thf(func_def_318,type,
    sK169: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression > $o ).

thf(func_def_319,type,
    sK170: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_320,type,
    sK171: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_321,type,
    sK172: ( ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression > $o ).

thf(func_def_322,type,
    sK173: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_323,type,
    sK174: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_324,type,
    sK175: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_325,type,
    sK176: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_326,type,
    sK177: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_327,type,
    sK178: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_328,type,
    sK179: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_329,type,
    sK180: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_330,type,
    sK181: ( list_S529945141ession > list_Secrecy_KS > $o ) > secrecy_Expression ).

thf(func_def_331,type,
    sK182: ( list_S529945141ession > list_Secrecy_KS > $o ) > list_S529945141ession ).

thf(func_def_332,type,
    sK183: ( list_S529945141ession > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_333,type,
    sK184: ( list_S529945141ession > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_334,type,
    sK185: ( list_S529945141ession > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_335,type,
    sK186: ( list_S529945141ession > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_336,type,
    sK187: ( list_S529945141ession > list_Secrecy_KS > $o ) > secrecy_Expression ).

thf(func_def_337,type,
    sK188: ( list_S529945141ession > list_Secrecy_KS > $o ) > list_S529945141ession ).

thf(func_def_338,type,
    sK189: ( list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_KS ).

thf(func_def_339,type,
    sK190: ( list_Secrecy_KS > list_S529945141ession > $o ) > list_Secrecy_KS ).

thf(func_def_340,type,
    sK191: ( list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_341,type,
    sK192: ( list_Secrecy_KS > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_342,type,
    sK193: ( list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_343,type,
    sK194: ( list_Secrecy_KS > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_344,type,
    sK195: ( list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_KS ).

thf(func_def_345,type,
    sK196: ( list_Secrecy_KS > list_S529945141ession > $o ) > list_Secrecy_KS ).

thf(func_def_346,type,
    sK197: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_347,type,
    sK198: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_348,type,
    sK199: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_349,type,
    sK200: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_350,type,
    sK201: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_351,type,
    sK202: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_352,type,
    sK203: ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_353,type,
    sK204: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_354,type,
    sK205: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_355,type,
    sK206: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_356,type,
    sK207: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_357,type,
    sK208: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_358,type,
    sK209: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_359,type,
    sK210: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_360,type,
    sK211: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > secrecy_KS ).

thf(func_def_361,type,
    sK212: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_362,type,
    sK213: list_S529945141ession > list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_363,type,
    sK214: list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_364,type,
    sK215: list_S529945141ession > list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_365,type,
    sK216: list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_366,type,
    sK217: list_S529945141ession > list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_367,type,
    sK218: list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_368,type,
    sK219: list_S529945141ession > list_S529945141ession > list_S529945141ession > secrecy_Expression ).

thf(func_def_369,type,
    sK220: list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_370,type,
    sK221: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_371,type,
    sK222: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_372,type,
    sK223: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_373,type,
    sK224: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_374,type,
    sK225: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_375,type,
    sK226: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_376,type,
    sK227: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_377,type,
    sK228: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_378,type,
    sK229: list_Secrecy_KS > secrecy_KS > secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_379,type,
    sK230: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_380,type,
    sK231: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_381,type,
    sK232: list_Secrecy_KS > list_Secrecy_KS > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_382,type,
    sK233: list_S529945141ession > list_Secrecy_KS > ( secrecy_Expression > secrecy_KS > $o ) > secrecy_Expression ).

thf(func_def_383,type,
    sK234: list_S529945141ession > list_Secrecy_KS > ( secrecy_Expression > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_384,type,
    sK235: list_S529945141ession > list_Secrecy_KS > ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession ).

thf(func_def_385,type,
    sK236: list_S529945141ession > list_Secrecy_KS > ( secrecy_Expression > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_386,type,
    sK237: list_Secrecy_KS > list_S529945141ession > ( secrecy_KS > secrecy_Expression > $o ) > secrecy_KS ).

thf(func_def_387,type,
    sK238: list_Secrecy_KS > list_S529945141ession > ( secrecy_KS > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_388,type,
    sK239: list_Secrecy_KS > list_S529945141ession > ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS ).

thf(func_def_389,type,
    sK240: list_Secrecy_KS > list_S529945141ession > ( secrecy_KS > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_390,type,
    sK241: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_391,type,
    sK242: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_392,type,
    sK243: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_393,type,
    sK244: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_394,type,
    sK245: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_395,type,
    sK246: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_396,type,
    sK247: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_397,type,
    sK248: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_398,type,
    sK249: list_S529945141ession > secrecy_Expression > secrecy_Expression > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession ).

thf(func_def_399,type,
    sK250: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_400,type,
    sK251: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_401,type,
    sK252: list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_402,type,
    sK253: list_S529945141ession > list_S529945141ession > list_Secrecy_KS > ( secrecy_KS > secrecy_Expression ) > secrecy_KS ).

thf(func_def_403,type,
    sK254: list_S529945141ession > list_S529945141ession > list_Secrecy_KS > ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS ).

thf(func_def_404,type,
    sK255: list_S529945141ession > list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression ) > secrecy_Expression ).

thf(func_def_405,type,
    sK256: list_S529945141ession > list_S529945141ession > list_S529945141ession > ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession ).

thf(func_def_406,type,
    sK257: ( ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_KS > secrecy_Expression ).

thf(func_def_407,type,
    sK258: ( ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_KS ).

thf(func_def_408,type,
    sK259: ( ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o ) > list_Secrecy_KS ).

thf(func_def_409,type,
    sK260: ( ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_410,type,
    sK261: ( ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o ) > secrecy_KS > secrecy_Expression ).

thf(func_def_411,type,
    sK262: ( ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_412,type,
    sK263: ( ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression ).

thf(func_def_413,type,
    sK264: ( ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_414,type,
    sK265: ( ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_415,type,
    sK266: ( ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_416,type,
    sK267: ( ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression > secrecy_Expression ).

thf(func_def_417,type,
    sK268: ( ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_418,type,
    sK269: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_419,type,
    sK270: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_420,type,
    sK271: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_421,type,
    sK272: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_422,type,
    sK273: ( secrecy_KS > secrecy_KS > $o ) > ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_423,type,
    sK274: ( secrecy_KS > secrecy_KS > $o ) > ( list_Secrecy_KS > list_Secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_424,type,
    sK275: ( secrecy_KS > secrecy_KS > $o ) > ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_425,type,
    sK276: ( secrecy_KS > secrecy_KS > $o ) > ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_426,type,
    sK277: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_427,type,
    sK278: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_428,type,
    sK279: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_429,type,
    sK280: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_430,type,
    sK281: ( list_Secrecy_KS > list_Secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_431,type,
    sK282: ( list_S529945141ession > list_Secrecy_KS > $o ) > ( secrecy_Expression > secrecy_KS > $o ) > secrecy_Expression ).

thf(func_def_432,type,
    sK283: ( list_S529945141ession > list_Secrecy_KS > $o ) > ( secrecy_Expression > secrecy_KS > $o ) > secrecy_KS ).

thf(func_def_433,type,
    sK284: ( list_S529945141ession > list_Secrecy_KS > $o ) > ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession ).

thf(func_def_434,type,
    sK285: ( list_S529945141ession > list_Secrecy_KS > $o ) > ( secrecy_Expression > secrecy_KS > $o ) > list_Secrecy_KS ).

thf(func_def_435,type,
    sK286: ( list_Secrecy_KS > list_S529945141ession > $o ) > ( secrecy_KS > secrecy_Expression > $o ) > secrecy_KS ).

thf(func_def_436,type,
    sK287: ( list_Secrecy_KS > list_S529945141ession > $o ) > ( secrecy_KS > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_437,type,
    sK288: ( list_Secrecy_KS > list_S529945141ession > $o ) > ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS ).

thf(func_def_438,type,
    sK289: ( list_Secrecy_KS > list_S529945141ession > $o ) > ( secrecy_KS > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_439,type,
    sK290: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_440,type,
    sK291: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_441,type,
    sK292: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_442,type,
    sK293: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_443,type,
    sK294: ( secrecy_Expression > secrecy_Expression > $o ) > ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_444,type,
    sK295: ( secrecy_Expression > secrecy_Expression > $o ) > ( list_S529945141ession > list_S529945141ession > $o ) > secrecy_Expression ).

thf(func_def_445,type,
    sK296: ( secrecy_Expression > secrecy_Expression > $o ) > ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_446,type,
    sK297: ( secrecy_Expression > secrecy_Expression > $o ) > ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_447,type,
    sK298: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_448,type,
    sK299: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > secrecy_Expression ).

thf(func_def_449,type,
    sK300: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_450,type,
    sK301: ( list_S529945141ession > list_S529945141ession > $o ) > ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession ).

thf(func_def_451,type,
    sK302: ( list_S529945141ession > list_S529945141ession > $o ) > list_S529945141ession ).

thf(func_def_453,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_454,type,
    sK304: list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_455,type,
    sK305: list_S529945141ession > secrecy_Expression > list_S529945141ession > list_S529945141ession > list_S529945141ession ).

thf(func_def_456,type,
    sK306: list_S529945141ession > list_S529945141ession > list_S529945141ession > secrecy_Expression > list_S529945141ession ).

thf(func_def_457,type,
    sK307: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > secrecy_KS > list_Secrecy_KS ).

thf(func_def_458,type,
    sK308: list_Secrecy_KS > secrecy_KS > list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).

thf(func_def_459,type,
    sK309: list_S529945141ession > list_l425507653ession > list_S529945141ession > list_l425507653ession ).

thf(func_def_460,type,
    sK310: list_Secrecy_KS > list_list_Secrecy_KS > list_Secrecy_KS > list_list_Secrecy_KS ).

thf(func_def_461,type,
    sK311: list_S529945141ession > secrecy_Expression ).

thf(func_def_462,type,
    sK312: list_S529945141ession > secrecy_Expression ).

thf(func_def_463,type,
    sK313: list_Secrecy_KS > secrecy_KS ).

thf(func_def_464,type,
    sK314: list_Secrecy_KS > secrecy_KS ).

thf(func_def_465,type,
    sK315: list_S529945141ession > list_S529945141ession ).

thf(func_def_466,type,
    sK316: list_Secrecy_KS > list_Secrecy_KS ).

thf(f16897,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3136,f3141,f3145,f3180,f3185,f3190,f3195,f3200,f3205,f3210,f3215,f3220,f3225,f3230,f3235,f3240,f3245,f3252,f3256,f3260,f3264,f3268,f3272,f3276,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3320,f3324,f3328,f3332,f3340,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3392,f3396,f3400,f3404,f3416,f3421,f3427,f3432,f3438,f3443,f3448,f3452,f3456,f3460,f3464,f3468,f3472,f3476,f3480,f3484,f3488,f3492,f3496,f3500,f3504,f3508,f3512,f3516,f3520,f3524,f3528,f3532,f3536,f3544,f3548,f3552,f3556,f3563,f3567,f3572,f3577,f3587,f3591,f3595,f3599,f3603,f3607,f3611,f3615,f3619,f3623,f3628,f3632,f3636,f3640,f3683,f3687,f3691,f3695,f3700,f3704,f3708,f3712,f3716,f3721,f3729,f3733,f3737,f3741,f3745,f3749,f3754,f3759,f3766,f3771,f3778,f3783,f3790,f3796,f3803,f3807,f3812,f3904,f3908,f3916,f3920,f3925,f3932,f3940,f3944,f3948,f3952,f3957,f3961,f3965,f3969,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4031,f4035,f4039,f4147,f4151,f4155,f4159,f4163,f4211,f4215,f4219,f4223,f4227,f4270,f4274,f4314,f4319,f4323,f4327,f4371,f4375,f4379,f4383,f4402,f4431,f4435,f4439,f4443,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4628,f4632,f4636,f4648,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4700,f4745,f4818,f4822,f4826,f4830,f4834,f4891,f4903,f4907,f4911,f4915,f4920,f4924,f4990,f4994,f4999,f5003,f5007,f5104,f5108,f5113,f5121,f5152,f5156,f5160,f5164,f5168,f5172,f5181,f5271,f5275,f5279,f5283,f5287,f5299,f5303,f5307,f5311,f5315,f5319,f5327,f5331,f5335,f5339,f5343,f5357,f5361,f5365,f5369,f5377,f5385,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5445,f5449,f5453,f5479,f5483,f5503,f5507,f5511,f5515,f5523,f5527,f5531,f5535,f5539,f5543,f5630,f5638,f5642,f5656,f5660,f5664,f5668,f5672,f5676,f5680,f5684,f5709,f5713,f5717,f5721,f5725,f5729,f5733,f5737,f5765,f5769,f5773,f5777,f5781,f5785,f5789,f5829,f5833,f5837,f5841,f5845,f5849,f5853,f5977,f5981,f5985,f5989,f5993,f6005,f6009,f6013,f6017,f6021,f6025,f6029,f6125,f6129,f6133,f6137,f6141,f6145,f6149,f6153,f6157,f6161,f6165,f6169,f6173,f6177,f6257,f6285,f6289,f6301,f6305,f6319,f6323,f6340,f6344,f6348,f6352,f6364,f6368,f6372,f6376,f6405,f6409,f6421,f6425,f6436,f6440,f6454,f6458,f6462,f6466,f6471,f6518,f6524,f6528,f6533,f6537,f6541,f6545,f6549,f6553,f6557,f6561,f6565,f6569,f6574,f6578,f6582,f6586,f6590,f6594,f6636,f6640,f6644,f6648,f6652,f6656,f6661,f6665,f6696,f6700,f6714,f6718,f6726,f6730,f6735,f6739,f6751,f6755,f6759,f6763,f6782,f6786,f6816,f6856,f6860,f6864,f6868,f6904,f6910,f6914,f6918,f6922,f6926,f6952,f6956,f6960,f6972,f6976,f6984,f6988,f7007,f7011,f7023,f7027,f7059,f7063,f7076,f7080,f7084,f7088,f7114,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7159,f7199,f7203,f7211,f7215,f7219,f7242,f7246,f7254,f7258,f7262,f7266,f7270,f7344,f7348,f7364,f7368,f7372,f7385,f7390,f7399,f7404,f7408,f7413,f7418,f7427,f7432,f7440,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7578,f7582,f7586,f7590,f7632,f7636,f7640,f7644,f7648,f7652,f7656,f7660,f7664,f7668,f7701,f7733,f7737,f7741,f7745,f7753,f7952,f7954,f8665,f8826,f8840,f9106,f9112,f9114,f10562,f10601,f10641,f10655,f10660,f10668,f10673,f10679,f10689,f10727,f10737,f10775,f10781,f10785,f10789,f10793,f10833,f10838,f10843,f10847,f10851,f10863,f10899,f10903,f10907,f10911,f10919,f10923,f10927,f10971,f10975,f10979,f10983,f10987,f10991,f10995,f10999,f11003,f11113,f11117,f11121,f11125,f11129,f11133,f11137,f11141,f11145,f11149,f11174,f11178,f11182,f11306,f11310,f11314,f11318,f11325,f11329,f11333,f11337,f11341,f11345,f11349,f12348,f12352,f12373,f12377,f12381,f12385,f12389,f12393,f12397,f12401,f12405,f12409,f12415,f12419,f12423,f12427,f12431,f12682,f12746,f12750,f12754,f12758,f12762,f12766,f12772,f12805,f12809,f12813,f12817,f12834,f12851,f12855,f12859,f12863,f12867,f12871,f12875,f12879,f12883,f12887,f12891,f12895,f12899,f12903,f12907,f12911,f12915,f13193,f13197,f13201,f13205,f13209,f13213,f13243,f13247,f13251,f13255,f13605,f13609,f13613,f13617,f13621,f13625,f13629,f13686,f13690,f13694,f13698,f13707,f13711,f13715,f13719,f13723,f13727,f13731,f13735,f13739,f13743,f13747,f13751,f13755,f13759,f13763,f13767,f13771,f13775,f13807,f14113,f14117,f14128,f14132,f14136,f14140,f14144,f14148,f14152,f14156,f14160,f14164,f14168,f14172,f14176,f14180,f14184,f14188,f14192,f14259,f14432,f14482,f14486,f14490,f14494,f14498,f14502,f14506,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14542,f14546,f14550,f14554,f14558,f14562,f14566,f14570,f14582,f14594,f14598,f14949,f14954,f14959,f14963,f15027,f15031,f15037,f15041,f15045,f15049,f15053,f15057,f15366,f15370,f15374,f15378,f15382,f15386,f15390,f15394,f15398,f15402,f15406,f15410,f15414,f15418,f15422,f15426,f15430,f15435,f15439,f15443,f15732,f15848,f15852,f15856,f15860,f15910,f15914,f15918,f15922,f15936,f16007,f16011,f16015,f16019,f16023,f16027,f16031,f16035,f16039,f16043,f16047,f16051,f16055,f16059,f16063,f16067,f16120,f16283,f16327,f16331,f16335,f16339,f16343,f16347,f16351,f16355,f16359,f16363,f16367,f16371,f16375,f16379,f16383,f16387,f16693,f16722,f16726,f16730,f16734,f16738,f16742,f16746,f16750,f16754,f16758,f16762,f16766,f16770,f16774,f16778,f16782,f16786,f16790,f16794,f16798,f16802,f16806,f16810,f16814,f16818,f16893,f16896]) ).

thf(f16896,plain,
    ( ~ spl303_10
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(avatar_contradiction_clause,[],[f16895]) ).

thf(f16895,plain,
    ( $false
    | ~ spl303_10
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(trivial_inequality_removal,[],[f16894]) ).

thf(f16894,plain,
    ( ( $true = $false )
    | ~ spl303_10
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(forward_demodulation,[],[f16888,f3209]) ).

thf(f3209,plain,
    ( ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $false )
    | ~ spl303_10 ),
    inference(avatar_component_clause,[],[f3207]) ).

thf(f3207,plain,
    ( spl303_10
  <=> ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_10])]) ).

thf(f16888,plain,
    ( ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $true )
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(trivial_inequality_removal,[],[f16874]) ).

thf(f16874,plain,
    ( ( $true = $false )
    | ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $true )
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(superposition,[],[f3811,f16729]) ).

thf(f16729,plain,
    ( ! [X0: secrecy_specID,X1: secrecy_Secrets] :
        ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) )
    | ~ spl303_778 ),
    inference(avatar_component_clause,[],[f16728]) ).

thf(f16728,plain,
    ( spl303_778
  <=> ! [X0: secrecy_specID,X1: secrecy_Secrets] :
        ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_778])]) ).

thf(f3811,plain,
    ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)) )
    | ~ spl303_131 ),
    inference(avatar_component_clause,[],[f3809]) ).

thf(f3809,plain,
    ( spl303_131
  <=> ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_131])]) ).

thf(f16893,plain,
    ( ~ spl303_10
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(avatar_contradiction_clause,[],[f16892]) ).

thf(f16892,plain,
    ( $false
    | ~ spl303_10
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(trivial_inequality_removal,[],[f16891]) ).

thf(f16891,plain,
    ( ( $true = $false )
    | ~ spl303_10
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(forward_demodulation,[],[f16890,f3209]) ).

thf(f16890,plain,
    ( ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $true )
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(trivial_inequality_removal,[],[f16872]) ).

thf(f16872,plain,
    ( ( $true = $false )
    | ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $true )
    | ~ spl303_131
    | ~ spl303_778 ),
    inference(superposition,[],[f16729,f3811]) ).

thf(f16818,plain,
    ( spl303_800
    | ~ spl303_37
    | ~ spl303_328 ),
    inference(avatar_split_clause,[],[f6212,f6155,f3326,f16816]) ).

thf(f16816,plain,
    ( spl303_800
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_800])]) ).

thf(f3326,plain,
    ( spl303_37
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_37])]) ).

thf(f6155,plain,
    ( spl303_328
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_328])]) ).

thf(f6212,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) )
    | ~ spl303_37
    | ~ spl303_328 ),
    inference(superposition,[],[f3327,f6156]) ).

thf(f6156,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) )
    | ~ spl303_328 ),
    inference(avatar_component_clause,[],[f6155]) ).

thf(f3327,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) != X1 )
    | ~ spl303_37 ),
    inference(avatar_component_clause,[],[f3326]) ).

thf(f16814,plain,
    ( spl303_799
    | ~ spl303_37
    | ~ spl303_222 ),
    inference(avatar_split_clause,[],[f5133,f5119,f3326,f16812]) ).

thf(f16812,plain,
    ( spl303_799
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_799])]) ).

thf(f5119,plain,
    ( spl303_222
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_222])]) ).

thf(f5133,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( X0 = X1 ) )
    | ~ spl303_37
    | ~ spl303_222 ),
    inference(superposition,[],[f3327,f5120]) ).

thf(f5120,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( X0 = X1 ) )
    | ~ spl303_222 ),
    inference(avatar_component_clause,[],[f5119]) ).

thf(f16810,plain,
    ( spl303_798
    | ~ spl303_99
    | ~ spl303_214 ),
    inference(avatar_split_clause,[],[f5009,f4988,f3617,f16808]) ).

thf(f16808,plain,
    ( spl303_798
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( nil_Se901661471ession = vAPP(secrecy_Expression,list_S529945141ession,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_798])]) ).

thf(f3617,plain,
    ( spl303_99
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_99])]) ).

thf(f4988,plain,
    ( spl303_214
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_214])]) ).

thf(f5009,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( nil_Se901661471ession = vAPP(secrecy_Expression,list_S529945141ession,X0,X1) ) )
    | ~ spl303_99
    | ~ spl303_214 ),
    inference(superposition,[],[f3618,f4989]) ).

thf(f4989,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),X2)) )
    | ~ spl303_214 ),
    inference(avatar_component_clause,[],[f4988]) ).

thf(f3618,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_99 ),
    inference(avatar_component_clause,[],[f3617]) ).

thf(f16806,plain,
    ( spl303_797
    | ~ spl303_131
    | ~ spl303_168
    | ~ spl303_207 ),
    inference(avatar_split_clause,[],[f4899,f4889,f4272,f3809,f16804]) ).

thf(f16804,plain,
    ( spl303_797
  <=> ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_797])]) ).

thf(f4272,plain,
    ( spl303_168
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_168])]) ).

thf(f4889,plain,
    ( spl303_207
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_207])]) ).

thf(f4899,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),X0) ) )
    | ~ spl303_131
    | ~ spl303_168
    | ~ spl303_207 ),
    inference(forward_demodulation,[],[f4896,f4273]) ).

thf(f4273,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_168 ),
    inference(avatar_component_clause,[],[f4272]) ).

thf(f4896,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),X0) ) )
    | ~ spl303_131
    | ~ spl303_207 ),
    inference(trivial_inequality_removal,[],[f4893]) ).

thf(f4893,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),X0) ) )
    | ~ spl303_131
    | ~ spl303_207 ),
    inference(superposition,[],[f4890,f3811]) ).

thf(f4890,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
    | ~ spl303_207 ),
    inference(avatar_component_clause,[],[f4889]) ).

thf(f16802,plain,
    ( spl303_796
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_156
    | ~ spl303_187
    | ~ spl303_188 ),
    inference(avatar_split_clause,[],[f4617,f4525,f4521,f4037,f3565,f3282,f16800]) ).

thf(f16800,plain,
    ( spl303_796
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_796])]) ).

thf(f3282,plain,
    ( spl303_26
  <=> ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_26])]) ).

thf(f3565,plain,
    ( spl303_88
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_88])]) ).

thf(f4037,plain,
    ( spl303_156
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_156])]) ).

thf(f4521,plain,
    ( spl303_187
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_187])]) ).

thf(f4525,plain,
    ( spl303_188
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_188])]) ).

thf(f4617,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_156
    | ~ spl303_187
    | ~ spl303_188 ),
    inference(forward_demodulation,[],[f4594,f4576]) ).

thf(f4576,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_187 ),
    inference(forward_demodulation,[],[f4559,f3283]) ).

thf(f3283,plain,
    ( ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X0) = X0 )
    | ~ spl303_26 ),
    inference(avatar_component_clause,[],[f3282]) ).

thf(f4559,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1) )
    | ~ spl303_88
    | ~ spl303_187 ),
    inference(superposition,[],[f4522,f3566]) ).

thf(f3566,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) )
    | ~ spl303_88 ),
    inference(avatar_component_clause,[],[f3565]) ).

thf(f4522,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
    | ~ spl303_187 ),
    inference(avatar_component_clause,[],[f4521]) ).

thf(f4594,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_156
    | ~ spl303_188 ),
    inference(superposition,[],[f4526,f4038]) ).

thf(f4038,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_156 ),
    inference(avatar_component_clause,[],[f4037]) ).

thf(f4526,plain,
    ( ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
    | ~ spl303_188 ),
    inference(avatar_component_clause,[],[f4525]) ).

thf(f16798,plain,
    ( spl303_795
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_155
    | ~ spl303_187
    | ~ spl303_188 ),
    inference(avatar_split_clause,[],[f4616,f4525,f4521,f4033,f3565,f3282,f16796]) ).

thf(f16796,plain,
    ( spl303_795
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_795])]) ).

thf(f4033,plain,
    ( spl303_155
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_155])]) ).

thf(f4616,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_155
    | ~ spl303_187
    | ~ spl303_188 ),
    inference(forward_demodulation,[],[f4593,f4576]) ).

thf(f4593,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_155
    | ~ spl303_188 ),
    inference(superposition,[],[f4526,f4034]) ).

thf(f4034,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_155 ),
    inference(avatar_component_clause,[],[f4033]) ).

thf(f16794,plain,
    ( spl303_794
    | ~ spl303_138
    | ~ spl303_520 ),
    inference(avatar_split_clause,[],[f12362,f10861,f3938,f16792]) ).

thf(f16792,plain,
    ( spl303_794
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_794])]) ).

thf(f3938,plain,
    ( spl303_138
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_138])]) ).

thf(f10861,plain,
    ( spl303_520
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X1 )
        | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_520])]) ).

thf(f12362,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X0),X1) ) )
    | ~ spl303_138
    | ~ spl303_520 ),
    inference(superposition,[],[f10862,f3939]) ).

thf(f3939,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) = X0 )
    | ~ spl303_138 ),
    inference(avatar_component_clause,[],[f3938]) ).

thf(f10862,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_520 ),
    inference(avatar_component_clause,[],[f10861]) ).

thf(f16790,plain,
    ( spl303_793
    | ~ spl303_94
    | ~ spl303_187 ),
    inference(avatar_split_clause,[],[f4562,f4521,f3597,f16788]) ).

thf(f16788,plain,
    ( spl303_793
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_793])]) ).

thf(f3597,plain,
    ( spl303_94
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_94])]) ).

thf(f4562,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_187 ),
    inference(superposition,[],[f4522,f3598]) ).

thf(f3598,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94 ),
    inference(avatar_component_clause,[],[f3597]) ).

thf(f16786,plain,
    ( spl303_792
    | ~ spl303_93
    | ~ spl303_187 ),
    inference(avatar_split_clause,[],[f4561,f4521,f3593,f16784]) ).

thf(f16784,plain,
    ( spl303_792
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_792])]) ).

thf(f3593,plain,
    ( spl303_93
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_93])]) ).

thf(f4561,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_187 ),
    inference(superposition,[],[f4522,f3594]) ).

thf(f3594,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93 ),
    inference(avatar_component_clause,[],[f3593]) ).

thf(f16782,plain,
    ( spl303_791
    | ~ spl303_94
    | ~ spl303_186 ),
    inference(avatar_split_clause,[],[f4553,f4517,f3597,f16780]) ).

thf(f16780,plain,
    ( spl303_791
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_791])]) ).

thf(f4517,plain,
    ( spl303_186
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_186])]) ).

thf(f4553,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_186 ),
    inference(superposition,[],[f4518,f3598]) ).

thf(f4518,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X2),X1)) )
    | ~ spl303_186 ),
    inference(avatar_component_clause,[],[f4517]) ).

thf(f16778,plain,
    ( spl303_790
    | ~ spl303_93
    | ~ spl303_186 ),
    inference(avatar_split_clause,[],[f4552,f4517,f3593,f16776]) ).

thf(f16776,plain,
    ( spl303_790
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_790])]) ).

thf(f4552,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_186 ),
    inference(superposition,[],[f4518,f3594]) ).

thf(f16774,plain,
    ( spl303_789
    | ~ spl303_166
    | ~ spl303_176 ),
    inference(avatar_split_clause,[],[f4422,f4381,f4225,f16772]) ).

thf(f16772,plain,
    ( spl303_789
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_789])]) ).

thf(f4225,plain,
    ( spl303_166
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_166])]) ).

thf(f4381,plain,
    ( spl303_176
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_176])]) ).

thf(f4422,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) )
    | ~ spl303_166
    | ~ spl303_176 ),
    inference(superposition,[],[f4226,f4382]) ).

thf(f4382,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_176 ),
    inference(avatar_component_clause,[],[f4381]) ).

thf(f4226,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
    | ~ spl303_166 ),
    inference(avatar_component_clause,[],[f4225]) ).

thf(f16770,plain,
    ( spl303_788
    | ~ spl303_157
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4264,f4225,f4145,f16768]) ).

thf(f16768,plain,
    ( spl303_788
  <=> ! [X2: secrecy_specID,X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_788])]) ).

thf(f4145,plain,
    ( spl303_157
  <=> ! [X0: list_l425507653ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_157])]) ).

thf(f4264,plain,
    ( ! [X2: secrecy_specID,X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) ) )
    | ~ spl303_157
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f4146]) ).

thf(f4146,plain,
    ( ! [X0: list_l425507653ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) )
    | ~ spl303_157 ),
    inference(avatar_component_clause,[],[f4145]) ).

thf(f16766,plain,
    ( spl303_787
    | ~ spl303_158
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4257,f4225,f4149,f16764]) ).

thf(f16764,plain,
    ( spl303_787
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_787])]) ).

thf(f4149,plain,
    ( spl303_158
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_158])]) ).

thf(f4257,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) )
    | ~ spl303_158
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f4150]) ).

thf(f4150,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
    | ~ spl303_158 ),
    inference(avatar_component_clause,[],[f4149]) ).

thf(f16762,plain,
    ( spl303_786
    | ~ spl303_157
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4250,f4221,f4145,f16760]) ).

thf(f16760,plain,
    ( spl303_786
  <=> ! [X2: secrecy_specID,X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_786])]) ).

thf(f4221,plain,
    ( spl303_165
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_165])]) ).

thf(f4250,plain,
    ( ! [X2: secrecy_specID,X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ) )
    | ~ spl303_157
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f4146]) ).

thf(f4222,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) ) )
    | ~ spl303_165 ),
    inference(avatar_component_clause,[],[f4221]) ).

thf(f16758,plain,
    ( spl303_785
    | ~ spl303_158
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4243,f4221,f4149,f16756]) ).

thf(f16756,plain,
    ( spl303_785
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_785])]) ).

thf(f4243,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)) ) )
    | ~ spl303_158
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f4150]) ).

thf(f16754,plain,
    spl303_784,
    inference(avatar_split_clause,[],[f3086,f16752]) ).

thf(f16752,plain,
    ( spl303_784
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_784])]) ).

thf(f3086,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ),
    inference(forward_demodulation,[],[f2497,f1527]) ).

thf(f1527,plain,
    ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f795]) ).

thf(f795,plain,
    ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) ),
    inference(rectify,[],[f71]) ).

thf(f71,axiom,
    ! [X39: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X39),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_insert__Nil) ).

thf(f2497,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X0 ) ),
    inference(equality_proxy_clausification,[],[f2496]) ).

thf(f2496,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X0) ) ),
    inference(equality_proxy_clausification,[],[f2495]) ).

thf(f2495,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X0) ) ),
    inference(binary_proxy_clausification,[],[f1800]) ).

thf(f1800,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X0) ),
    inference(cnf_transformation,[],[f596]) ).

thf(f596,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X0) ),
    inference(fool_elimination,[],[f595]) ).

thf(f595,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      = ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X0 ) ),
    inference(rectify,[],[f251]) ).

thf(f251,axiom,
    ! [X28: list_S529945141ession,X15: secrecy_Expression,X31: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X31) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28) )
      = ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X31)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),nil_Se901661471ession)) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_rev__eq__Cons__iff) ).

thf(f16750,plain,
    ( spl303_783
    | ~ spl303_141
    | ~ spl303_513 ),
    inference(avatar_split_clause,[],[f12034,f10787,f3950,f16748]) ).

thf(f16748,plain,
    ( spl303_783
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_783])]) ).

thf(f3950,plain,
    ( spl303_141
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_141])]) ).

thf(f10787,plain,
    ( spl303_513
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_513])]) ).

thf(f12034,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X0),X1) ) )
    | ~ spl303_141
    | ~ spl303_513 ),
    inference(superposition,[],[f10788,f3951]) ).

thf(f3951,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X1 )
    | ~ spl303_141 ),
    inference(avatar_component_clause,[],[f3950]) ).

thf(f10788,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_513 ),
    inference(avatar_component_clause,[],[f10787]) ).

thf(f16746,plain,
    spl303_782,
    inference(avatar_split_clause,[],[f3085,f16744]) ).

thf(f16744,plain,
    ( spl303_782
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_782])]) ).

thf(f3085,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) != X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ),
    inference(forward_demodulation,[],[f2499,f1527]) ).

thf(f2499,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) != X0 ) ),
    inference(equality_proxy_clausification,[],[f2498]) ).

thf(f2498,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X0) ) ),
    inference(equality_proxy_clausification,[],[f2494]) ).

thf(f2494,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X2)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X0) ) ),
    inference(binary_proxy_clausification,[],[f1800]) ).

thf(f16742,plain,
    spl303_781,
    inference(avatar_split_clause,[],[f3084,f16740]) ).

thf(f16740,plain,
    ( spl303_781
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) != vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_781])]) ).

thf(f3084,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) != vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ),
    inference(forward_demodulation,[],[f2537,f1526]) ).

thf(f1526,plain,
    ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f794]) ).

thf(f794,plain,
    ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(rectify,[],[f70]) ).

thf(f70,axiom,
    ! [X39: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X39),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_insert__Nil) ).

thf(f2537,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) != vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X0 ) ),
    inference(equality_proxy_clausification,[],[f2536]) ).

thf(f2536,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) != vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X0) ) ),
    inference(equality_proxy_clausification,[],[f2535]) ).

thf(f2535,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X0) ) ),
    inference(binary_proxy_clausification,[],[f1798]) ).

thf(f1798,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X0) ),
    inference(cnf_transformation,[],[f592]) ).

thf(f592,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X0) ),
    inference(fool_elimination,[],[f591]) ).

thf(f591,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
      = ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X0 ) ),
    inference(rectify,[],[f250]) ).

thf(f250,axiom,
    ! [X28: list_Secrecy_KS,X15: secrecy_KS,X31: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X15),X31) )
      = ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X31)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X15),nil_Secrecy_KS)) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_rev__eq__Cons__iff) ).

thf(f16738,plain,
    spl303_780,
    inference(avatar_split_clause,[],[f3083,f16736]) ).

thf(f16736,plain,
    ( spl303_780
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) != X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_780])]) ).

thf(f3083,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) != X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ),
    inference(forward_demodulation,[],[f2539,f1526]) ).

thf(f2539,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) != X0 ) ),
    inference(equality_proxy_clausification,[],[f2538]) ).

thf(f2538,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X0) ) ),
    inference(equality_proxy_clausification,[],[f2534]) ).

thf(f2534,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X2)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X0) ) ),
    inference(binary_proxy_clausification,[],[f1798]) ).

thf(f16734,plain,
    spl303_779,
    inference(avatar_split_clause,[],[f3013,f16732]) ).

thf(f16732,plain,
    ( spl303_779
  <=> ! [X0: secrecy_specID,X1: secrecy_Secrets] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
        | ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_779])]) ).

thf(f3013,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
      | ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(forward_demodulation,[],[f3012,f1520]) ).

thf(f1520,plain,
    ! [X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)) ),
    inference(cnf_transformation,[],[f788]) ).

thf(f788,plain,
    ! [X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)) ),
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    ! [X3: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X3) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_KS2Expression_Osimps_I2_J) ).

thf(f3012,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))),nil_Se901661471ession)) )
      | ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(forward_demodulation,[],[f2871,f1527]) ).

thf(f2871,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))),nil_Se901661471ession)) ) ),
    inference(binary_proxy_clausification,[],[f1614]) ).

thf(f1614,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))),nil_Se901661471ession)) ),
    inference(cnf_transformation,[],[f854]) ).

thf(f854,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))),nil_Se901661471ession)) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X4: secrecy_specID,X5: secrecy_Secrets] : ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5))),nil_Se901661471ession)) = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X4),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_know1s) ).

thf(f16730,plain,
    spl303_778,
    inference(avatar_split_clause,[],[f3011,f16728]) ).

thf(f3011,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(forward_demodulation,[],[f3010,f1520]) ).

thf(f3010,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))),nil_Se901661471ession)) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(forward_demodulation,[],[f2870,f1527]) ).

thf(f2870,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))),nil_Se901661471ession)) ) ),
    inference(binary_proxy_clausification,[],[f1614]) ).

thf(f16726,plain,
    spl303_777,
    inference(avatar_split_clause,[],[f3007,f16724]) ).

thf(f16724,plain,
    ( spl303_777
  <=> ! [X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
        | ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_777])]) ).

thf(f3007,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
      | ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(forward_demodulation,[],[f2873,f1527]) ).

thf(f2873,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ) ),
    inference(binary_proxy_clausification,[],[f1610]) ).

thf(f1610,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ),
    inference(cnf_transformation,[],[f850]) ).

thf(f850,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ),
    inference(rectify,[],[f62]) ).

thf(f62,axiom,
    ! [X2: secrecy_specID,X3: secrecy_Keys] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3)),nil_Se901661471ession)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_knows1k) ).

thf(f16722,plain,
    spl303_776,
    inference(avatar_split_clause,[],[f3006,f16720]) ).

thf(f16720,plain,
    ( spl303_776
  <=> ! [X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_776])]) ).

thf(f3006,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(forward_demodulation,[],[f2872,f1527]) ).

thf(f2872,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ) ),
    inference(binary_proxy_clausification,[],[f1610]) ).

thf(f16693,plain,
    ( spl303_775
    | ~ spl303_140
    | ~ spl303_513 ),
    inference(avatar_split_clause,[],[f12033,f10787,f3946,f16691]) ).

thf(f16691,plain,
    ( spl303_775
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_775])]) ).

thf(f3946,plain,
    ( spl303_140
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_140])]) ).

thf(f12033,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X0),X1) ) )
    | ~ spl303_140
    | ~ spl303_513 ),
    inference(superposition,[],[f10788,f3947]) ).

thf(f3947,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X0 )
    | ~ spl303_140 ),
    inference(avatar_component_clause,[],[f3946]) ).

thf(f16387,plain,
    ( spl303_774
    | ~ spl303_88
    | ~ spl303_90
    | ~ spl303_268 ),
    inference(avatar_split_clause,[],[f5557,f5513,f3574,f3565,f16385]) ).

thf(f16385,plain,
    ( spl303_774
  <=> ! [X0: secrecy_Expression] : ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_774])]) ).

thf(f3574,plain,
    ( spl303_90
  <=> ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_90])]) ).

thf(f5513,plain,
    ( spl303_268
  <=> ! [X0: list_S529945141ession,X3: secrecy_Expression,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X1)),X2)) )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_268])]) ).

thf(f5557,plain,
    ( ! [X0: secrecy_Expression] : ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),nil_Se901661471ession)) )
    | ~ spl303_88
    | ~ spl303_90
    | ~ spl303_268 ),
    inference(forward_demodulation,[],[f5556,f3566]) ).

thf(f5556,plain,
    ( ! [X0: secrecy_Expression] : ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),nil_Se901661471ession)) )
    | ~ spl303_90
    | ~ spl303_268 ),
    inference(trivial_inequality_removal,[],[f5553]) ).

thf(f5553,plain,
    ( ! [X0: secrecy_Expression] :
        ( ( $true != $true )
        | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),nil_Se901661471ession)) ) )
    | ~ spl303_90
    | ~ spl303_268 ),
    inference(superposition,[],[f5514,f3576]) ).

thf(f3576,plain,
    ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),nil_Se901661471ession)) )
    | ~ spl303_90 ),
    inference(avatar_component_clause,[],[f3574]) ).

thf(f5514,plain,
    ( ! [X2: list_S529945141ession,X3: secrecy_Expression,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) )
        | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X1)),X2)) ) )
    | ~ spl303_268 ),
    inference(avatar_component_clause,[],[f5513]) ).

thf(f16383,plain,
    ( spl303_773
    | ~ spl303_88
    | ~ spl303_90
    | ~ spl303_267 ),
    inference(avatar_split_clause,[],[f5552,f5509,f3574,f3565,f16381]) ).

thf(f16381,plain,
    ( spl303_773
  <=> ! [X0: secrecy_Expression] : ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_773])]) ).

thf(f5509,plain,
    ( spl303_267
  <=> ! [X0: list_S529945141ession,X3: secrecy_Expression,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X2))) )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_267])]) ).

thf(f5552,plain,
    ( ! [X0: secrecy_Expression] : ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) )
    | ~ spl303_88
    | ~ spl303_90
    | ~ spl303_267 ),
    inference(forward_demodulation,[],[f5551,f3566]) ).

thf(f5551,plain,
    ( ! [X0: secrecy_Expression] : ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession))) )
    | ~ spl303_90
    | ~ spl303_267 ),
    inference(trivial_inequality_removal,[],[f5548]) ).

thf(f5548,plain,
    ( ! [X0: secrecy_Expression] :
        ( ( $true != $true )
        | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession))) ) )
    | ~ spl303_90
    | ~ spl303_267 ),
    inference(superposition,[],[f5510,f3576]) ).

thf(f5510,plain,
    ( ! [X2: list_S529945141ession,X3: secrecy_Expression,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) )
        | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X2))) ) )
    | ~ spl303_267 ),
    inference(avatar_component_clause,[],[f5509]) ).

thf(f16379,plain,
    ( spl303_772
    | ~ spl303_94
    | ~ spl303_200 ),
    inference(avatar_split_clause,[],[f4812,f4698,f3597,f16377]) ).

thf(f16377,plain,
    ( spl303_772
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_772])]) ).

thf(f4698,plain,
    ( spl303_200
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_200])]) ).

thf(f4812,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_200 ),
    inference(superposition,[],[f4699,f3598]) ).

thf(f4699,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) ) )
    | ~ spl303_200 ),
    inference(avatar_component_clause,[],[f4698]) ).

thf(f16375,plain,
    ( spl303_771
    | ~ spl303_93
    | ~ spl303_200 ),
    inference(avatar_split_clause,[],[f4810,f4698,f3593,f16373]) ).

thf(f16373,plain,
    ( spl303_771
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_771])]) ).

thf(f4810,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_200 ),
    inference(superposition,[],[f4699,f3594]) ).

thf(f16371,plain,
    ( spl303_770
    | ~ spl303_128
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4661,f4646,f3794,f16369]) ).

thf(f16369,plain,
    ( spl303_770
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_770])]) ).

thf(f3794,plain,
    ( spl303_128
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_128])]) ).

thf(f4646,plain,
    ( spl303_192
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_192])]) ).

thf(f4661,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) )
    | ~ spl303_128
    | ~ spl303_192 ),
    inference(superposition,[],[f3795,f4647]) ).

thf(f4647,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) )
    | ~ spl303_192 ),
    inference(avatar_component_clause,[],[f4646]) ).

thf(f3795,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X0 )
    | ~ spl303_128 ),
    inference(avatar_component_clause,[],[f3794]) ).

thf(f16367,plain,
    ( spl303_769
    | ~ spl303_3
    | ~ spl303_184 ),
    inference(avatar_split_clause,[],[f4545,f4509,f3143,f16365]) ).

thf(f16365,plain,
    ( spl303_769
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_769])]) ).

thf(f3143,plain,
    ( spl303_3
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_3])]) ).

thf(f4509,plain,
    ( spl303_184
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_184])]) ).

thf(f4545,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) ) )
    | ~ spl303_3
    | ~ spl303_184 ),
    inference(trivial_inequality_removal,[],[f4544]) ).

thf(f4544,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) ) )
    | ~ spl303_3
    | ~ spl303_184 ),
    inference(superposition,[],[f4510,f3144]) ).

thf(f3144,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl303_3 ),
    inference(avatar_component_clause,[],[f3143]) ).

thf(f4510,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) )
    | ~ spl303_184 ),
    inference(avatar_component_clause,[],[f4509]) ).

thf(f16363,plain,
    ( spl303_768
    | ~ spl303_3
    | ~ spl303_183 ),
    inference(avatar_split_clause,[],[f4534,f4505,f3143,f16361]) ).

thf(f16361,plain,
    ( spl303_768
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_768])]) ).

thf(f4505,plain,
    ( spl303_183
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_183])]) ).

thf(f4534,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) ) )
    | ~ spl303_3
    | ~ spl303_183 ),
    inference(trivial_inequality_removal,[],[f4533]) ).

thf(f4533,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) ) )
    | ~ spl303_3
    | ~ spl303_183 ),
    inference(superposition,[],[f4506,f3144]) ).

thf(f4506,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) )
    | ~ spl303_183 ),
    inference(avatar_component_clause,[],[f4505]) ).

thf(f16359,plain,
    ( spl303_767
    | ~ spl303_161
    | ~ spl303_176 ),
    inference(avatar_split_clause,[],[f4420,f4381,f4161,f16357]) ).

thf(f16357,plain,
    ( spl303_767
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_767])]) ).

thf(f4161,plain,
    ( spl303_161
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_161])]) ).

thf(f4420,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
    | ~ spl303_161
    | ~ spl303_176 ),
    inference(superposition,[],[f4162,f4382]) ).

thf(f4162,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
    | ~ spl303_161 ),
    inference(avatar_component_clause,[],[f4161]) ).

thf(f16355,plain,
    ( spl303_766
    | ~ spl303_646
    | ~ spl303_754 ),
    inference(avatar_split_clause,[],[f16294,f16057,f13773,f16353]) ).

thf(f16353,plain,
    ( spl303_766
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) != X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_766])]) ).

thf(f13773,plain,
    ( spl303_646
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) != X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_646])]) ).

thf(f16057,plain,
    ( spl303_754
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_754])]) ).

thf(f16294,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) != X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_646
    | ~ spl303_754 ),
    inference(duplicate_literal_removal,[],[f16290]) ).

thf(f16290,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) != X0 )
        | ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_646
    | ~ spl303_754 ),
    inference(superposition,[],[f13774,f16058]) ).

thf(f16058,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_754 ),
    inference(avatar_component_clause,[],[f16057]) ).

thf(f13774,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) != X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_646 ),
    inference(avatar_component_clause,[],[f13773]) ).

thf(f16351,plain,
    ( spl303_765
    | ~ spl303_173 ),
    inference(avatar_split_clause,[],[f4392,f4369,f16349]) ).

thf(f16349,plain,
    ( spl303_765
  <=> ! [X0: secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0))) != X0 )
        | ( X0 = X1 )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0))) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_765])]) ).

thf(f4369,plain,
    ( spl303_173
  <=> ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
        ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) )
        | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_173])]) ).

thf(f4392,plain,
    ( ! [X0: secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0))) != X0 )
        | ( X0 = X1 )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0))) != X0 ) )
    | ~ spl303_173 ),
    inference(equality_proxy_clausification,[],[f4391]) ).

thf(f4391,plain,
    ( ! [X0: secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0))) != X0 )
        | ( X0 = X1 )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0)))) ) )
    | ~ spl303_173 ),
    inference(equality_proxy_clausification,[],[f4390]) ).

thf(f4390,plain,
    ( ! [X0: secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0))) != X0 )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0),X1) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0)))) ) )
    | ~ spl303_173 ),
    inference(equality_proxy_clausification,[],[f4387]) ).

thf(f4387,plain,
    ( ! [X0: secrecy_KS,X1: secrecy_KS] :
        ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0)))) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0),X1) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),X0)))) ) )
    | ~ spl303_173 ),
    inference(primitive_instantiation,[],[f4370]) ).

thf(f4370,plain,
    ( ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
        ( ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) )
        | ( $true = vAPP(secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) ) )
    | ~ spl303_173 ),
    inference(avatar_component_clause,[],[f4369]) ).

thf(f16347,plain,
    ( spl303_764
    | ~ spl303_149
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4256,f4225,f4008,f16345]) ).

thf(f16345,plain,
    ( spl303_764
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_764])]) ).

thf(f4008,plain,
    ( spl303_149
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_149])]) ).

thf(f4256,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_149
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f4009]) ).

thf(f4009,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_149 ),
    inference(avatar_component_clause,[],[f4008]) ).

thf(f16343,plain,
    ( spl303_763
    | ~ spl303_156
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4249,f4221,f4037,f16341]) ).

thf(f16341,plain,
    ( spl303_763
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_763])]) ).

thf(f4249,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_156
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f4038]) ).

thf(f16339,plain,
    ( spl303_762
    | ~ spl303_155
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4248,f4221,f4033,f16337]) ).

thf(f16337,plain,
    ( spl303_762
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_762])]) ).

thf(f4248,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_155
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f4034]) ).

thf(f16335,plain,
    ( spl303_761
    | ~ spl303_151
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4240,f4221,f4016,f16333]) ).

thf(f16333,plain,
    ( spl303_761
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_761])]) ).

thf(f4016,plain,
    ( spl303_151
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_151])]) ).

thf(f4240,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f4017]) ).

thf(f4017,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151 ),
    inference(avatar_component_clause,[],[f4016]) ).

thf(f16331,plain,
    ( spl303_760
    | ~ spl303_157
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4207,f4161,f4145,f16329]) ).

thf(f16329,plain,
    ( spl303_760
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_l425507653ession,X1: list_l425507653ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_760])]) ).

thf(f4207,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_l425507653ession,X1: list_l425507653ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
    | ~ spl303_157
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f4146]) ).

thf(f16327,plain,
    ( spl303_759
    | ~ spl303_158
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4200,f4161,f4149,f16325]) ).

thf(f16325,plain,
    ( spl303_759
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_759])]) ).

thf(f4200,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
    | ~ spl303_158
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f4150]) ).

thf(f16283,plain,
    ( spl303_758
    | ~ spl303_139
    | ~ spl303_513 ),
    inference(avatar_split_clause,[],[f12032,f10787,f3942,f16281]) ).

thf(f16281,plain,
    ( spl303_758
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_758])]) ).

thf(f3942,plain,
    ( spl303_139
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_139])]) ).

thf(f12032,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) )
    | ~ spl303_139
    | ~ spl303_513 ),
    inference(superposition,[],[f10788,f3943]) ).

thf(f3943,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) = X1 )
    | ~ spl303_139 ),
    inference(avatar_component_clause,[],[f3942]) ).

thf(f16120,plain,
    ( spl303_757
    | ~ spl303_138
    | ~ spl303_513 ),
    inference(avatar_split_clause,[],[f12031,f10787,f3938,f16118]) ).

thf(f16118,plain,
    ( spl303_757
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_757])]) ).

thf(f12031,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) )
    | ~ spl303_138
    | ~ spl303_513 ),
    inference(superposition,[],[f10788,f3939]) ).

thf(f16067,plain,
    ( spl303_756
    | ~ spl303_160
    | ~ spl303_346 ),
    inference(avatar_split_clause,[],[f6385,f6366,f4157,f16065]) ).

thf(f16065,plain,
    ( spl303_756
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_756])]) ).

thf(f4157,plain,
    ( spl303_160
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_160])]) ).

thf(f6366,plain,
    ( spl303_346
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) = X1 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_346])]) ).

thf(f6385,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X1),X0) ) )
    | ~ spl303_160
    | ~ spl303_346 ),
    inference(superposition,[],[f4158,f6367]) ).

thf(f6367,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) = X1 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) )
    | ~ spl303_346 ),
    inference(avatar_component_clause,[],[f6366]) ).

thf(f4158,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) )
    | ~ spl303_160 ),
    inference(avatar_component_clause,[],[f4157]) ).

thf(f16063,plain,
    ( spl303_755
    | ~ spl303_68
    | ~ spl303_346 ),
    inference(avatar_split_clause,[],[f6379,f6366,f3478,f16061]) ).

thf(f16061,plain,
    ( spl303_755
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X0),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_755])]) ).

thf(f3478,plain,
    ( spl303_68
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_68])]) ).

thf(f6379,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X0),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X1),X0) ) )
    | ~ spl303_68
    | ~ spl303_346 ),
    inference(superposition,[],[f3479,f6367]) ).

thf(f3479,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X0 )
    | ~ spl303_68 ),
    inference(avatar_component_clause,[],[f3478]) ).

thf(f16059,plain,
    ( spl303_754
    | ~ spl303_128
    | ~ spl303_299 ),
    inference(avatar_split_clause,[],[f5816,f5783,f3794,f16057]) ).

thf(f5783,plain,
    ( spl303_299
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_299])]) ).

thf(f5816,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_128
    | ~ spl303_299 ),
    inference(superposition,[],[f3795,f5784]) ).

thf(f5784,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_299 ),
    inference(avatar_component_clause,[],[f5783]) ).

thf(f16055,plain,
    ( spl303_753
    | ~ spl303_126
    | ~ spl303_299 ),
    inference(avatar_split_clause,[],[f5815,f5783,f3781,f16053]) ).

thf(f16053,plain,
    ( spl303_753
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_753])]) ).

thf(f3781,plain,
    ( spl303_126
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_126])]) ).

thf(f5815,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_126
    | ~ spl303_299 ),
    inference(superposition,[],[f3782,f5784]) ).

thf(f3782,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X1 )
    | ~ spl303_126 ),
    inference(avatar_component_clause,[],[f3781]) ).

thf(f16051,plain,
    ( spl303_752
    | ~ spl303_122
    | ~ spl303_298 ),
    inference(avatar_split_clause,[],[f5803,f5779,f3757,f16049]) ).

thf(f16049,plain,
    ( spl303_752
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_752])]) ).

thf(f3757,plain,
    ( spl303_122
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_122])]) ).

thf(f5779,plain,
    ( spl303_298
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_298])]) ).

thf(f5803,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_122
    | ~ spl303_298 ),
    inference(superposition,[],[f3758,f5780]) ).

thf(f5780,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_298 ),
    inference(avatar_component_clause,[],[f5779]) ).

thf(f3758,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X1 )
    | ~ spl303_122 ),
    inference(avatar_component_clause,[],[f3757]) ).

thf(f16047,plain,
    ( spl303_751
    | ~ spl303_124
    | ~ spl303_298 ),
    inference(avatar_split_clause,[],[f5802,f5779,f3769,f16045]) ).

thf(f16045,plain,
    ( spl303_751
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_751])]) ).

thf(f3769,plain,
    ( spl303_124
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_124])]) ).

thf(f5802,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_124
    | ~ spl303_298 ),
    inference(superposition,[],[f3770,f5780]) ).

thf(f3770,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X0 )
    | ~ spl303_124 ),
    inference(avatar_component_clause,[],[f3769]) ).

thf(f16043,plain,
    ( spl303_750
    | ~ spl303_3
    | ~ spl303_181 ),
    inference(avatar_split_clause,[],[f4494,f4441,f3143,f16041]) ).

thf(f16041,plain,
    ( spl303_750
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X0)),nil_Se901661471ession)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_750])]) ).

thf(f4441,plain,
    ( spl303_181
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_181])]) ).

thf(f4494,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X0)),nil_Se901661471ession)) ) )
    | ~ spl303_3
    | ~ spl303_181 ),
    inference(trivial_inequality_removal,[],[f4493]) ).

thf(f4493,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X0)),nil_Se901661471ession)) ) )
    | ~ spl303_3
    | ~ spl303_181 ),
    inference(superposition,[],[f4442,f3144]) ).

thf(f4442,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_181 ),
    inference(avatar_component_clause,[],[f4441]) ).

thf(f16039,plain,
    ( spl303_749
    | ~ spl303_3
    | ~ spl303_180 ),
    inference(avatar_split_clause,[],[f4480,f4437,f3143,f16037]) ).

thf(f16037,plain,
    ( spl303_749
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X0)),nil_Se901661471ession)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_749])]) ).

thf(f4437,plain,
    ( spl303_180
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_180])]) ).

thf(f4480,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X0)),nil_Se901661471ession)) ) )
    | ~ spl303_3
    | ~ spl303_180 ),
    inference(trivial_inequality_removal,[],[f4479]) ).

thf(f4479,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X0)),nil_Se901661471ession)) ) )
    | ~ spl303_3
    | ~ spl303_180 ),
    inference(superposition,[],[f4438,f3144]) ).

thf(f4438,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_180 ),
    inference(avatar_component_clause,[],[f4437]) ).

thf(f16035,plain,
    ( spl303_748
    | ~ spl303_145
    | ~ spl303_481 ),
    inference(avatar_split_clause,[],[f11158,f7646,f3967,f16033]) ).

thf(f16033,plain,
    ( spl303_748
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_748])]) ).

thf(f3967,plain,
    ( spl303_145
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_145])]) ).

thf(f7646,plain,
    ( spl303_481
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = X1 )
        | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_481])]) ).

thf(f11158,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) )
    | ~ spl303_145
    | ~ spl303_481 ),
    inference(superposition,[],[f7647,f3968]) ).

thf(f3968,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X1 )
    | ~ spl303_145 ),
    inference(avatar_component_clause,[],[f3967]) ).

thf(f7647,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_481 ),
    inference(avatar_component_clause,[],[f7646]) ).

thf(f16031,plain,
    ( spl303_747
    | ~ spl303_3
    | ~ spl303_179 ),
    inference(avatar_split_clause,[],[f4466,f4433,f3143,f16029]) ).

thf(f16029,plain,
    ( spl303_747
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X0)),nil_Secrecy_KS)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_747])]) ).

thf(f4433,plain,
    ( spl303_179
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_179])]) ).

thf(f4466,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X0)),nil_Secrecy_KS)) ) )
    | ~ spl303_3
    | ~ spl303_179 ),
    inference(trivial_inequality_removal,[],[f4465]) ).

thf(f4465,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X0)),nil_Secrecy_KS)) ) )
    | ~ spl303_3
    | ~ spl303_179 ),
    inference(superposition,[],[f4434,f3144]) ).

thf(f4434,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_179 ),
    inference(avatar_component_clause,[],[f4433]) ).

thf(f16027,plain,
    ( spl303_746
    | ~ spl303_3
    | ~ spl303_178 ),
    inference(avatar_split_clause,[],[f4452,f4429,f3143,f16025]) ).

thf(f16025,plain,
    ( spl303_746
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X0)),nil_Secrecy_KS)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_746])]) ).

thf(f4429,plain,
    ( spl303_178
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_178])]) ).

thf(f4452,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X0)),nil_Secrecy_KS)) ) )
    | ~ spl303_3
    | ~ spl303_178 ),
    inference(trivial_inequality_removal,[],[f4451]) ).

thf(f4451,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X0)),nil_Secrecy_KS)) ) )
    | ~ spl303_3
    | ~ spl303_178 ),
    inference(superposition,[],[f4430,f3144]) ).

thf(f4430,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_178 ),
    inference(avatar_component_clause,[],[f4429]) ).

thf(f16023,plain,
    ( spl303_745
    | ~ spl303_151
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4306,f4272,f4016,f16021]) ).

thf(f16021,plain,
    ( spl303_745
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_745])]) ).

thf(f4306,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151
    | ~ spl303_168 ),
    inference(forward_demodulation,[],[f4293,f4273]) ).

thf(f4293,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151
    | ~ spl303_168 ),
    inference(superposition,[],[f4273,f4017]) ).

thf(f16019,plain,
    ( spl303_744
    | ~ spl303_150
    | ~ spl303_167 ),
    inference(avatar_split_clause,[],[f4286,f4268,f4012,f16017]) ).

thf(f16017,plain,
    ( spl303_744
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_744])]) ).

thf(f4012,plain,
    ( spl303_150
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),X1) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_150])]) ).

thf(f4268,plain,
    ( spl303_167
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_167])]) ).

thf(f4286,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_150
    | ~ spl303_167 ),
    inference(forward_demodulation,[],[f4278,f4269]) ).

thf(f4269,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_167 ),
    inference(avatar_component_clause,[],[f4268]) ).

thf(f4278,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_150
    | ~ spl303_167 ),
    inference(superposition,[],[f4269,f4013]) ).

thf(f4013,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),X1) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_150 ),
    inference(avatar_component_clause,[],[f4012]) ).

thf(f16015,plain,
    ( spl303_743
    | ~ spl303_149
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4199,f4161,f4008,f16013]) ).

thf(f16013,plain,
    ( spl303_743
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_743])]) ).

thf(f4199,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_149
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f4009]) ).

thf(f16011,plain,
    ( spl303_742
    | ~ spl303_148
    | ~ spl303_160 ),
    inference(avatar_split_clause,[],[f4191,f4157,f4004,f16009]) ).

thf(f16009,plain,
    ( spl303_742
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))),nil_Se901661471ession) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_742])]) ).

thf(f4004,plain,
    ( spl303_148
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_148])]) ).

thf(f4191,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))),nil_Se901661471ession) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_148
    | ~ spl303_160 ),
    inference(superposition,[],[f4158,f4005]) ).

thf(f4005,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_148 ),
    inference(avatar_component_clause,[],[f4004]) ).

thf(f16007,plain,
    ( spl303_741
    | ~ spl303_146
    | ~ spl303_159 ),
    inference(avatar_split_clause,[],[f4185,f4153,f3996,f16005]) ).

thf(f16005,plain,
    ( spl303_741
  <=> ! [X2: secrecy_KS > secrecy_KS > $o,X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1))),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_741])]) ).

thf(f3996,plain,
    ( spl303_146
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_146])]) ).

thf(f4153,plain,
    ( spl303_159
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_159])]) ).

thf(f4185,plain,
    ( ! [X2: secrecy_KS > secrecy_KS > $o,X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1))),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_146
    | ~ spl303_159 ),
    inference(superposition,[],[f4154,f3997]) ).

thf(f3997,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_146 ),
    inference(avatar_component_clause,[],[f3996]) ).

thf(f4154,plain,
    ( ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) )
    | ~ spl303_159 ),
    inference(avatar_component_clause,[],[f4153]) ).

thf(f15936,plain,
    ( spl303_740
    | ~ spl303_144
    | ~ spl303_481 ),
    inference(avatar_split_clause,[],[f11157,f7646,f3963,f15934]) ).

thf(f15934,plain,
    ( spl303_740
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_740])]) ).

thf(f3963,plain,
    ( spl303_144
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_144])]) ).

thf(f11157,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) )
    | ~ spl303_144
    | ~ spl303_481 ),
    inference(superposition,[],[f7647,f3964]) ).

thf(f3964,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X0 )
    | ~ spl303_144 ),
    inference(avatar_component_clause,[],[f3963]) ).

thf(f15922,plain,
    ( spl303_739
    | ~ spl303_37
    | ~ spl303_229 ),
    inference(avatar_split_clause,[],[f5251,f5179,f3326,f15920]) ).

thf(f15920,plain,
    ( spl303_739
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0)) != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_739])]) ).

thf(f5179,plain,
    ( spl303_229
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK34,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0))) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_229])]) ).

thf(f5251,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0)) != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_37
    | ~ spl303_229 ),
    inference(superposition,[],[f3327,f5180]) ).

thf(f5180,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK34,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0))) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_229 ),
    inference(avatar_component_clause,[],[f5179]) ).

thf(f15918,plain,
    ( spl303_738
    | ~ spl303_94
    | ~ spl303_222 ),
    inference(avatar_split_clause,[],[f5130,f5119,f3597,f15916]) ).

thf(f15916,plain,
    ( spl303_738
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,sK38,X0) = X1 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_738])]) ).

thf(f5130,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,sK38,X0) = X1 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_222 ),
    inference(superposition,[],[f5120,f3598]) ).

thf(f15914,plain,
    ( spl303_737
    | ~ spl303_68
    | ~ spl303_203 ),
    inference(avatar_split_clause,[],[f4851,f4820,f3478,f15912]) ).

thf(f15912,plain,
    ( spl303_737
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_737])]) ).

thf(f4820,plain,
    ( spl303_203
  <=> ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_203])]) ).

thf(f4851,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_68
    | ~ spl303_203 ),
    inference(superposition,[],[f3479,f4821]) ).

thf(f4821,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_203 ),
    inference(avatar_component_clause,[],[f4820]) ).

thf(f15910,plain,
    ( spl303_736
    | ~ spl303_3
    | ~ spl303_173 ),
    inference(avatar_split_clause,[],[f4389,f4369,f3143,f15908]) ).

thf(f15908,plain,
    ( spl303_736
  <=> ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
        ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) )
        | ( $false = vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_736])]) ).

thf(f4389,plain,
    ( ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
        ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) )
        | ( $false = vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) ) )
    | ~ spl303_3
    | ~ spl303_173 ),
    inference(trivial_inequality_removal,[],[f4388]) ).

thf(f4388,plain,
    ( ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) )
        | ( $false = vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) ) )
    | ~ spl303_3
    | ~ spl303_173 ),
    inference(superposition,[],[f4370,f3144]) ).

thf(f15860,plain,
    ( spl303_735
    | ~ spl303_166
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4303,f4272,f4225,f15858]) ).

thf(f15858,plain,
    ( spl303_735
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_735])]) ).

thf(f4303,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) ) )
    | ~ spl303_166
    | ~ spl303_168 ),
    inference(superposition,[],[f4226,f4273]) ).

thf(f15856,plain,
    spl303_734,
    inference(avatar_split_clause,[],[f3091,f15854]) ).

thf(f15854,plain,
    ( spl303_734
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X2 )
        | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2) != X0 )
        | ( nil_Se901661471ession = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_734])]) ).

thf(f3091,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X2 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2) != X0 )
      | ( nil_Se901661471ession = X2 ) ),
    inference(forward_demodulation,[],[f2429,f1527]) ).

thf(f2429,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2) != X0 )
      | ( nil_Se901661471ession = X2 ) ),
    inference(equality_proxy_clausification,[],[f2428]) ).

thf(f2428,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2) != X0 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2) ) ),
    inference(not_proxy_clausification,[],[f2427]) ).

thf(f2427,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2) != X0 )
      | ( $false = vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2426]) ).

thf(f2426,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0) )
      | ( $false = vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2)) ) ),
    inference(binary_proxy_clausification,[],[f2425]) ).

thf(f2425,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) != X1 )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2))),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0)) ) ),
    inference(equality_proxy_clausification,[],[f2424]) ).

thf(f2424,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2)),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2))),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0)) ) ),
    inference(binary_proxy_clausification,[],[f2423]) ).

thf(f2423,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2))),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0))),vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2)),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2412]) ).

thf(f2412,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2))),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0))),vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2)),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1805]) ).

thf(f1805,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2))),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0))),vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2)),X1)) ),
    inference(cnf_transformation,[],[f606]) ).

thf(f606,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X2))),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2)),X0))),vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2)),X1)) ),
    inference(fool_elimination,[],[f605]) ).

thf(f605,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X2 )
        = ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) = X1 ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X2) = X0 )
      & ( nil_Se901661471ession != X2 ) ),
    inference(rectify,[],[f222]) ).

thf(f222,axiom,
    ! [X28: list_S529945141ession,X39: secrecy_Expression,X31: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)) = X31 )
        = ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X31) = X39 ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X31) = X28 )
      & ( nil_Se901661471ession != X31 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_snoc__eq__iff__butlast) ).

thf(f15852,plain,
    ( spl303_733
    | ~ spl303_143
    | ~ spl303_481 ),
    inference(avatar_split_clause,[],[f11156,f7646,f3959,f15850]) ).

thf(f15850,plain,
    ( spl303_733
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_733])]) ).

thf(f3959,plain,
    ( spl303_143
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_143])]) ).

thf(f11156,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1) ) )
    | ~ spl303_143
    | ~ spl303_481 ),
    inference(superposition,[],[f7647,f3960]) ).

thf(f3960,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) = X1 )
    | ~ spl303_143 ),
    inference(avatar_component_clause,[],[f3959]) ).

thf(f15848,plain,
    spl303_732,
    inference(avatar_split_clause,[],[f3087,f15846]) ).

thf(f15846,plain,
    ( spl303_732
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
        | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2) != X0 )
        | ( nil_Secrecy_KS = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_732])]) ).

thf(f3087,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2) != X0 )
      | ( nil_Secrecy_KS = X2 ) ),
    inference(forward_demodulation,[],[f2447,f1526]) ).

thf(f2447,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2) != X0 )
      | ( nil_Secrecy_KS = X2 ) ),
    inference(equality_proxy_clausification,[],[f2446]) ).

thf(f2446,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2) != X0 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2) ) ),
    inference(not_proxy_clausification,[],[f2445]) ).

thf(f2445,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2) != X0 )
      | ( $false = vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2)) ) ),
    inference(equality_proxy_clausification,[],[f2444]) ).

thf(f2444,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0) )
      | ( $false = vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2)) ) ),
    inference(binary_proxy_clausification,[],[f2443]) ).

thf(f2443,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) != X1 )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2))),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0)) ) ),
    inference(equality_proxy_clausification,[],[f2442]) ).

thf(f2442,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2)),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2))),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0)) ) ),
    inference(binary_proxy_clausification,[],[f2441]) ).

thf(f2441,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2))),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0))),vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2)),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2430]) ).

thf(f2430,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2))),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0))),vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2)),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1804]) ).

thf(f1804,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2))),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0))),vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2)),X1)) ),
    inference(cnf_transformation,[],[f604]) ).

thf(f604,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X2))),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2)),X0))),vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2)),X1)) ),
    inference(fool_elimination,[],[f603]) ).

thf(f603,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X2 )
        = ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X2) = X1 ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X2) = X0 )
      & ( nil_Secrecy_KS != X2 ) ),
    inference(rectify,[],[f221]) ).

thf(f221,axiom,
    ! [X28: list_Secrecy_KS,X39: secrecy_KS,X31: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)) = X31 )
        = ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X31) = X39 ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X31) = X28 )
      & ( nil_Secrecy_KS != X31 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_snoc__eq__iff__butlast) ).

thf(f15732,plain,
    ( spl303_731
    | ~ spl303_142
    | ~ spl303_481 ),
    inference(avatar_split_clause,[],[f11155,f7646,f3955,f15730]) ).

thf(f15730,plain,
    ( spl303_731
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_731])]) ).

thf(f3955,plain,
    ( spl303_142
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_142])]) ).

thf(f11155,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1) ) )
    | ~ spl303_142
    | ~ spl303_481 ),
    inference(superposition,[],[f7647,f3956]) ).

thf(f3956,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) = X0 )
    | ~ spl303_142 ),
    inference(avatar_component_clause,[],[f3955]) ).

thf(f15443,plain,
    ( spl303_730
    | ~ spl303_128
    | ~ spl303_227 ),
    inference(avatar_split_clause,[],[f5228,f5166,f3794,f15441]) ).

thf(f15441,plain,
    ( spl303_730
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_730])]) ).

thf(f5166,plain,
    ( spl303_227
  <=> ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_227])]) ).

thf(f5228,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_128
    | ~ spl303_227 ),
    inference(superposition,[],[f3795,f5167]) ).

thf(f5167,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_227 ),
    inference(avatar_component_clause,[],[f5166]) ).

thf(f15439,plain,
    ( spl303_729
    | ~ spl303_124
    | ~ spl303_226 ),
    inference(avatar_split_clause,[],[f5204,f5162,f3769,f15437]) ).

thf(f15437,plain,
    ( spl303_729
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_729])]) ).

thf(f5162,plain,
    ( spl303_226
  <=> ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_226])]) ).

thf(f5204,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_124
    | ~ spl303_226 ),
    inference(superposition,[],[f3770,f5163]) ).

thf(f5163,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_226 ),
    inference(avatar_component_clause,[],[f5162]) ).

thf(f15435,plain,
    ( spl303_728
    | ~ spl303_145
    | ~ spl303_473 ),
    inference(avatar_split_clause,[],[f11097,f7576,f3967,f15433]) ).

thf(f15433,plain,
    ( spl303_728
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_728])]) ).

thf(f7576,plain,
    ( spl303_473
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_473])]) ).

thf(f11097,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1) ) )
    | ~ spl303_145
    | ~ spl303_473 ),
    inference(superposition,[],[f7577,f3968]) ).

thf(f7577,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_473 ),
    inference(avatar_component_clause,[],[f7576]) ).

thf(f15430,plain,
    ( spl303_727
    | ~ spl303_160
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4662,f4646,f4157,f15428]) ).

thf(f15428,plain,
    ( spl303_727
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: secrecy_Expression,X1: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_727])]) ).

thf(f4662,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: secrecy_Expression,X1: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))),nil_Se901661471ession) )
    | ~ spl303_160
    | ~ spl303_192 ),
    inference(superposition,[],[f4158,f4647]) ).

thf(f15426,plain,
    ( spl303_726
    | ~ spl303_130
    | ~ spl303_181 ),
    inference(avatar_split_clause,[],[f4496,f4441,f3805,f15424]) ).

thf(f15424,plain,
    ( spl303_726
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0)) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_726])]) ).

thf(f3805,plain,
    ( spl303_130
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_130])]) ).

thf(f4496,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0)) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_130
    | ~ spl303_181 ),
    inference(trivial_inequality_removal,[],[f4491]) ).

thf(f4491,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0)) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_130
    | ~ spl303_181 ),
    inference(superposition,[],[f4442,f3806]) ).

thf(f3806,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
    | ~ spl303_130 ),
    inference(avatar_component_clause,[],[f3805]) ).

thf(f15422,plain,
    ( spl303_725
    | ~ spl303_130
    | ~ spl303_180 ),
    inference(avatar_split_clause,[],[f4482,f4437,f3805,f15420]) ).

thf(f15420,plain,
    ( spl303_725
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0)) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_725])]) ).

thf(f4482,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0)) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_130
    | ~ spl303_180 ),
    inference(trivial_inequality_removal,[],[f4477]) ).

thf(f4477,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0)) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_130
    | ~ spl303_180 ),
    inference(superposition,[],[f4438,f3806]) ).

thf(f15418,plain,
    ( spl303_724
    | ~ spl303_129
    | ~ spl303_179 ),
    inference(avatar_split_clause,[],[f4468,f4433,f3801,f15416]) ).

thf(f15416,plain,
    ( spl303_724
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_724])]) ).

thf(f3801,plain,
    ( spl303_129
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_129])]) ).

thf(f4468,plain,
    ( ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_129
    | ~ spl303_179 ),
    inference(trivial_inequality_removal,[],[f4463]) ).

thf(f4463,plain,
    ( ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_129
    | ~ spl303_179 ),
    inference(superposition,[],[f4434,f3802]) ).

thf(f3802,plain,
    ( ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) )
    | ~ spl303_129 ),
    inference(avatar_component_clause,[],[f3801]) ).

thf(f15414,plain,
    ( spl303_723
    | ~ spl303_129
    | ~ spl303_178 ),
    inference(avatar_split_clause,[],[f4454,f4429,f3801,f15412]) ).

thf(f15412,plain,
    ( spl303_723
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_723])]) ).

thf(f4454,plain,
    ( ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_129
    | ~ spl303_178 ),
    inference(trivial_inequality_removal,[],[f4449]) ).

thf(f4449,plain,
    ( ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_129
    | ~ spl303_178 ),
    inference(superposition,[],[f4430,f3802]) ).

thf(f15410,plain,
    ( spl303_722
    | ~ spl303_161
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4301,f4272,f4161,f15408]) ).

thf(f15408,plain,
    ( spl303_722
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_722])]) ).

thf(f4301,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
    | ~ spl303_161
    | ~ spl303_168 ),
    inference(superposition,[],[f4162,f4273]) ).

thf(f15406,plain,
    ( spl303_721
    | ~ spl303_99
    | ~ spl303_151 ),
    inference(avatar_split_clause,[],[f4094,f4016,f3617,f15404]) ).

thf(f15404,plain,
    ( spl303_721
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_721])]) ).

thf(f4094,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_99
    | ~ spl303_151 ),
    inference(superposition,[],[f3618,f4017]) ).

thf(f15402,plain,
    ( spl303_720
    | ~ spl303_96
    | ~ spl303_150 ),
    inference(avatar_split_clause,[],[f4084,f4012,f3605,f15400]) ).

thf(f15400,plain,
    ( spl303_720
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_720])]) ).

thf(f3605,plain,
    ( spl303_96
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_96])]) ).

thf(f4084,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_96
    | ~ spl303_150 ),
    inference(superposition,[],[f3606,f4013]) ).

thf(f3606,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_96 ),
    inference(avatar_component_clause,[],[f3605]) ).

thf(f15398,plain,
    ( spl303_719
    | ~ spl303_100
    | ~ spl303_149 ),
    inference(avatar_split_clause,[],[f4076,f4008,f3621,f15396]) ).

thf(f15396,plain,
    ( spl303_719
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_719])]) ).

thf(f3621,plain,
    ( spl303_100
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_100])]) ).

thf(f4076,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_100
    | ~ spl303_149 ),
    inference(superposition,[],[f3622,f4009]) ).

thf(f3622,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_100 ),
    inference(avatar_component_clause,[],[f3621]) ).

thf(f15394,plain,
    ( spl303_718
    | ~ spl303_98
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4064,f4004,f3613,f15392]) ).

thf(f15392,plain,
    ( spl303_718
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_718])]) ).

thf(f3613,plain,
    ( spl303_98
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_98])]) ).

thf(f4064,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_98
    | ~ spl303_148 ),
    inference(superposition,[],[f3614,f4005]) ).

thf(f3614,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_98 ),
    inference(avatar_component_clause,[],[f3613]) ).

thf(f15390,plain,
    ( spl303_717
    | ~ spl303_144
    | ~ spl303_473 ),
    inference(avatar_split_clause,[],[f11096,f7576,f3963,f15388]) ).

thf(f15388,plain,
    ( spl303_717
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_717])]) ).

thf(f11096,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1) ) )
    | ~ spl303_144
    | ~ spl303_473 ),
    inference(superposition,[],[f7577,f3964]) ).

thf(f15386,plain,
    ( spl303_716
    | ~ spl303_97
    | ~ spl303_147 ),
    inference(avatar_split_clause,[],[f4053,f4000,f3609,f15384]) ).

thf(f15384,plain,
    ( spl303_716
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_716])]) ).

thf(f3609,plain,
    ( spl303_97
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_97])]) ).

thf(f4000,plain,
    ( spl303_147
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_147])]) ).

thf(f4053,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_97
    | ~ spl303_147 ),
    inference(superposition,[],[f3610,f4001]) ).

thf(f4001,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_147 ),
    inference(avatar_component_clause,[],[f4000]) ).

thf(f3610,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_97 ),
    inference(avatar_component_clause,[],[f3609]) ).

thf(f15382,plain,
    ( spl303_715
    | ~ spl303_95
    | ~ spl303_146 ),
    inference(avatar_split_clause,[],[f4045,f3996,f3601,f15380]) ).

thf(f15380,plain,
    ( spl303_715
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_715])]) ).

thf(f3601,plain,
    ( spl303_95
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_95])]) ).

thf(f4045,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_95
    | ~ spl303_146 ),
    inference(superposition,[],[f3602,f3997]) ).

thf(f3602,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_95 ),
    inference(avatar_component_clause,[],[f3601]) ).

thf(f15378,plain,
    ( spl303_714
    | ~ spl303_81
    | ~ spl303_93 ),
    inference(avatar_split_clause,[],[f3646,f3593,f3530,f15376]) ).

thf(f15376,plain,
    ( spl303_714
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_714])]) ).

thf(f3530,plain,
    ( spl303_81
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_81])]) ).

thf(f3646,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_81
    | ~ spl303_93 ),
    inference(superposition,[],[f3594,f3531]) ).

thf(f3531,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_81 ),
    inference(avatar_component_clause,[],[f3530]) ).

thf(f15374,plain,
    ( spl303_713
    | ~ spl303_78
    | ~ spl303_91 ),
    inference(avatar_split_clause,[],[f3641,f3585,f3518,f15372]) ).

thf(f15372,plain,
    ( spl303_713
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_713])]) ).

thf(f3518,plain,
    ( spl303_78
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_78])]) ).

thf(f3585,plain,
    ( spl303_91
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_91])]) ).

thf(f3641,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_78
    | ~ spl303_91 ),
    inference(superposition,[],[f3586,f3519]) ).

thf(f3519,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_78 ),
    inference(avatar_component_clause,[],[f3518]) ).

thf(f3586,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_91 ),
    inference(avatar_component_clause,[],[f3585]) ).

thf(f15370,plain,
    spl303_712,
    inference(avatar_split_clause,[],[f2408,f15368]) ).

thf(f15368,plain,
    ( spl303_712
  <=> ! [X2: secrecy_Expression,X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2) )
        | ( X0 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_712])]) ).

thf(f2408,plain,
    ! [X2: secrecy_Expression,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2) )
      | ( X0 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2407]) ).

thf(f2407,plain,
    ! [X2: secrecy_Expression,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f2406]) ).

thf(f2406,plain,
    ! [X2: secrecy_Expression,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1806]) ).

thf(f1806,plain,
    ! [X2: secrecy_Expression,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2)) ),
    inference(cnf_transformation,[],[f608]) ).

thf(f608,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: secrecy_Expression] : ( vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2)) ),
    inference(fool_elimination,[],[f607]) ).

thf(f607,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: secrecy_Expression] :
      ( ( vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X1),X2) )
      | ( X0 = X2 ) ),
    inference(rectify,[],[f130]) ).

thf(f130,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession,X15: secrecy_Expression] :
      ( ( vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),X15) = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,X28),X15) )
      | ( X15 = X39 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_member__rec_I1_J) ).

thf(f15366,plain,
    spl303_711,
    inference(avatar_split_clause,[],[f2401,f15364]) ).

thf(f15364,plain,
    ( spl303_711
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
        ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_711])]) ).

thf(f2401,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2) )
      | ( X0 = X1 ) ),
    inference(equality_proxy_clausification,[],[f2400]) ).

thf(f2400,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f2399]) ).

thf(f2399,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X1)),vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1807]) ).

thf(f1807,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X1)),vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2)) ),
    inference(cnf_transformation,[],[f610]) ).

thf(f610,plain,
    ! [X0: secrecy_Expression,X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X1)),vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2)) ),
    inference(fool_elimination,[],[f609]) ).

thf(f609,plain,
    ! [X0: secrecy_Expression,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),X2) )
      | ( X0 = X1 ) ),
    inference(rectify,[],[f239]) ).

thf(f239,axiom,
    ! [X39: secrecy_Expression,X15: secrecy_Expression,X68: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X68)) = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X39),X68) )
      | ( X15 = X39 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mem_Osimps_I2_J) ).

thf(f15057,plain,
    ( spl303_710
    | ~ spl303_159
    | ~ spl303_340 ),
    inference(avatar_split_clause,[],[f6331,f6321,f4153,f15055]) ).

thf(f15055,plain,
    ( spl303_710
  <=> ! [X2: secrecy_KS > secrecy_KS > $o,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_710])]) ).

thf(f6321,plain,
    ( spl303_340
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0))) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_340])]) ).

thf(f6331,plain,
    ( ! [X2: secrecy_KS > secrecy_KS > $o,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_159
    | ~ spl303_340 ),
    inference(superposition,[],[f4154,f6322]) ).

thf(f6322,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_340 ),
    inference(avatar_component_clause,[],[f6321]) ).

thf(f15053,plain,
    ( spl303_709
    | ~ spl303_160
    | ~ spl303_328 ),
    inference(avatar_split_clause,[],[f6219,f6155,f4157,f15051]) ).

thf(f15051,plain,
    ( spl303_709
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),nil_Se901661471ession) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_709])]) ).

thf(f6219,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),X0),nil_Se901661471ession) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) )
    | ~ spl303_160
    | ~ spl303_328 ),
    inference(superposition,[],[f4158,f6156]) ).

thf(f15049,plain,
    ( spl303_708
    | ~ spl303_159
    | ~ spl303_327 ),
    inference(avatar_split_clause,[],[f6204,f6151,f4153,f15047]) ).

thf(f15047,plain,
    ( spl303_708
  <=> ! [X2: secrecy_KS > secrecy_KS > $o,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X2),X0),nil_Secrecy_KS) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_708])]) ).

thf(f6151,plain,
    ( spl303_327
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)) = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_327])]) ).

thf(f6204,plain,
    ( ! [X2: secrecy_KS > secrecy_KS > $o,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X2),X0),nil_Secrecy_KS) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) )
    | ~ spl303_159
    | ~ spl303_327 ),
    inference(superposition,[],[f4154,f6152]) ).

thf(f6152,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)) = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) )
    | ~ spl303_327 ),
    inference(avatar_component_clause,[],[f6151]) ).

thf(f15045,plain,
    ( spl303_707
    | ~ spl303_69
    | ~ spl303_299 ),
    inference(avatar_split_clause,[],[f5812,f5783,f3482,f15043]) ).

thf(f15043,plain,
    ( spl303_707
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_707])]) ).

thf(f3482,plain,
    ( spl303_69
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_69])]) ).

thf(f5812,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_69
    | ~ spl303_299 ),
    inference(superposition,[],[f3483,f5784]) ).

thf(f3483,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X1 )
    | ~ spl303_69 ),
    inference(avatar_component_clause,[],[f3482]) ).

thf(f15041,plain,
    ( spl303_706
    | ~ spl303_68
    | ~ spl303_299 ),
    inference(avatar_split_clause,[],[f5811,f5783,f3478,f15039]) ).

thf(f15039,plain,
    ( spl303_706
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_706])]) ).

thf(f5811,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_68
    | ~ spl303_299 ),
    inference(superposition,[],[f3479,f5784]) ).

thf(f15037,plain,
    ( spl303_705
    | ~ spl303_26
    | ~ spl303_76
    | ~ spl303_88
    | ~ spl303_120
    | ~ spl303_187
    | ~ spl303_194 ),
    inference(avatar_split_clause,[],[f4733,f4674,f4521,f3747,f3565,f3510,f3282,f15035]) ).

thf(f15035,plain,
    ( spl303_705
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_705])]) ).

thf(f3510,plain,
    ( spl303_76
  <=> ! [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_76])]) ).

thf(f3747,plain,
    ( spl303_120
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_120])]) ).

thf(f4674,plain,
    ( spl303_194
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_194])]) ).

thf(f4733,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) ) )
    | ~ spl303_26
    | ~ spl303_76
    | ~ spl303_88
    | ~ spl303_120
    | ~ spl303_187
    | ~ spl303_194 ),
    inference(forward_demodulation,[],[f4732,f3511]) ).

thf(f3511,plain,
    ( ! [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X1 )
    | ~ spl303_76 ),
    inference(avatar_component_clause,[],[f3510]) ).

thf(f4732,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_120
    | ~ spl303_187
    | ~ spl303_194 ),
    inference(forward_demodulation,[],[f4731,f4576]) ).

thf(f4731,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_120
    | ~ spl303_187
    | ~ spl303_194 ),
    inference(forward_demodulation,[],[f4717,f4576]) ).

thf(f4717,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) )
    | ~ spl303_120
    | ~ spl303_194 ),
    inference(superposition,[],[f4675,f3748]) ).

thf(f3748,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_120 ),
    inference(avatar_component_clause,[],[f3747]) ).

thf(f4675,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) ) )
    | ~ spl303_194 ),
    inference(avatar_component_clause,[],[f4674]) ).

thf(f15031,plain,
    ( spl303_704
    | ~ spl303_34
    | ~ spl303_118 ),
    inference(avatar_split_clause,[],[f3891,f3739,f3314,f15029]) ).

thf(f15029,plain,
    ( spl303_704
  <=> ! [X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_704])]) ).

thf(f3314,plain,
    ( spl303_34
  <=> ! [X0: secrecy_specID] : ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_34])]) ).

thf(f3739,plain,
    ( spl303_118
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_118])]) ).

thf(f3891,plain,
    ( ! [X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
    | ~ spl303_34
    | ~ spl303_118 ),
    inference(trivial_inequality_removal,[],[f3880]) ).

thf(f3880,plain,
    ( ! [X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
    | ~ spl303_34
    | ~ spl303_118 ),
    inference(superposition,[],[f3740,f3315]) ).

thf(f3315,plain,
    ( ! [X0: secrecy_specID] : ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),nil_Se901661471ession) )
    | ~ spl303_34 ),
    inference(avatar_component_clause,[],[f3314]) ).

thf(f3740,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) ) )
    | ~ spl303_118 ),
    inference(avatar_component_clause,[],[f3739]) ).

thf(f15027,plain,
    ( spl303_703
    | ~ spl303_34
    | ~ spl303_117 ),
    inference(avatar_split_clause,[],[f3869,f3735,f3314,f15025]) ).

thf(f15025,plain,
    ( spl303_703
  <=> ! [X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_703])]) ).

thf(f3735,plain,
    ( spl303_117
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_117])]) ).

thf(f3869,plain,
    ( ! [X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
    | ~ spl303_34
    | ~ spl303_117 ),
    inference(trivial_inequality_removal,[],[f3858]) ).

thf(f3858,plain,
    ( ! [X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
    | ~ spl303_34
    | ~ spl303_117 ),
    inference(superposition,[],[f3736,f3315]) ).

thf(f3736,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) ) )
    | ~ spl303_117 ),
    inference(avatar_component_clause,[],[f3735]) ).

thf(f14963,plain,
    ( spl303_702
    | ~ spl303_88
    | ~ spl303_120
    | ~ spl303_174 ),
    inference(avatar_split_clause,[],[f4398,f4373,f3747,f3565,f14961]) ).

thf(f14961,plain,
    ( spl303_702
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_702])]) ).

thf(f4373,plain,
    ( spl303_174
  <=> ! [X2: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_174])]) ).

thf(f4398,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) )
    | ~ spl303_88
    | ~ spl303_120
    | ~ spl303_174 ),
    inference(forward_demodulation,[],[f4393,f3748]) ).

thf(f4393,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) )
    | ~ spl303_88
    | ~ spl303_174 ),
    inference(superposition,[],[f4374,f3566]) ).

thf(f4374,plain,
    ( ! [X2: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
    | ~ spl303_174 ),
    inference(avatar_component_clause,[],[f4373]) ).

thf(f14959,plain,
    ( spl303_701
    | ~ spl303_166
    | ~ spl303_172 ),
    inference(avatar_split_clause,[],[f4360,f4325,f4225,f14957]) ).

thf(f14957,plain,
    ( spl303_701
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_701])]) ).

thf(f4325,plain,
    ( spl303_172
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_172])]) ).

thf(f4360,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_166
    | ~ spl303_172 ),
    inference(superposition,[],[f4226,f4326]) ).

thf(f4326,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_172 ),
    inference(avatar_component_clause,[],[f4325]) ).

thf(f14954,plain,
    ( spl303_700
    | ~ spl303_111
    | ~ spl303_119 ),
    inference(avatar_split_clause,[],[f3898,f3743,f3706,f14952]) ).

thf(f14952,plain,
    ( spl303_700
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_700])]) ).

thf(f3706,plain,
    ( spl303_111
  <=> ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_111])]) ).

thf(f3743,plain,
    ( spl303_119
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_119])]) ).

thf(f3898,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)) )
    | ~ spl303_111
    | ~ spl303_119 ),
    inference(superposition,[],[f3707,f3744]) ).

thf(f3744,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_119 ),
    inference(avatar_component_clause,[],[f3743]) ).

thf(f3707,plain,
    ( ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)) )
    | ~ spl303_111 ),
    inference(avatar_component_clause,[],[f3706]) ).

thf(f14949,plain,
    ( spl303_699
    | ~ spl303_112
    | ~ spl303_119 ),
    inference(avatar_split_clause,[],[f3897,f3743,f3710,f14947]) ).

thf(f14947,plain,
    ( spl303_699
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_699])]) ).

thf(f3710,plain,
    ( spl303_112
  <=> ! [X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_112])]) ).

thf(f3897,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_112
    | ~ spl303_119 ),
    inference(superposition,[],[f3711,f3744]) ).

thf(f3711,plain,
    ( ! [X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) )
    | ~ spl303_112 ),
    inference(avatar_component_clause,[],[f3710]) ).

thf(f14598,plain,
    ( spl303_698
    | ~ spl303_562
    | ~ spl303_655 ),
    inference(avatar_split_clause,[],[f14337,f14146,f12350,f14596]) ).

thf(f14596,plain,
    ( spl303_698
  <=> ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,nil_Se901661471ession),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_698])]) ).

thf(f12350,plain,
    ( spl303_562
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = X1 )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_562])]) ).

thf(f14146,plain,
    ( spl303_655
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_655])]) ).

thf(f14337,plain,
    ( ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,nil_Se901661471ession),X1) )
    | ~ spl303_562
    | ~ spl303_655 ),
    inference(trivial_inequality_removal,[],[f14320]) ).

thf(f14320,plain,
    ( ! [X1: list_S529945141ession] :
        ( ( $true = $false )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,nil_Se901661471ession),X1) ) )
    | ~ spl303_562
    | ~ spl303_655 ),
    inference(superposition,[],[f14147,f12351]) ).

thf(f12351,plain,
    ( ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_562 ),
    inference(avatar_component_clause,[],[f12350]) ).

thf(f14147,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)),X0) )
    | ~ spl303_655 ),
    inference(avatar_component_clause,[],[f14146]) ).

thf(f14594,plain,
    ( spl303_695
    | spl303_696
    | ~ spl303_697
    | ~ spl303_264 ),
    inference(avatar_split_clause,[],[f5499,f5481,f14591,f14587,f14584]) ).

thf(f14584,plain,
    ( spl303_695
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_695])]) ).

thf(f14587,plain,
    ( spl303_696
  <=> ( vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,vEQ(list_S529945141ession)) = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,vEQ(list_S529945141ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_696])]) ).

thf(f14591,plain,
    ( spl303_697
  <=> ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,vEQ(list_S529945141ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_697])]) ).

thf(f5481,plain,
    ( spl303_264
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_264])]) ).

thf(f5499,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,vEQ(list_S529945141ession)) )
        | ( vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,vEQ(list_S529945141ession)) = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,vEQ(list_S529945141ession)) )
        | ( X0 = X1 ) )
    | ~ spl303_264 ),
    inference(equality_proxy_clausification,[],[f5498]) ).

thf(f5498,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,vEQ(list_S529945141ession)) )
        | ( vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,vEQ(list_S529945141ession)) = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,vEQ(list_S529945141ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_264 ),
    inference(equality_proxy_clausification,[],[f5497]) ).

thf(f5497,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,vEQ(list_S529945141ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,vEQ(list_S529945141ession))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,vEQ(list_S529945141ession))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_264 ),
    inference(equality_proxy_clausification,[],[f5492]) ).

thf(f5492,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,vEQ(list_S529945141ession))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,vEQ(list_S529945141ession))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,vEQ(list_S529945141ession))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_264 ),
    inference(primitive_instantiation,[],[f5482]) ).

thf(f5482,plain,
    ( ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) )
    | ~ spl303_264 ),
    inference(avatar_component_clause,[],[f5481]) ).

thf(f14582,plain,
    ( spl303_692
    | spl303_693
    | ~ spl303_694
    | ~ spl303_263 ),
    inference(avatar_split_clause,[],[f5491,f5477,f14579,f14575,f14572]) ).

thf(f14572,plain,
    ( spl303_692
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_692])]) ).

thf(f14575,plain,
    ( spl303_693
  <=> ( vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,vEQ(list_Secrecy_KS)) = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,vEQ(list_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_693])]) ).

thf(f14579,plain,
    ( spl303_694
  <=> ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,vEQ(list_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_694])]) ).

thf(f5477,plain,
    ( spl303_263
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_263])]) ).

thf(f5491,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,vEQ(list_Secrecy_KS)) )
        | ( vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,vEQ(list_Secrecy_KS)) = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,vEQ(list_Secrecy_KS)) )
        | ( X0 = X1 ) )
    | ~ spl303_263 ),
    inference(equality_proxy_clausification,[],[f5490]) ).

thf(f5490,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,vEQ(list_Secrecy_KS)) )
        | ( vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,vEQ(list_Secrecy_KS)) = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,vEQ(list_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_263 ),
    inference(equality_proxy_clausification,[],[f5489]) ).

thf(f5489,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,vEQ(list_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,vEQ(list_Secrecy_KS))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,vEQ(list_Secrecy_KS))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_263 ),
    inference(equality_proxy_clausification,[],[f5484]) ).

thf(f5484,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,vEQ(list_Secrecy_KS))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,vEQ(list_Secrecy_KS))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,vEQ(list_Secrecy_KS))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_263 ),
    inference(primitive_instantiation,[],[f5478]) ).

thf(f5478,plain,
    ( ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) )
    | ~ spl303_263 ),
    inference(avatar_component_clause,[],[f5477]) ).

thf(f14570,plain,
    ( spl303_691
    | ~ spl303_99
    | ~ spl303_176 ),
    inference(avatar_split_clause,[],[f4416,f4381,f3617,f14568]) ).

thf(f14568,plain,
    ( spl303_691
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_691])]) ).

thf(f4416,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) )
    | ~ spl303_99
    | ~ spl303_176 ),
    inference(superposition,[],[f3618,f4382]) ).

thf(f14566,plain,
    ( spl303_690
    | ~ spl303_96
    | ~ spl303_175 ),
    inference(avatar_split_clause,[],[f4407,f4377,f3605,f14564]) ).

thf(f14564,plain,
    ( spl303_690
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_690])]) ).

thf(f4377,plain,
    ( spl303_175
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_175])]) ).

thf(f4407,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) )
    | ~ spl303_96
    | ~ spl303_175 ),
    inference(superposition,[],[f3606,f4378]) ).

thf(f4378,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_175 ),
    inference(avatar_component_clause,[],[f4377]) ).

thf(f14562,plain,
    ( spl303_689
    | ~ spl303_161
    | ~ spl303_172 ),
    inference(avatar_split_clause,[],[f4358,f4325,f4161,f14560]) ).

thf(f14560,plain,
    ( spl303_689
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_689])]) ).

thf(f4358,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_161
    | ~ spl303_172 ),
    inference(superposition,[],[f4162,f4326]) ).

thf(f14558,plain,
    ( spl303_688
    | ~ spl303_3
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4266,f4225,f3143,f14556]) ).

thf(f14556,plain,
    ( spl303_688
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_688])]) ).

thf(f4266,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) )
    | ~ spl303_3
    | ~ spl303_166 ),
    inference(trivial_inequality_removal,[],[f4265]) ).

thf(f4265,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) )
    | ~ spl303_3
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f3144]) ).

thf(f14554,plain,
    ( spl303_687
    | ~ spl303_145
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4261,f4225,f3967,f14552]) ).

thf(f14552,plain,
    ( spl303_687
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_687])]) ).

thf(f4261,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)) ) )
    | ~ spl303_145
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f3968]) ).

thf(f14550,plain,
    ( spl303_686
    | ~ spl303_562
    | ~ spl303_654 ),
    inference(avatar_split_clause,[],[f14317,f14142,f12350,f14548]) ).

thf(f14548,plain,
    ( spl303_686
  <=> ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_686])]) ).

thf(f14142,plain,
    ( spl303_654
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_654])]) ).

thf(f14317,plain,
    ( ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),nil_Se901661471ession) )
    | ~ spl303_562
    | ~ spl303_654 ),
    inference(trivial_inequality_removal,[],[f14300]) ).

thf(f14300,plain,
    ( ! [X1: list_S529945141ession] :
        ( ( $true = $false )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),nil_Se901661471ession) ) )
    | ~ spl303_562
    | ~ spl303_654 ),
    inference(superposition,[],[f14143,f12351]) ).

thf(f14143,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)),X1) )
    | ~ spl303_654 ),
    inference(avatar_component_clause,[],[f14142]) ).

thf(f14546,plain,
    ( spl303_685
    | ~ spl303_144
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4260,f4225,f3963,f14544]) ).

thf(f14544,plain,
    ( spl303_685
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_685])]) ).

thf(f4260,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)) ) )
    | ~ spl303_144
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f3964]) ).

thf(f14542,plain,
    ( spl303_684
    | ~ spl303_143
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4259,f4225,f3959,f14540]) ).

thf(f14540,plain,
    ( spl303_684
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_684])]) ).

thf(f4259,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) ) )
    | ~ spl303_143
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f3960]) ).

thf(f14538,plain,
    ( spl303_683
    | ~ spl303_142
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4258,f4225,f3955,f14536]) ).

thf(f14536,plain,
    ( spl303_683
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_683])]) ).

thf(f4258,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) ) )
    | ~ spl303_142
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f3956]) ).

thf(f14534,plain,
    ( spl303_682
    | ~ spl303_3
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4252,f4221,f3143,f14532]) ).

thf(f14532,plain,
    ( spl303_682
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_682])]) ).

thf(f4252,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) )
    | ~ spl303_3
    | ~ spl303_165 ),
    inference(trivial_inequality_removal,[],[f4251]) ).

thf(f4251,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) )
    | ~ spl303_3
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f3144]) ).

thf(f14530,plain,
    ( spl303_681
    | ~ spl303_145
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4247,f4221,f3967,f14528]) ).

thf(f14528,plain,
    ( spl303_681
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_681])]) ).

thf(f4247,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) ) )
    | ~ spl303_145
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f3968]) ).

thf(f14526,plain,
    ( spl303_680
    | ~ spl303_144
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4246,f4221,f3963,f14524]) ).

thf(f14524,plain,
    ( spl303_680
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_680])]) ).

thf(f4246,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) ) )
    | ~ spl303_144
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f3964]) ).

thf(f14522,plain,
    ( spl303_679
    | ~ spl303_143
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4245,f4221,f3959,f14520]) ).

thf(f14520,plain,
    ( spl303_679
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_679])]) ).

thf(f4245,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1)) ) )
    | ~ spl303_143
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f3960]) ).

thf(f14518,plain,
    ( spl303_678
    | ~ spl303_142
    | ~ spl303_165 ),
    inference(avatar_split_clause,[],[f4244,f4221,f3955,f14516]) ).

thf(f14516,plain,
    ( spl303_678
  <=> ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_678])]) ).

thf(f4244,plain,
    ( ! [X2: secrecy_specID,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1)) ) )
    | ~ spl303_142
    | ~ spl303_165 ),
    inference(superposition,[],[f4222,f3956]) ).

thf(f14514,plain,
    ( spl303_677
    | ~ spl303_3
    | ~ spl303_164 ),
    inference(avatar_split_clause,[],[f4237,f4217,f3143,f14512]) ).

thf(f14512,plain,
    ( spl303_677
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_677])]) ).

thf(f4217,plain,
    ( spl303_164
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_164])]) ).

thf(f4237,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) )
    | ~ spl303_3
    | ~ spl303_164 ),
    inference(trivial_inequality_removal,[],[f4236]) ).

thf(f4236,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) )
    | ~ spl303_3
    | ~ spl303_164 ),
    inference(superposition,[],[f4218,f3144]) ).

thf(f4218,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) ) )
    | ~ spl303_164 ),
    inference(avatar_component_clause,[],[f4217]) ).

thf(f14510,plain,
    ( spl303_676
    | ~ spl303_88
    | ~ spl303_164 ),
    inference(avatar_split_clause,[],[f4232,f4217,f3565,f14508]) ).

thf(f14508,plain,
    ( spl303_676
  <=> ! [X0: secrecy_Expression,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_676])]) ).

thf(f4232,plain,
    ( ! [X0: secrecy_Expression,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),nil_Se901661471ession) ) )
    | ~ spl303_88
    | ~ spl303_164 ),
    inference(superposition,[],[f4218,f3566]) ).

thf(f14506,plain,
    ( spl303_675
    | ~ spl303_562
    | ~ spl303_653 ),
    inference(avatar_split_clause,[],[f14297,f14138,f12350,f14504]) ).

thf(f14504,plain,
    ( spl303_675
  <=> ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,nil_Se901661471ession),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_675])]) ).

thf(f14138,plain,
    ( spl303_653
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_653])]) ).

thf(f14297,plain,
    ( ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,nil_Se901661471ession),X1) )
    | ~ spl303_562
    | ~ spl303_653 ),
    inference(trivial_inequality_removal,[],[f14280]) ).

thf(f14280,plain,
    ( ! [X1: list_S529945141ession] :
        ( ( $true = $false )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,nil_Se901661471ession),X1) ) )
    | ~ spl303_562
    | ~ spl303_653 ),
    inference(superposition,[],[f14139,f12351]) ).

thf(f14139,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)),X0) )
    | ~ spl303_653 ),
    inference(avatar_component_clause,[],[f14138]) ).

thf(f14502,plain,
    ( spl303_674
    | ~ spl303_3
    | ~ spl303_163 ),
    inference(avatar_split_clause,[],[f4231,f4213,f3143,f14500]) ).

thf(f14500,plain,
    ( spl303_674
  <=> ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 )
        | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_674])]) ).

thf(f4213,plain,
    ( spl303_163
  <=> ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 )
        | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_163])]) ).

thf(f4231,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 )
        | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_163 ),
    inference(trivial_inequality_removal,[],[f4230]) ).

thf(f4230,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true != $true )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 )
        | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_163 ),
    inference(superposition,[],[f4214,f3144]) ).

thf(f4214,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 ) )
    | ~ spl303_163 ),
    inference(avatar_component_clause,[],[f4213]) ).

thf(f14498,plain,
    ( spl303_673
    | ~ spl303_3
    | ~ spl303_162 ),
    inference(avatar_split_clause,[],[f4229,f4209,f3143,f14496]) ).

thf(f14496,plain,
    ( spl303_673
  <=> ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 )
        | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_673])]) ).

thf(f4209,plain,
    ( spl303_162
  <=> ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 )
        | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_162])]) ).

thf(f4229,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 )
        | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_162 ),
    inference(trivial_inequality_removal,[],[f4228]) ).

thf(f4228,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true != $true )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 )
        | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_162 ),
    inference(superposition,[],[f4210,f3144]) ).

thf(f4210,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 ) )
    | ~ spl303_162 ),
    inference(avatar_component_clause,[],[f4209]) ).

thf(f14494,plain,
    ( spl303_672
    | ~ spl303_99
    | ~ spl303_158 ),
    inference(avatar_split_clause,[],[f4179,f4149,f3617,f14492]) ).

thf(f14492,plain,
    ( spl303_672
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_672])]) ).

thf(f4179,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) )
    | ~ spl303_99
    | ~ spl303_158 ),
    inference(superposition,[],[f3618,f4150]) ).

thf(f14490,plain,
    ( spl303_671
    | ~ spl303_100
    | ~ spl303_158 ),
    inference(avatar_split_clause,[],[f4178,f4149,f3621,f14488]) ).

thf(f14488,plain,
    ( spl303_671
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_671])]) ).

thf(f4178,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1) ) )
    | ~ spl303_100
    | ~ spl303_158 ),
    inference(superposition,[],[f3622,f4150]) ).

thf(f14486,plain,
    ( spl303_670
    | ~ spl303_99
    | ~ spl303_157 ),
    inference(avatar_split_clause,[],[f4171,f4145,f3617,f14484]) ).

thf(f14484,plain,
    ( spl303_670
  <=> ! [X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_670])]) ).

thf(f4171,plain,
    ( ! [X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) )
    | ~ spl303_99
    | ~ spl303_157 ),
    inference(superposition,[],[f3618,f4146]) ).

thf(f14482,plain,
    ( spl303_669
    | ~ spl303_100
    | ~ spl303_157 ),
    inference(avatar_split_clause,[],[f4170,f4145,f3621,f14480]) ).

thf(f14480,plain,
    ( spl303_669
  <=> ! [X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_669])]) ).

thf(f4170,plain,
    ( ! [X0: list_l425507653ession,X1: list_l425507653ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1))) )
        | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1) ) )
    | ~ spl303_100
    | ~ spl303_157 ),
    inference(superposition,[],[f3622,f4146]) ).

thf(f14432,plain,
    ( spl303_668
    | ~ spl303_562
    | ~ spl303_652 ),
    inference(avatar_split_clause,[],[f14277,f14134,f12350,f14430]) ).

thf(f14430,plain,
    ( spl303_668
  <=> ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_668])]) ).

thf(f14134,plain,
    ( spl303_652
  <=> ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_652])]) ).

thf(f14277,plain,
    ( ! [X1: list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),nil_Se901661471ession) )
    | ~ spl303_562
    | ~ spl303_652 ),
    inference(trivial_inequality_removal,[],[f14260]) ).

thf(f14260,plain,
    ( ! [X1: list_S529945141ession] :
        ( ( $true = $false )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),nil_Se901661471ession) ) )
    | ~ spl303_562
    | ~ spl303_652 ),
    inference(superposition,[],[f14135,f12351]) ).

thf(f14135,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)),X1) )
    | ~ spl303_652 ),
    inference(avatar_component_clause,[],[f14134]) ).

thf(f14259,plain,
    ( spl303_667
    | ~ spl303_143
    | ~ spl303_473 ),
    inference(avatar_split_clause,[],[f11095,f7576,f3959,f14257]) ).

thf(f14257,plain,
    ( spl303_667
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_667])]) ).

thf(f11095,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) )
    | ~ spl303_143
    | ~ spl303_473 ),
    inference(superposition,[],[f7577,f3960]) ).

thf(f14192,plain,
    ( spl303_666
    | ~ spl303_126
    | ~ spl303_229 ),
    inference(avatar_split_clause,[],[f5256,f5179,f3781,f14190]) ).

thf(f14190,plain,
    ( spl303_666
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,sK34,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_666])]) ).

thf(f5256,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,sK34,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_126
    | ~ spl303_229 ),
    inference(superposition,[],[f3782,f5180]) ).

thf(f14188,plain,
    ( spl303_665
    | ~ spl303_122
    | ~ spl303_228 ),
    inference(avatar_split_clause,[],[f5247,f5170,f3757,f14186]) ).

thf(f14186,plain,
    ( spl303_665
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_665])]) ).

thf(f5170,plain,
    ( spl303_228
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK27,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK28,X0))) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_228])]) ).

thf(f5247,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_122
    | ~ spl303_228 ),
    inference(superposition,[],[f3758,f5171]) ).

thf(f5171,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK27,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK28,X0))) = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_228 ),
    inference(avatar_component_clause,[],[f5170]) ).

thf(f14184,plain,
    ( spl303_664
    | ~ spl303_69
    | ~ spl303_227 ),
    inference(avatar_split_clause,[],[f5224,f5166,f3482,f14182]) ).

thf(f14182,plain,
    ( spl303_664
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_664])]) ).

thf(f5224,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_69
    | ~ spl303_227 ),
    inference(superposition,[],[f3483,f5167]) ).

thf(f14180,plain,
    ( spl303_663
    | ~ spl303_128
    | ~ spl303_218 ),
    inference(avatar_split_clause,[],[f5088,f5005,f3794,f14178]) ).

thf(f14178,plain,
    ( spl303_663
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_663])]) ).

thf(f5005,plain,
    ( spl303_218
  <=> ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_218])]) ).

thf(f5088,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_128
    | ~ spl303_218 ),
    inference(superposition,[],[f3795,f5006]) ).

thf(f5006,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_218 ),
    inference(avatar_component_clause,[],[f5005]) ).

thf(f14176,plain,
    ( spl303_662
    | ~ spl303_128
    | ~ spl303_217 ),
    inference(avatar_split_clause,[],[f5061,f5001,f3794,f14174]) ).

thf(f14174,plain,
    ( spl303_662
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_662])]) ).

thf(f5001,plain,
    ( spl303_217
  <=> ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_217])]) ).

thf(f5061,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_128
    | ~ spl303_217 ),
    inference(superposition,[],[f3795,f5002]) ).

thf(f5002,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_217 ),
    inference(avatar_component_clause,[],[f5001]) ).

thf(f14172,plain,
    ( spl303_661
    | ~ spl303_124
    | ~ spl303_216 ),
    inference(avatar_split_clause,[],[f5041,f4997,f3769,f14170]) ).

thf(f14170,plain,
    ( spl303_661
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_661])]) ).

thf(f4997,plain,
    ( spl303_216
  <=> ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) = X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_216])]) ).

thf(f5041,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_124
    | ~ spl303_216 ),
    inference(superposition,[],[f3770,f4998]) ).

thf(f4998,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_216 ),
    inference(avatar_component_clause,[],[f4997]) ).

thf(f14168,plain,
    ( spl303_660
    | ~ spl303_142
    | ~ spl303_473 ),
    inference(avatar_split_clause,[],[f11094,f7576,f3955,f14166]) ).

thf(f14166,plain,
    ( spl303_660
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_660])]) ).

thf(f11094,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) )
    | ~ spl303_142
    | ~ spl303_473 ),
    inference(superposition,[],[f7577,f3956]) ).

thf(f14164,plain,
    ( spl303_659
    | ~ spl303_124
    | ~ spl303_215 ),
    inference(avatar_split_clause,[],[f5027,f4992,f3769,f14162]) ).

thf(f14162,plain,
    ( spl303_659
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_659])]) ).

thf(f4992,plain,
    ( spl303_215
  <=> ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_215])]) ).

thf(f5027,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_124
    | ~ spl303_215 ),
    inference(superposition,[],[f3770,f4993]) ).

thf(f4993,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_215 ),
    inference(avatar_component_clause,[],[f4992]) ).

thf(f14160,plain,
    ( spl303_658
    | ~ spl303_37
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4656,f4646,f3326,f14158]) ).

thf(f14158,plain,
    ( spl303_658
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_658])]) ).

thf(f4656,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) )
    | ~ spl303_37
    | ~ spl303_192 ),
    inference(superposition,[],[f3327,f4647]) ).

thf(f14156,plain,
    ( spl303_657
    | ~ spl303_168
    | ~ spl303_176 ),
    inference(avatar_split_clause,[],[f4414,f4381,f4272,f14154]) ).

thf(f14154,plain,
    ( spl303_657
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_657])]) ).

thf(f4414,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0))) )
    | ~ spl303_168
    | ~ spl303_176 ),
    inference(superposition,[],[f4382,f4273]) ).

thf(f14152,plain,
    ( spl303_656
    | ~ spl303_167
    | ~ spl303_175 ),
    inference(avatar_split_clause,[],[f4404,f4377,f4268,f14150]) ).

thf(f14150,plain,
    ( spl303_656
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_656])]) ).

thf(f4404,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0))) )
    | ~ spl303_167
    | ~ spl303_175 ),
    inference(superposition,[],[f4378,f4269]) ).

thf(f14148,plain,
    ( spl303_655
    | ~ spl303_145
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4204,f4161,f3967,f14146]) ).

thf(f4204,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)),X0) )
    | ~ spl303_145
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f3968]) ).

thf(f14144,plain,
    ( spl303_654
    | ~ spl303_144
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4203,f4161,f3963,f14142]) ).

thf(f4203,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)),X1) )
    | ~ spl303_144
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f3964]) ).

thf(f14140,plain,
    ( spl303_653
    | ~ spl303_143
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4202,f4161,f3959,f14138]) ).

thf(f4202,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)),X0) )
    | ~ spl303_143
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f3960]) ).

thf(f14136,plain,
    ( spl303_652
    | ~ spl303_142
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4201,f4161,f3955,f14134]) ).

thf(f4201,plain,
    ( ! [X2: secrecy_Expression > secrecy_Expression > $o,X0: list_S529945141ession,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)),X1) )
    | ~ spl303_142
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f3956]) ).

thf(f14132,plain,
    ( spl303_651
    | ~ spl303_3
    | ~ spl303_160 ),
    inference(avatar_split_clause,[],[f4195,f4157,f3143,f14130]) ).

thf(f14130,plain,
    ( spl303_651
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_651])]) ).

thf(f4195,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) )
    | ~ spl303_3
    | ~ spl303_160 ),
    inference(trivial_inequality_removal,[],[f4194]) ).

thf(f4194,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] :
        ( ( $true != $true )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_160 ),
    inference(superposition,[],[f4158,f3144]) ).

thf(f14128,plain,
    ( spl303_650
    | ~ spl303_88
    | ~ spl303_160 ),
    inference(avatar_split_clause,[],[f4190,f4157,f3565,f14126]) ).

thf(f14126,plain,
    ( spl303_650
  <=> ! [X0: secrecy_Expression,X1: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_650])]) ).

thf(f4190,plain,
    ( ! [X0: secrecy_Expression,X1: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),nil_Se901661471ession) )
    | ~ spl303_88
    | ~ spl303_160 ),
    inference(superposition,[],[f4158,f3566]) ).

thf(f14117,plain,
    ( spl303_649
    | ~ spl303_3
    | ~ spl303_159 ),
    inference(avatar_split_clause,[],[f4187,f4153,f3143,f14115]) ).

thf(f14115,plain,
    ( spl303_649
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_649])]) ).

thf(f4187,plain,
    ( ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) )
    | ~ spl303_3
    | ~ spl303_159 ),
    inference(trivial_inequality_removal,[],[f4186]) ).

thf(f4186,plain,
    ( ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] :
        ( ( $true != $true )
        | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_159 ),
    inference(superposition,[],[f4154,f3144]) ).

thf(f14113,plain,
    ( spl303_648
    | ~ spl303_87
    | ~ spl303_159 ),
    inference(avatar_split_clause,[],[f4182,f4153,f3561,f14111]) ).

thf(f14111,plain,
    ( spl303_648
  <=> ! [X0: secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_648])]) ).

thf(f3561,plain,
    ( spl303_87
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_87])]) ).

thf(f4182,plain,
    ( ! [X0: secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)),nil_Secrecy_KS) )
    | ~ spl303_87
    | ~ spl303_159 ),
    inference(superposition,[],[f4154,f3562]) ).

thf(f3562,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_87 ),
    inference(avatar_component_clause,[],[f3561]) ).

thf(f13807,plain,
    ( spl303_647
    | ~ spl303_26
    | ~ spl303_539 ),
    inference(avatar_split_clause,[],[f11227,f11119,f3282,f13805]) ).

thf(f13805,plain,
    ( spl303_647
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X1) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_647])]) ).

thf(f11119,plain,
    ( spl303_539
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_539])]) ).

thf(f11227,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X1) != X0 )
        | ( X0 = X1 ) )
    | ~ spl303_26
    | ~ spl303_539 ),
    inference(superposition,[],[f11120,f3283]) ).

thf(f11120,plain,
    ( ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
        | ( X1 = X2 ) )
    | ~ spl303_539 ),
    inference(avatar_component_clause,[],[f11119]) ).

thf(f13775,plain,
    ( spl303_646
    | ~ spl303_37
    | ~ spl303_299 ),
    inference(avatar_split_clause,[],[f5810,f5783,f3326,f13773]) ).

thf(f5810,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0) != X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_37
    | ~ spl303_299 ),
    inference(superposition,[],[f3327,f5784]) ).

thf(f13771,plain,
    ( spl303_645
    | ~ spl303_100
    | ~ spl303_188 ),
    inference(avatar_split_clause,[],[f4603,f4525,f3621,f13769]) ).

thf(f13769,plain,
    ( spl303_645
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2))) )
        | ( nil_Se901661471ession = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_645])]) ).

thf(f4603,plain,
    ( ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2))) )
        | ( nil_Se901661471ession = X2 ) )
    | ~ spl303_100
    | ~ spl303_188 ),
    inference(superposition,[],[f3622,f4526]) ).

thf(f13767,plain,
    ( spl303_644
    | ~ spl303_100
    | ~ spl303_187 ),
    inference(avatar_split_clause,[],[f4567,f4521,f3621,f13765]) ).

thf(f13765,plain,
    ( spl303_644
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2))) )
        | ( nil_Se901661471ession = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_644])]) ).

thf(f4567,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X2) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2))) )
        | ( nil_Se901661471ession = X2 ) )
    | ~ spl303_100
    | ~ spl303_187 ),
    inference(superposition,[],[f3622,f4522]) ).

thf(f13763,plain,
    ( spl303_643
    | ~ spl303_76
    | ~ spl303_100
    | ~ spl303_176 ),
    inference(avatar_split_clause,[],[f4427,f4381,f3621,f3510,f13761]) ).

thf(f13761,plain,
    ( spl303_643
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_643])]) ).

thf(f4427,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession) ) )
    | ~ spl303_76
    | ~ spl303_100
    | ~ spl303_176 ),
    inference(forward_demodulation,[],[f4417,f3511]) ).

thf(f4417,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession) ) )
    | ~ spl303_100
    | ~ spl303_176 ),
    inference(superposition,[],[f3622,f4382]) ).

thf(f13759,plain,
    ( spl303_642
    | ~ spl303_73
    | ~ spl303_97
    | ~ spl303_175 ),
    inference(avatar_split_clause,[],[f4412,f4377,f3609,f3498,f13757]) ).

thf(f13757,plain,
    ( spl303_642
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_642])]) ).

thf(f3498,plain,
    ( spl303_73
  <=> ! [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_73])]) ).

thf(f4412,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS) ) )
    | ~ spl303_73
    | ~ spl303_97
    | ~ spl303_175 ),
    inference(forward_demodulation,[],[f4406,f3499]) ).

thf(f3499,plain,
    ( ! [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X1 )
    | ~ spl303_73 ),
    inference(avatar_component_clause,[],[f3498]) ).

thf(f4406,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS) ) )
    | ~ spl303_97
    | ~ spl303_175 ),
    inference(superposition,[],[f3610,f4378]) ).

thf(f13755,plain,
    ( spl303_641
    | ~ spl303_99
    | ~ spl303_145 ),
    inference(avatar_split_clause,[],[f3994,f3967,f3617,f13753]) ).

thf(f13753,plain,
    ( spl303_641
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_641])]) ).

thf(f3994,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X0),X1) ) )
    | ~ spl303_99
    | ~ spl303_145 ),
    inference(superposition,[],[f3618,f3968]) ).

thf(f13751,plain,
    ( spl303_640
    | ~ spl303_100
    | ~ spl303_145 ),
    inference(avatar_split_clause,[],[f3993,f3967,f3621,f13749]) ).

thf(f13749,plain,
    ( spl303_640
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_640])]) ).

thf(f3993,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) )
    | ~ spl303_100
    | ~ spl303_145 ),
    inference(superposition,[],[f3622,f3968]) ).

thf(f13747,plain,
    ( spl303_639
    | ~ spl303_29
    | ~ spl303_537 ),
    inference(avatar_split_clause,[],[f11187,f11111,f3294,f13745]) ).

thf(f13745,plain,
    ( spl303_639
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),nil_Se901661471ession) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_639])]) ).

thf(f3294,plain,
    ( spl303_29
  <=> ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),nil_Se901661471ession) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_29])]) ).

thf(f11111,plain,
    ( spl303_537
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
        | ( X0 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_537])]) ).

thf(f11187,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),nil_Se901661471ession) != X0 )
        | ( X0 = X1 ) )
    | ~ spl303_29
    | ~ spl303_537 ),
    inference(superposition,[],[f11112,f3295]) ).

thf(f3295,plain,
    ( ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),nil_Se901661471ession) = X0 )
    | ~ spl303_29 ),
    inference(avatar_component_clause,[],[f3294]) ).

thf(f11112,plain,
    ( ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
        | ( X0 = X2 ) )
    | ~ spl303_537 ),
    inference(avatar_component_clause,[],[f11111]) ).

thf(f13743,plain,
    ( spl303_638
    | ~ spl303_99
    | ~ spl303_144 ),
    inference(avatar_split_clause,[],[f3990,f3963,f3617,f13741]) ).

thf(f13741,plain,
    ( spl303_638
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_638])]) ).

thf(f3990,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X0),X1) ) )
    | ~ spl303_99
    | ~ spl303_144 ),
    inference(superposition,[],[f3618,f3964]) ).

thf(f13739,plain,
    ( spl303_637
    | ~ spl303_100
    | ~ spl303_144 ),
    inference(avatar_split_clause,[],[f3989,f3963,f3621,f13737]) ).

thf(f13737,plain,
    ( spl303_637
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_637])]) ).

thf(f3989,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X0),X1) ) )
    | ~ spl303_100
    | ~ spl303_144 ),
    inference(superposition,[],[f3622,f3964]) ).

thf(f13735,plain,
    ( spl303_636
    | ~ spl303_99
    | ~ spl303_143 ),
    inference(avatar_split_clause,[],[f3985,f3959,f3617,f13733]) ).

thf(f13733,plain,
    ( spl303_636
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_636])]) ).

thf(f3985,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) )
    | ~ spl303_99
    | ~ spl303_143 ),
    inference(superposition,[],[f3618,f3960]) ).

thf(f13731,plain,
    ( spl303_635
    | ~ spl303_100
    | ~ spl303_143 ),
    inference(avatar_split_clause,[],[f3984,f3959,f3621,f13729]) ).

thf(f13729,plain,
    ( spl303_635
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_635])]) ).

thf(f3984,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X0),X1) ) )
    | ~ spl303_100
    | ~ spl303_143 ),
    inference(superposition,[],[f3622,f3960]) ).

thf(f13727,plain,
    ( spl303_634
    | ~ spl303_99
    | ~ spl303_142 ),
    inference(avatar_split_clause,[],[f3981,f3955,f3617,f13725]) ).

thf(f13725,plain,
    ( spl303_634
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_634])]) ).

thf(f3981,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X0),X1) ) )
    | ~ spl303_99
    | ~ spl303_142 ),
    inference(superposition,[],[f3618,f3956]) ).

thf(f13723,plain,
    ( spl303_633
    | ~ spl303_100
    | ~ spl303_142 ),
    inference(avatar_split_clause,[],[f3980,f3955,f3621,f13721]) ).

thf(f13721,plain,
    ( spl303_633
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_633])]) ).

thf(f3980,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X0),X1) ) )
    | ~ spl303_100
    | ~ spl303_142 ),
    inference(superposition,[],[f3622,f3956]) ).

thf(f13719,plain,
    ( spl303_632
    | ~ spl303_96
    | ~ spl303_141 ),
    inference(avatar_split_clause,[],[f3977,f3950,f3605,f13717]) ).

thf(f13717,plain,
    ( spl303_632
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_632])]) ).

thf(f3977,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X0),X1) ) )
    | ~ spl303_96
    | ~ spl303_141 ),
    inference(superposition,[],[f3606,f3951]) ).

thf(f13715,plain,
    ( spl303_631
    | ~ spl303_97
    | ~ spl303_141 ),
    inference(avatar_split_clause,[],[f3976,f3950,f3609,f13713]) ).

thf(f13713,plain,
    ( spl303_631
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_631])]) ).

thf(f3976,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1) ) )
    | ~ spl303_97
    | ~ spl303_141 ),
    inference(superposition,[],[f3610,f3951]) ).

thf(f13711,plain,
    ( spl303_630
    | ~ spl303_96
    | ~ spl303_140 ),
    inference(avatar_split_clause,[],[f3975,f3946,f3605,f13709]) ).

thf(f13709,plain,
    ( spl303_630
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_630])]) ).

thf(f3975,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X0),X1) ) )
    | ~ spl303_96
    | ~ spl303_140 ),
    inference(superposition,[],[f3606,f3947]) ).

thf(f13707,plain,
    ( spl303_629
    | ~ spl303_97
    | ~ spl303_140 ),
    inference(avatar_split_clause,[],[f3974,f3946,f3609,f13705]) ).

thf(f13705,plain,
    ( spl303_629
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_629])]) ).

thf(f3974,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X0),X1) ) )
    | ~ spl303_97
    | ~ spl303_140 ),
    inference(superposition,[],[f3610,f3947]) ).

thf(f13698,plain,
    ( spl303_628
    | ~ spl303_96
    | ~ spl303_139 ),
    inference(avatar_split_clause,[],[f3973,f3942,f3605,f13696]) ).

thf(f13696,plain,
    ( spl303_628
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_628])]) ).

thf(f3973,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) )
    | ~ spl303_96
    | ~ spl303_139 ),
    inference(superposition,[],[f3606,f3943]) ).

thf(f13694,plain,
    ( spl303_627
    | ~ spl303_97
    | ~ spl303_139 ),
    inference(avatar_split_clause,[],[f3972,f3942,f3609,f13692]) ).

thf(f13692,plain,
    ( spl303_627
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_627])]) ).

thf(f3972,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X0),X1) ) )
    | ~ spl303_97
    | ~ spl303_139 ),
    inference(superposition,[],[f3610,f3943]) ).

thf(f13690,plain,
    ( spl303_626
    | ~ spl303_96
    | ~ spl303_138 ),
    inference(avatar_split_clause,[],[f3971,f3938,f3605,f13688]) ).

thf(f13688,plain,
    ( spl303_626
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_626])]) ).

thf(f3971,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X0),X1) ) )
    | ~ spl303_96
    | ~ spl303_138 ),
    inference(superposition,[],[f3606,f3939]) ).

thf(f13686,plain,
    ( spl303_625
    | ~ spl303_97
    | ~ spl303_138 ),
    inference(avatar_split_clause,[],[f3970,f3938,f3609,f13684]) ).

thf(f13684,plain,
    ( spl303_625
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_625])]) ).

thf(f3970,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X0),X1)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X0),X1) ) )
    | ~ spl303_97
    | ~ spl303_138 ),
    inference(superposition,[],[f3610,f3939]) ).

thf(f13629,plain,
    ( spl303_624
    | ~ spl303_476
    | ~ spl303_616 ),
    inference(avatar_split_clause,[],[f13551,f13249,f7588,f13627]) ).

thf(f13627,plain,
    ( spl303_624
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_624])]) ).

thf(f7588,plain,
    ( spl303_476
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_476])]) ).

thf(f13249,plain,
    ( spl303_616
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_616])]) ).

thf(f13551,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_476
    | ~ spl303_616 ),
    inference(superposition,[],[f7589,f13250]) ).

thf(f13250,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_616 ),
    inference(avatar_component_clause,[],[f13249]) ).

thf(f7589,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
    | ~ spl303_476 ),
    inference(avatar_component_clause,[],[f7588]) ).

thf(f13625,plain,
    ( spl303_623
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_187 ),
    inference(avatar_split_clause,[],[f4576,f4521,f3565,f3282,f13623]) ).

thf(f13623,plain,
    ( spl303_623
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_623])]) ).

thf(f13621,plain,
    ( spl303_622
    | ~ spl303_28
    | ~ spl303_88
    | ~ spl303_186 ),
    inference(avatar_split_clause,[],[f4556,f4517,f3565,f3290,f13619]) ).

thf(f13619,plain,
    ( spl303_622
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_622])]) ).

thf(f3290,plain,
    ( spl303_28
  <=> ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),nil_Se901661471ession) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_28])]) ).

thf(f4556,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1) )
    | ~ spl303_28
    | ~ spl303_88
    | ~ spl303_186 ),
    inference(forward_demodulation,[],[f4550,f3291]) ).

thf(f3291,plain,
    ( ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),nil_Se901661471ession) = X0 )
    | ~ spl303_28 ),
    inference(avatar_component_clause,[],[f3290]) ).

thf(f4550,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)),X1) )
    | ~ spl303_88
    | ~ spl303_186 ),
    inference(superposition,[],[f4518,f3566]) ).

thf(f13617,plain,
    ( spl303_621
    | ~ spl303_156
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4263,f4225,f4037,f13615]) ).

thf(f13615,plain,
    ( spl303_621
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_621])]) ).

thf(f4263,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_156
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f4038]) ).

thf(f13613,plain,
    ( spl303_620
    | ~ spl303_155
    | ~ spl303_166 ),
    inference(avatar_split_clause,[],[f4262,f4225,f4033,f13611]) ).

thf(f13611,plain,
    ( spl303_620
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_620])]) ).

thf(f4262,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_155
    | ~ spl303_166 ),
    inference(superposition,[],[f4226,f4034]) ).

thf(f13609,plain,
    ( spl303_619
    | ~ spl303_94
    | ~ spl303_164 ),
    inference(avatar_split_clause,[],[f4235,f4217,f3597,f13607]) ).

thf(f13607,plain,
    ( spl303_619
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_619])]) ).

thf(f4235,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_164 ),
    inference(superposition,[],[f4218,f3598]) ).

thf(f13605,plain,
    ( spl303_618
    | ~ spl303_93
    | ~ spl303_164 ),
    inference(avatar_split_clause,[],[f4234,f4217,f3593,f13603]) ).

thf(f13603,plain,
    ( spl303_618
  <=> ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_618])]) ).

thf(f4234,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_specID] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X1),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_164 ),
    inference(superposition,[],[f4218,f3594]) ).

thf(f13255,plain,
    ( spl303_617
    | ~ spl303_94
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4653,f4646,f3597,f13253]) ).

thf(f13253,plain,
    ( spl303_617
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_617])]) ).

thf(f4653,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_192 ),
    inference(superposition,[],[f4647,f3598]) ).

thf(f13251,plain,
    ( spl303_616
    | ~ spl303_93
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4651,f4646,f3593,f13249]) ).

thf(f4651,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_192 ),
    inference(superposition,[],[f4647,f3594]) ).

thf(f13247,plain,
    ( spl303_615
    | ~ spl303_151
    | ~ spl303_168
    | ~ spl303_172 ),
    inference(avatar_split_clause,[],[f4365,f4325,f4272,f4016,f13245]) ).

thf(f13245,plain,
    ( spl303_615
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_615])]) ).

thf(f4365,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151
    | ~ spl303_168
    | ~ spl303_172 ),
    inference(forward_demodulation,[],[f4362,f4273]) ).

thf(f4362,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151
    | ~ spl303_172 ),
    inference(duplicate_literal_removal,[],[f4351]) ).

thf(f4351,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession))) )
        | ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_151
    | ~ spl303_172 ),
    inference(superposition,[],[f4326,f4017]) ).

thf(f13243,plain,
    ( spl303_614
    | ~ spl303_168
    | ~ spl303_172 ),
    inference(avatar_split_clause,[],[f4350,f4325,f4272,f13241]) ).

thf(f13241,plain,
    ( spl303_614
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_614])]) ).

thf(f4350,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_168
    | ~ spl303_172 ),
    inference(superposition,[],[f4326,f4273]) ).

thf(f13213,plain,
    ( spl303_613
    | ~ spl303_150
    | ~ spl303_167
    | ~ spl303_171 ),
    inference(avatar_split_clause,[],[f4341,f4321,f4268,f4012,f13211]) ).

thf(f13211,plain,
    ( spl303_613
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),X0))) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_613])]) ).

thf(f4321,plain,
    ( spl303_171
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_171])]) ).

thf(f4341,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),X0))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_150
    | ~ spl303_167
    | ~ spl303_171 ),
    inference(forward_demodulation,[],[f4340,f4269]) ).

thf(f4340,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_150
    | ~ spl303_171 ),
    inference(duplicate_literal_removal,[],[f4334]) ).

thf(f4334,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS))) )
        | ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_150
    | ~ spl303_171 ),
    inference(superposition,[],[f4322,f4013]) ).

thf(f4322,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_171 ),
    inference(avatar_component_clause,[],[f4321]) ).

thf(f13209,plain,
    ( spl303_612
    | ~ spl303_167
    | ~ spl303_171 ),
    inference(avatar_split_clause,[],[f4333,f4321,f4268,f13207]) ).

thf(f13207,plain,
    ( spl303_612
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0))) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_612])]) ).

thf(f4333,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_167
    | ~ spl303_171 ),
    inference(superposition,[],[f4322,f4269]) ).

thf(f13205,plain,
    ( spl303_611
    | ~ spl303_156
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4206,f4161,f4037,f13203]) ).

thf(f13203,plain,
    ( spl303_611
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_611])]) ).

thf(f4206,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_156
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f4038]) ).

thf(f13201,plain,
    ( spl303_610
    | ~ spl303_155
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4205,f4161,f4033,f13199]) ).

thf(f13199,plain,
    ( spl303_610
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_610])]) ).

thf(f4205,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_155
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f4034]) ).

thf(f13197,plain,
    ( spl303_609
    | ~ spl303_128
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4067,f4004,f3794,f13195]) ).

thf(f13195,plain,
    ( spl303_609
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_609])]) ).

thf(f4067,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_128
    | ~ spl303_148 ),
    inference(superposition,[],[f3795,f4005]) ).

thf(f13193,plain,
    ( spl303_608
    | ~ spl303_124
    | ~ spl303_146 ),
    inference(avatar_split_clause,[],[f4043,f3996,f3769,f13191]) ).

thf(f13191,plain,
    ( spl303_608
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)))) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_608])]) ).

thf(f4043,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)))) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_124
    | ~ spl303_146 ),
    inference(superposition,[],[f3770,f3997]) ).

thf(f12915,plain,
    ( spl303_607
    | ~ spl303_68
    | ~ spl303_229 ),
    inference(avatar_split_clause,[],[f5252,f5179,f3478,f12913]) ).

thf(f12913,plain,
    ( spl303_607
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,sK34,X0) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_607])]) ).

thf(f5252,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,sK34,X0) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_68
    | ~ spl303_229 ),
    inference(superposition,[],[f3479,f5180]) ).

thf(f12911,plain,
    ( spl303_606
    | ~ spl303_218
    | ~ spl303_227 ),
    inference(avatar_split_clause,[],[f5241,f5166,f5005,f12909]) ).

thf(f12909,plain,
    ( spl303_606
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_606])]) ).

thf(f5241,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_218
    | ~ spl303_227 ),
    inference(duplicate_literal_removal,[],[f5215]) ).

thf(f5215,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_218
    | ~ spl303_227 ),
    inference(superposition,[],[f5167,f5006]) ).

thf(f12907,plain,
    ( spl303_605
    | ~ spl303_216
    | ~ spl303_226 ),
    inference(avatar_split_clause,[],[f5211,f5162,f4997,f12905]) ).

thf(f12905,plain,
    ( spl303_605
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_605])]) ).

thf(f5211,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_216
    | ~ spl303_226 ),
    inference(duplicate_literal_removal,[],[f5196]) ).

thf(f5196,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_216
    | ~ spl303_226 ),
    inference(superposition,[],[f5163,f4998]) ).

thf(f12903,plain,
    ( spl303_604
    | ~ spl303_29
    | ~ spl303_65
    | ~ spl303_88
    | ~ spl303_225 ),
    inference(avatar_split_clause,[],[f5193,f5158,f3565,f3466,f3294,f12901]) ).

thf(f12901,plain,
    ( spl303_604
  <=> ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(secrecy_Expression,list_S529945141ession,X0,X1) = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_604])]) ).

thf(f3466,plain,
    ( spl303_65
  <=> ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,nil_Se901661471ession),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_65])]) ).

thf(f5158,plain,
    ( spl303_225
  <=> ! [X2: secrecy_Expression > list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X2,X0)),vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_225])]) ).

thf(f5193,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(secrecy_Expression,list_S529945141ession,X0,X1) = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)),X0) )
    | ~ spl303_29
    | ~ spl303_65
    | ~ spl303_88
    | ~ spl303_225 ),
    inference(forward_demodulation,[],[f5192,f3295]) ).

thf(f5192,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),nil_Se901661471ession) = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)),X0) )
    | ~ spl303_65
    | ~ spl303_88
    | ~ spl303_225 ),
    inference(forward_demodulation,[],[f5183,f3566]) ).

thf(f5183,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),nil_Se901661471ession) = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),X0) )
    | ~ spl303_65
    | ~ spl303_225 ),
    inference(superposition,[],[f5159,f3467]) ).

thf(f3467,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,nil_Se901661471ession),X0) )
    | ~ spl303_65 ),
    inference(avatar_component_clause,[],[f3466]) ).

thf(f5159,plain,
    ( ! [X2: secrecy_Expression > list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X2,X0)),vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,X1),X2)) )
    | ~ spl303_225 ),
    inference(avatar_component_clause,[],[f5158]) ).

thf(f12899,plain,
    ( spl303_603
    | ~ spl303_69
    | ~ spl303_218 ),
    inference(avatar_split_clause,[],[f5084,f5005,f3482,f12897]) ).

thf(f12897,plain,
    ( spl303_603
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_603])]) ).

thf(f5084,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_69
    | ~ spl303_218 ),
    inference(superposition,[],[f3483,f5006]) ).

thf(f12895,plain,
    ( spl303_602
    | ~ spl303_69
    | ~ spl303_217 ),
    inference(avatar_split_clause,[],[f5057,f5001,f3482,f12893]) ).

thf(f12893,plain,
    ( spl303_602
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_602])]) ).

thf(f5057,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_69
    | ~ spl303_217 ),
    inference(superposition,[],[f3483,f5002]) ).

thf(f12891,plain,
    ( spl303_601
    | ~ spl303_128
    | ~ spl303_203 ),
    inference(avatar_split_clause,[],[f4856,f4820,f3794,f12889]) ).

thf(f12889,plain,
    ( spl303_601
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_601])]) ).

thf(f4856,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_128
    | ~ spl303_203 ),
    inference(superposition,[],[f3795,f4821]) ).

thf(f12887,plain,
    ( spl303_600
    | ~ spl303_124
    | ~ spl303_202 ),
    inference(avatar_split_clause,[],[f4840,f4816,f3769,f12885]) ).

thf(f12885,plain,
    ( spl303_600
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_600])]) ).

thf(f4816,plain,
    ( spl303_202
  <=> ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_202])]) ).

thf(f4840,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_124
    | ~ spl303_202 ),
    inference(superposition,[],[f3770,f4817]) ).

thf(f4817,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_202 ),
    inference(avatar_component_clause,[],[f4816]) ).

thf(f12883,plain,
    ( spl303_599
    | ~ spl303_126
    | ~ spl303_574 ),
    inference(avatar_split_clause,[],[f12645,f12417,f3781,f12881]) ).

thf(f12881,plain,
    ( spl303_599
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,sK41,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_599])]) ).

thf(f12417,plain,
    ( spl303_574
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0))) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_574])]) ).

thf(f12645,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,sK41,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_126
    | ~ spl303_574 ),
    inference(superposition,[],[f3782,f12418]) ).

thf(f12418,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0))) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_574 ),
    inference(avatar_component_clause,[],[f12417]) ).

thf(f12879,plain,
    ( spl303_598
    | ~ spl303_100
    | ~ spl303_151 ),
    inference(avatar_split_clause,[],[f4093,f4016,f3621,f12877]) ).

thf(f12877,plain,
    ( spl303_598
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = X1 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_598])]) ).

thf(f4093,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = X1 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_100
    | ~ spl303_151 ),
    inference(superposition,[],[f3622,f4017]) ).

thf(f12875,plain,
    ( spl303_597
    | ~ spl303_97
    | ~ spl303_150 ),
    inference(avatar_split_clause,[],[f4083,f4012,f3609,f12873]) ).

thf(f12873,plain,
    ( spl303_597
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = X1 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_597])]) ).

thf(f4083,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = X1 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_97
    | ~ spl303_150 ),
    inference(superposition,[],[f3610,f4013]) ).

thf(f12871,plain,
    ( spl303_596
    | ~ spl303_99
    | ~ spl303_149 ),
    inference(avatar_split_clause,[],[f4077,f4008,f3617,f12869]) ).

thf(f12869,plain,
    ( spl303_596
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_596])]) ).

thf(f4077,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))) )
        | ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_99
    | ~ spl303_149 ),
    inference(superposition,[],[f3618,f4009]) ).

thf(f12867,plain,
    ( spl303_595
    | ~ spl303_96
    | ~ spl303_147 ),
    inference(avatar_split_clause,[],[f4054,f4000,f3605,f12865]) ).

thf(f12865,plain,
    ( spl303_595
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_595])]) ).

thf(f4054,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1))) )
        | ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_96
    | ~ spl303_147 ),
    inference(superposition,[],[f3606,f4001]) ).

thf(f12863,plain,
    spl303_594,
    inference(avatar_split_clause,[],[f2559,f12861]) ).

thf(f12861,plain,
    ( spl303_594
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( X0 = X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
        | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_594])]) ).

thf(f2559,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(equality_proxy_clausification,[],[f2558]) ).

thf(f2558,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(equality_proxy_clausification,[],[f2554]) ).

thf(f2554,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f1714]) ).

thf(f1714,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(cnf_transformation,[],[f1000]) ).

thf(f1000,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
          | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) ) )
        & ( nil_Secrecy_KS != X1 )
        & ( nil_Secrecy_KS != X0 ) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(flattening,[],[f999]) ).

thf(f999,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
          | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) ) )
        & ( nil_Secrecy_KS != X1 )
        & ( nil_Secrecy_KS != X0 ) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(ennf_transformation,[],[f522]) ).

thf(f522,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
     => ( ( ( nil_Secrecy_KS != X0 )
         => ( ( nil_Secrecy_KS != X1 )
           => ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
              & ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) ) ) ) )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f521]) ).

thf(f521,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = X0 )
        = ( nil_Secrecy_KS = X1 ) )
     => ( ( ( nil_Secrecy_KS != X0 )
         => ( ( nil_Secrecy_KS != X1 )
           => ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
              & ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) ) ) ) )
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f296]) ).

thf(f296,axiom,
    ! [X25: list_Secrecy_KS,X97: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = X25 )
        = ( nil_Secrecy_KS = X97 ) )
     => ( ( ( nil_Secrecy_KS != X25 )
         => ( ( nil_Secrecy_KS != X97 )
           => ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X25) = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X97) )
              & ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X25) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X97) ) ) ) )
       => ( X25 = X97 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_list_Oexpand) ).

thf(f12859,plain,
    spl303_593,
    inference(avatar_split_clause,[],[f2557,f12857]) ).

thf(f12857,plain,
    ( spl303_593
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( X0 = X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
        | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_593])]) ).

thf(f2557,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(equality_proxy_clausification,[],[f2556]) ).

thf(f2556,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( nil_Secrecy_KS != X1 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(equality_proxy_clausification,[],[f2555]) ).

thf(f2555,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( X0 = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X1) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f1714]) ).

thf(f12855,plain,
    spl303_592,
    inference(avatar_split_clause,[],[f2549,f12853]) ).

thf(f12853,plain,
    ( spl303_592
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( X0 = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_592])]) ).

thf(f2549,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( nil_Se901661471ession = X1 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(equality_proxy_clausification,[],[f2548]) ).

thf(f2548,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(equality_proxy_clausification,[],[f2544]) ).

thf(f2544,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f1717]) ).

thf(f1717,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(cnf_transformation,[],[f1002]) ).

thf(f1002,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
          | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) ) )
        & ( nil_Se901661471ession != X1 )
        & ( nil_Se901661471ession != X0 ) )
      | ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(flattening,[],[f1001]) ).

thf(f1001,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
          | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) ) )
        & ( nil_Se901661471ession != X1 )
        & ( nil_Se901661471ession != X0 ) )
      | ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(ennf_transformation,[],[f524]) ).

thf(f524,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
     => ( ( ( nil_Se901661471ession != X0 )
         => ( ( nil_Se901661471ession != X1 )
           => ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
              & ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) ) ) ) )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f523]) ).

thf(f523,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = X0 )
        = ( nil_Se901661471ession = X1 ) )
     => ( ( ( nil_Se901661471ession != X0 )
         => ( ( nil_Se901661471ession != X1 )
           => ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
              & ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) ) ) ) )
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f295]) ).

thf(f295,axiom,
    ! [X25: list_S529945141ession,X97: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = X25 )
        = ( nil_Se901661471ession = X97 ) )
     => ( ( ( nil_Se901661471ession != X25 )
         => ( ( nil_Se901661471ession != X97 )
           => ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X25) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X97) )
              & ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X25) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X97) ) ) ) )
       => ( X25 = X97 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_list_Oexpand) ).

thf(f12851,plain,
    spl303_591,
    inference(avatar_split_clause,[],[f2547,f12849]) ).

thf(f12849,plain,
    ( spl303_591
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( X0 = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
        | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
        | ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_591])]) ).

thf(f2547,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession != X0 ) ),
    inference(equality_proxy_clausification,[],[f2546]) ).

thf(f2546,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( nil_Se901661471ession != X1 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(equality_proxy_clausification,[],[f2545]) ).

thf(f2545,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( X0 = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X1) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f1717]) ).

thf(f12834,plain,
    ( spl303_590
    | ~ spl303_128
    | ~ spl303_574 ),
    inference(avatar_split_clause,[],[f12643,f12417,f3794,f12832]) ).

thf(f12832,plain,
    ( spl303_590
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,sK40,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_590])]) ).

thf(f12643,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,sK40,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_128
    | ~ spl303_574 ),
    inference(superposition,[],[f3795,f12418]) ).

thf(f12817,plain,
    spl303_589,
    inference(avatar_split_clause,[],[f2725,f12815]) ).

thf(f12815,plain,
    ( spl303_589
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_589])]) ).

thf(f2725,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) ) ),
    inference(equality_proxy_clausification,[],[f2724]) ).

thf(f2724,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ) ),
    inference(equality_proxy_clausification,[],[f2720]) ).

thf(f2720,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)),X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ) ),
    inference(binary_proxy_clausification,[],[f1634]) ).

thf(f1634,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(cnf_transformation,[],[f478]) ).

thf(f478,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(fool_elimination,[],[f477]) ).

thf(f477,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) )
      = ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 ) ),
    inference(rectify,[],[f259]) ).

thf(f259,axiom,
    ! [X28: list_Secrecy_KS,X39: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X28) )
      = ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_rev__singleton__conv) ).

thf(f12813,plain,
    spl303_588,
    inference(avatar_split_clause,[],[f2723,f12811]) ).

thf(f12811,plain,
    ( spl303_588
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) != X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_588])]) ).

thf(f2723,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) != X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) ) ),
    inference(equality_proxy_clausification,[],[f2722]) ).

thf(f2722,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) != X0 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ) ),
    inference(equality_proxy_clausification,[],[f2721]) ).

thf(f2721,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)),X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ) ),
    inference(binary_proxy_clausification,[],[f1634]) ).

thf(f12809,plain,
    spl303_587,
    inference(avatar_split_clause,[],[f2713,f12807]) ).

thf(f12807,plain,
    ( spl303_587
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_587])]) ).

thf(f2713,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2712]) ).

thf(f2712,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2708]) ).

thf(f2708,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1636]) ).

thf(f1636,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ),
    inference(cnf_transformation,[],[f482]) ).

thf(f482,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ),
    inference(fool_elimination,[],[f481]) ).

thf(f481,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      = ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 ) ),
    inference(rectify,[],[f260]) ).

thf(f260,axiom,
    ! [X28: list_S529945141ession,X39: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28) )
      = ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_rev__singleton__conv) ).

thf(f12805,plain,
    spl303_586,
    inference(avatar_split_clause,[],[f2711,f12803]) ).

thf(f12803,plain,
    ( spl303_586
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_586])]) ).

thf(f2711,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) != X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2710]) ).

thf(f2710,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) != X0 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2709]) ).

thf(f2709,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1636]) ).

thf(f12772,plain,
    ( spl303_585
    | ~ spl303_122
    | ~ spl303_571 ),
    inference(avatar_split_clause,[],[f12581,f12403,f3757,f12770]) ).

thf(f12770,plain,
    ( spl303_585
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_585])]) ).

thf(f12403,plain,
    ( spl303_571
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0))) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_571])]) ).

thf(f12581,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_122
    | ~ spl303_571 ),
    inference(superposition,[],[f3758,f12404]) ).

thf(f12404,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0))) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_571 ),
    inference(avatar_component_clause,[],[f12403]) ).

thf(f12766,plain,
    ( spl303_584
    | ~ spl303_29
    | ~ spl303_43
    | ~ spl303_88
    | ~ spl303_214 ),
    inference(avatar_split_clause,[],[f5018,f4988,f3565,f3358,f3294,f12764]) ).

thf(f12764,plain,
    ( spl303_584
  <=> ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(secrecy_Expression,list_S529945141ession,X0,X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_584])]) ).

thf(f3358,plain,
    ( spl303_43
  <=> ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_43])]) ).

thf(f5018,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(secrecy_Expression,list_S529945141ession,X0,X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
    | ~ spl303_29
    | ~ spl303_43
    | ~ spl303_88
    | ~ spl303_214 ),
    inference(forward_demodulation,[],[f5017,f3566]) ).

thf(f5017,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(secrecy_Expression,list_S529945141ession,X0,X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
    | ~ spl303_29
    | ~ spl303_43
    | ~ spl303_214 ),
    inference(forward_demodulation,[],[f5008,f3295]) ).

thf(f5008,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),nil_Se901661471ession) )
    | ~ spl303_43
    | ~ spl303_214 ),
    inference(superposition,[],[f4989,f3359]) ).

thf(f3359,plain,
    ( ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),nil_Se901661471ession) )
    | ~ spl303_43 ),
    inference(avatar_component_clause,[],[f3358]) ).

thf(f12762,plain,
    ( spl303_583
    | ~ spl303_99
    | ~ spl303_172 ),
    inference(avatar_split_clause,[],[f4354,f4325,f3617,f12760]) ).

thf(f12760,plain,
    ( spl303_583
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_583])]) ).

thf(f4354,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_99
    | ~ spl303_172 ),
    inference(superposition,[],[f3618,f4326]) ).

thf(f12758,plain,
    ( spl303_582
    | ~ spl303_96
    | ~ spl303_171 ),
    inference(avatar_split_clause,[],[f4338,f4321,f3605,f12756]) ).

thf(f12756,plain,
    ( spl303_582
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_582])]) ).

thf(f4338,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_96
    | ~ spl303_171 ),
    inference(superposition,[],[f3606,f4322]) ).

thf(f12754,plain,
    spl303_581,
    inference(avatar_split_clause,[],[f2581,f12752]) ).

thf(f12752,plain,
    ( spl303_581
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_581])]) ).

thf(f2581,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(equality_proxy_clausification,[],[f2580]) ).

thf(f2580,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(equality_proxy_clausification,[],[f2579]) ).

thf(f2579,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f2578]) ).

thf(f2578,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) )
      | ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1646]) ).

thf(f1646,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) ),
    inference(cnf_transformation,[],[f502]) ).

thf(f502,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) ),
    inference(fool_elimination,[],[f501]) ).

thf(f501,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1))
        = ( nil_Secrecy_KS = X1 ) )
      & ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f322]) ).

thf(f322,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X28),X31))
        = ( nil_Secrecy_KS = X31 ) )
      & ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_Nil__in__shuffles) ).

thf(f12750,plain,
    spl303_580,
    inference(avatar_split_clause,[],[f2572,f12748]) ).

thf(f12748,plain,
    ( spl303_580
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
        | ( nil_Se901661471ession != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_580])]) ).

thf(f2572,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
      | ( nil_Se901661471ession != X0 ) ),
    inference(equality_proxy_clausification,[],[f2571]) ).

thf(f2571,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(equality_proxy_clausification,[],[f2570]) ).

thf(f2570,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f2569]) ).

thf(f2569,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) )
      | ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1647]) ).

thf(f1647,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) ),
    inference(cnf_transformation,[],[f504]) ).

thf(f504,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) ),
    inference(fool_elimination,[],[f503]) ).

thf(f503,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1))
        = ( nil_Se901661471ession = X1 ) )
      & ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f321]) ).

thf(f321,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),X31))
        = ( nil_Se901661471ession = X31 ) )
      & ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_Nil__in__shuffles) ).

thf(f12746,plain,
    spl303_579,
    inference(avatar_split_clause,[],[f2264,f12744]) ).

thf(f12744,plain,
    ( spl303_579
  <=> ! [X0: secrecy_Expression,X3: list_S529945141ession,X2: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3) )
        | ( X1 != X3 )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_579])]) ).

thf(f2264,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3) )
      | ( X1 != X3 )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2263]) ).

thf(f2263,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3) )
      | ( X1 != X3 )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2262]) ).

thf(f2262,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X3) )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f2261]) ).

thf(f2261,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X3)) ) ),
    inference(equality_proxy_clausification,[],[f2254]) ).

thf(f2254,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X3)) ) ),
    inference(binary_proxy_clausification,[],[f1960]) ).

thf(f1960,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X3)) ),
    inference(cnf_transformation,[],[f716]) ).

thf(f716,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: secrecy_Expression,X3: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),X0),X2)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X3)) ),
    inference(fool_elimination,[],[f715]) ).

thf(f715,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: secrecy_Expression,X3: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3) )
        = ( X1 = X3 ) )
      & ( X0 = X2 ) ),
    inference(rectify,[],[f20]) ).

thf(f20,axiom,
    ! [X21: secrecy_Expression,X22: list_S529945141ession,X23: secrecy_Expression,X24: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X21),X22) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X23),X24) )
        = ( X22 = X24 ) )
      & ( X21 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list_Oinject) ).

thf(f12682,plain,
    ( spl303_578
    | ~ spl303_124
    | ~ spl303_571 ),
    inference(avatar_split_clause,[],[f12579,f12403,f3769,f12680]) ).

thf(f12680,plain,
    ( spl303_578
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_578])]) ).

thf(f12579,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_124
    | ~ spl303_571 ),
    inference(superposition,[],[f3770,f12404]) ).

thf(f12431,plain,
    ( spl303_577
    | ~ spl303_94
    | ~ spl303_174 ),
    inference(avatar_split_clause,[],[f4396,f4373,f3597,f12429]) ).

thf(f12429,plain,
    ( spl303_577
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_577])]) ).

thf(f4396,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_174 ),
    inference(superposition,[],[f4374,f3598]) ).

thf(f12427,plain,
    ( spl303_576
    | ~ spl303_93
    | ~ spl303_174 ),
    inference(avatar_split_clause,[],[f4395,f4373,f3593,f12425]) ).

thf(f12425,plain,
    ( spl303_576
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_576])]) ).

thf(f4395,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_174 ),
    inference(superposition,[],[f4374,f3594]) ).

thf(f12423,plain,
    ( spl303_575
    | ~ spl303_99
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4297,f4272,f3617,f12421]) ).

thf(f12421,plain,
    ( spl303_575
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_575])]) ).

thf(f4297,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_99
    | ~ spl303_168 ),
    inference(superposition,[],[f3618,f4273]) ).

thf(f12419,plain,
    ( spl303_574
    | ~ spl303_156
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4291,f4272,f4037,f12417]) ).

thf(f4291,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK40,X0))) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_156
    | ~ spl303_168 ),
    inference(superposition,[],[f4273,f4038]) ).

thf(f12415,plain,
    ( spl303_573
    | ~ spl303_155
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4290,f4272,f4033,f12413]) ).

thf(f12413,plain,
    ( spl303_573
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0))) = X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_573])]) ).

thf(f4290,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0))) = X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_155
    | ~ spl303_168 ),
    inference(superposition,[],[f4273,f4034]) ).

thf(f12409,plain,
    ( spl303_572
    | ~ spl303_96
    | ~ spl303_167 ),
    inference(avatar_split_clause,[],[f4283,f4268,f3605,f12407]) ).

thf(f12407,plain,
    ( spl303_572
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_572])]) ).

thf(f4283,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_96
    | ~ spl303_167 ),
    inference(superposition,[],[f3606,f4269]) ).

thf(f12405,plain,
    ( spl303_571
    | ~ spl303_153
    | ~ spl303_167 ),
    inference(avatar_split_clause,[],[f4276,f4268,f4024,f12403]) ).

thf(f4024,plain,
    ( spl303_153
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),nil_Secrecy_KS)) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_153])]) ).

thf(f4276,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0))) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_153
    | ~ spl303_167 ),
    inference(superposition,[],[f4269,f4025]) ).

thf(f4025,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),nil_Secrecy_KS)) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_153 ),
    inference(avatar_component_clause,[],[f4024]) ).

thf(f12401,plain,
    ( spl303_570
    | ~ spl303_152
    | ~ spl303_167 ),
    inference(avatar_split_clause,[],[f4275,f4268,f4020,f12399]) ).

thf(f12399,plain,
    ( spl303_570
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0))) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_570])]) ).

thf(f4020,plain,
    ( spl303_152
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),nil_Secrecy_KS)) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_152])]) ).

thf(f4275,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0))) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_152
    | ~ spl303_167 ),
    inference(superposition,[],[f4269,f4021]) ).

thf(f4021,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),nil_Secrecy_KS)) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_152 ),
    inference(avatar_component_clause,[],[f4020]) ).

thf(f12397,plain,
    ( spl303_569
    | ~ spl303_93
    | ~ spl303_160 ),
    inference(avatar_split_clause,[],[f4192,f4157,f3593,f12395]) ).

thf(f12395,plain,
    ( spl303_569
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),nil_Se901661471ession) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_569])]) ).

thf(f4192,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),nil_Se901661471ession) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_160 ),
    inference(superposition,[],[f4158,f3594]) ).

thf(f12393,plain,
    ( spl303_568
    | ~ spl303_91
    | ~ spl303_159 ),
    inference(avatar_split_clause,[],[f4183,f4153,f3585,f12391]) ).

thf(f12391,plain,
    ( spl303_568
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_568])]) ).

thf(f4183,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),nil_Secrecy_KS) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_91
    | ~ spl303_159 ),
    inference(superposition,[],[f4154,f3586]) ).

thf(f12389,plain,
    ( spl303_567
    | ~ spl303_126
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4066,f4004,f3781,f12387]) ).

thf(f12387,plain,
    ( spl303_567
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) = X0 )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_567])]) ).

thf(f4066,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) = X0 )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_126
    | ~ spl303_148 ),
    inference(superposition,[],[f3782,f4005]) ).

thf(f12385,plain,
    ( spl303_566
    | ~ spl303_69
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4063,f4004,f3482,f12383]) ).

thf(f12383,plain,
    ( spl303_566
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_566])]) ).

thf(f4063,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_69
    | ~ spl303_148 ),
    inference(superposition,[],[f3483,f4005]) ).

thf(f12381,plain,
    ( spl303_565
    | ~ spl303_122
    | ~ spl303_146 ),
    inference(avatar_split_clause,[],[f4044,f3996,f3757,f12379]) ).

thf(f12379,plain,
    ( spl303_565
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)))) = X0 )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_565])]) ).

thf(f4044,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)))) = X0 )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_122
    | ~ spl303_146 ),
    inference(superposition,[],[f3758,f3997]) ).

thf(f12377,plain,
    spl303_564,
    inference(avatar_split_clause,[],[f2567,f12375]) ).

thf(f12375,plain,
    ( spl303_564
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X1 )
        | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_564])]) ).

thf(f2567,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X1 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ) ),
    inference(equality_proxy_clausification,[],[f2564]) ).

thf(f2564,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ) ),
    inference(binary_proxy_clausification,[],[f1648]) ).

thf(f1648,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f506]) ).

thf(f506,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f505]) ).

thf(f505,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS)
      = ( nil_Secrecy_KS = X1 ) ),
    inference(rectify,[],[f104]) ).

thf(f104,axiom,
    ! [X58: secrecy_KS > secrecy_KS > $o,X28: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),X28),nil_Secrecy_KS)
      = ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_ord_Olexordp__eq__simps_I2_J) ).

thf(f12373,plain,
    spl303_563,
    inference(avatar_split_clause,[],[f2566,f12371]) ).

thf(f12371,plain,
    ( spl303_563
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_563])]) ).

thf(f2566,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ) ),
    inference(equality_proxy_clausification,[],[f2565]) ).

thf(f2565,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),nil_Secrecy_KS) ) ),
    inference(binary_proxy_clausification,[],[f1648]) ).

thf(f12352,plain,
    spl303_562,
    inference(avatar_split_clause,[],[f2563,f12350]) ).

thf(f2563,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X1 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ) ),
    inference(equality_proxy_clausification,[],[f2560]) ).

thf(f2560,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ) ),
    inference(binary_proxy_clausification,[],[f1649]) ).

thf(f1649,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f508]) ).

thf(f508,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f507]) ).

thf(f507,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession)
      = ( nil_Se901661471ession = X1 ) ),
    inference(rectify,[],[f103]) ).

thf(f103,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X28: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X28),nil_Se901661471ession)
      = ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord_Olexordp__eq__simps_I2_J) ).

thf(f12348,plain,
    spl303_561,
    inference(avatar_split_clause,[],[f2562,f12346]) ).

thf(f12346,plain,
    ( spl303_561
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_561])]) ).

thf(f2562,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ) ),
    inference(equality_proxy_clausification,[],[f2561]) ).

thf(f2561,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),nil_Se901661471ession) ) ),
    inference(binary_proxy_clausification,[],[f1649]) ).

thf(f11349,plain,
    ( spl303_560
    | ~ spl303_203
    | ~ spl303_217 ),
    inference(avatar_split_clause,[],[f5071,f5001,f4820,f11347]) ).

thf(f11347,plain,
    ( spl303_560
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_560])]) ).

thf(f5071,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_203
    | ~ spl303_217 ),
    inference(duplicate_literal_removal,[],[f5050]) ).

thf(f5050,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_203
    | ~ spl303_217 ),
    inference(superposition,[],[f5002,f4821]) ).

thf(f11345,plain,
    ( spl303_559
    | ~ spl303_202
    | ~ spl303_215 ),
    inference(avatar_split_clause,[],[f5032,f4992,f4816,f11343]) ).

thf(f11343,plain,
    ( spl303_559
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_559])]) ).

thf(f5032,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_202
    | ~ spl303_215 ),
    inference(duplicate_literal_removal,[],[f5021]) ).

thf(f5021,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_202
    | ~ spl303_215 ),
    inference(superposition,[],[f4993,f4817]) ).

thf(f11341,plain,
    ( spl303_558
    | ~ spl303_69
    | ~ spl303_203 ),
    inference(avatar_split_clause,[],[f4852,f4820,f3482,f11339]) ).

thf(f11339,plain,
    ( spl303_558
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_558])]) ).

thf(f4852,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_69
    | ~ spl303_203 ),
    inference(superposition,[],[f3483,f4821]) ).

thf(f11337,plain,
    ( spl303_557
    | ~ spl303_14
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_168
    | ~ spl303_176 ),
    inference(avatar_split_clause,[],[f4426,f4381,f4272,f3565,f3282,f3227,f11335]) ).

thf(f11335,plain,
    ( spl303_557
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_557])]) ).

thf(f3227,plain,
    ( spl303_14
  <=> ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_14])]) ).

thf(f4426,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_14
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_168
    | ~ spl303_176 ),
    inference(forward_demodulation,[],[f4425,f4305]) ).

thf(f4305,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_168 ),
    inference(forward_demodulation,[],[f4292,f3566]) ).

thf(f4292,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) )
    | ~ spl303_26
    | ~ spl303_168 ),
    inference(superposition,[],[f4273,f3283]) ).

thf(f4425,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_14
    | ~ spl303_88
    | ~ spl303_168
    | ~ spl303_176 ),
    inference(forward_demodulation,[],[f4424,f3566]) ).

thf(f4424,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_14
    | ~ spl303_88
    | ~ spl303_168
    | ~ spl303_176 ),
    inference(forward_demodulation,[],[f4423,f4273]) ).

thf(f4423,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_14
    | ~ spl303_88
    | ~ spl303_176 ),
    inference(forward_demodulation,[],[f4413,f3566]) ).

thf(f4413,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) )
    | ~ spl303_14
    | ~ spl303_176 ),
    inference(superposition,[],[f4382,f3229]) ).

thf(f3229,plain,
    ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,nil_Se901661471ession) )
    | ~ spl303_14 ),
    inference(avatar_component_clause,[],[f3227]) ).

thf(f11333,plain,
    ( spl303_556
    | ~ spl303_6
    | ~ spl303_22
    | ~ spl303_87
    | ~ spl303_167
    | ~ spl303_175 ),
    inference(avatar_split_clause,[],[f4411,f4377,f4268,f3561,f3266,f3187,f11331]) ).

thf(f11331,plain,
    ( spl303_556
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_556])]) ).

thf(f3187,plain,
    ( spl303_6
  <=> ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_6])]) ).

thf(f3266,plain,
    ( spl303_22
  <=> ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_22])]) ).

thf(f4411,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_6
    | ~ spl303_22
    | ~ spl303_87
    | ~ spl303_167
    | ~ spl303_175 ),
    inference(forward_demodulation,[],[f4410,f4285]) ).

thf(f4285,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_22
    | ~ spl303_87
    | ~ spl303_167 ),
    inference(forward_demodulation,[],[f4277,f3562]) ).

thf(f4277,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_22
    | ~ spl303_167 ),
    inference(superposition,[],[f4269,f3267]) ).

thf(f3267,plain,
    ( ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),X0) = X0 )
    | ~ spl303_22 ),
    inference(avatar_component_clause,[],[f3266]) ).

thf(f4410,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_6
    | ~ spl303_87
    | ~ spl303_167
    | ~ spl303_175 ),
    inference(forward_demodulation,[],[f4409,f3562]) ).

thf(f4409,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_6
    | ~ spl303_87
    | ~ spl303_167
    | ~ spl303_175 ),
    inference(forward_demodulation,[],[f4408,f4269]) ).

thf(f4408,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_6
    | ~ spl303_87
    | ~ spl303_175 ),
    inference(forward_demodulation,[],[f4403,f3562]) ).

thf(f4403,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_6
    | ~ spl303_175 ),
    inference(superposition,[],[f4378,f3189]) ).

thf(f3189,plain,
    ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,nil_Secrecy_KS) )
    | ~ spl303_6 ),
    inference(avatar_component_clause,[],[f3187]) ).

thf(f11329,plain,
    ( spl303_555
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f4305,f4272,f3565,f3282,f11327]) ).

thf(f11327,plain,
    ( spl303_555
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_555])]) ).

thf(f11325,plain,
    ( spl303_554
    | ~ spl303_22
    | ~ spl303_87
    | ~ spl303_167 ),
    inference(avatar_split_clause,[],[f4285,f4268,f3561,f3266,f11323]) ).

thf(f11323,plain,
    ( spl303_554
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_554])]) ).

thf(f11318,plain,
    ( spl303_553
    | ~ spl303_3
    | ~ spl303_118 ),
    inference(avatar_split_clause,[],[f3886,f3739,f3143,f11316]) ).

thf(f11316,plain,
    ( spl303_553
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_553])]) ).

thf(f3886,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_118 ),
    inference(trivial_inequality_removal,[],[f3885]) ).

thf(f3885,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_118 ),
    inference(superposition,[],[f3740,f3144]) ).

thf(f11314,plain,
    ( spl303_552
    | ~ spl303_3
    | ~ spl303_117 ),
    inference(avatar_split_clause,[],[f3864,f3735,f3143,f11312]) ).

thf(f11312,plain,
    ( spl303_552
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_552])]) ).

thf(f3864,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_117 ),
    inference(trivial_inequality_removal,[],[f3863]) ).

thf(f3863,plain,
    ( ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $false = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_117 ),
    inference(superposition,[],[f3736,f3144]) ).

thf(f11310,plain,
    ( spl303_551
    | ~ spl303_3
    | ~ spl303_116 ),
    inference(avatar_split_clause,[],[f3843,f3731,f3143,f11308]) ).

thf(f11308,plain,
    ( spl303_551
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_551])]) ).

thf(f3731,plain,
    ( spl303_116
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_116])]) ).

thf(f3843,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_116 ),
    inference(trivial_inequality_removal,[],[f3842]) ).

thf(f3842,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_116 ),
    inference(superposition,[],[f3732,f3144]) ).

thf(f3732,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) ) )
    | ~ spl303_116 ),
    inference(avatar_component_clause,[],[f3731]) ).

thf(f11306,plain,
    ( spl303_550
    | ~ spl303_3
    | ~ spl303_115 ),
    inference(avatar_split_clause,[],[f3823,f3727,f3143,f11304]) ).

thf(f11304,plain,
    ( spl303_550
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_550])]) ).

thf(f3727,plain,
    ( spl303_115
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_115])]) ).

thf(f3823,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_115 ),
    inference(trivial_inequality_removal,[],[f3822]) ).

thf(f3822,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $false = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_115 ),
    inference(superposition,[],[f3728,f3144]) ).

thf(f3728,plain,
    ( ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) ) )
    | ~ spl303_115 ),
    inference(avatar_component_clause,[],[f3727]) ).

thf(f11182,plain,
    ( spl303_549
    | ~ spl303_36
    | ~ spl303_422 ),
    inference(avatar_split_clause,[],[f7037,f7025,f3322,f11180]) ).

thf(f11180,plain,
    ( spl303_549
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_549])]) ).

thf(f3322,plain,
    ( spl303_36
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_36])]) ).

thf(f7025,plain,
    ( spl303_422
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)) = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_422])]) ).

thf(f7037,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) )
    | ~ spl303_36
    | ~ spl303_422 ),
    inference(superposition,[],[f3323,f7026]) ).

thf(f7026,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)) = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) )
    | ~ spl303_422 ),
    inference(avatar_component_clause,[],[f7025]) ).

thf(f3323,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) )
    | ~ spl303_36 ),
    inference(avatar_component_clause,[],[f3322]) ).

thf(f11178,plain,
    ( spl303_548
    | ~ spl303_35
    | ~ spl303_421 ),
    inference(avatar_split_clause,[],[f7028,f7021,f3318,f11176]) ).

thf(f11176,plain,
    ( spl303_548
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_548])]) ).

thf(f3318,plain,
    ( spl303_35
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_35])]) ).

thf(f7021,plain,
    ( spl303_421
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)) = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_421])]) ).

thf(f7028,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) )
    | ~ spl303_35
    | ~ spl303_421 ),
    inference(superposition,[],[f3319,f7022]) ).

thf(f7022,plain,
    ( ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)) = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) )
    | ~ spl303_421 ),
    inference(avatar_component_clause,[],[f7021]) ).

thf(f3319,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1) )
    | ~ spl303_35 ),
    inference(avatar_component_clause,[],[f3318]) ).

thf(f11174,plain,
    ( spl303_547
    | ~ spl303_45
    | ~ spl303_85 ),
    inference(avatar_split_clause,[],[f3558,f3550,f3366,f11172]) ).

thf(f11172,plain,
    ( spl303_547
  <=> ! [X0: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,X0) )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_547])]) ).

thf(f3366,plain,
    ( spl303_45
  <=> ! [X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_45])]) ).

thf(f3550,plain,
    ( spl303_85
  <=> ! [X0: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = X0 )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_85])]) ).

thf(f3558,plain,
    ( ! [X0: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,X0) )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) )
    | ~ spl303_45
    | ~ spl303_85 ),
    inference(superposition,[],[f3367,f3551]) ).

thf(f3551,plain,
    ( ! [X0: secrecy_KS] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = X0 )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) )
    | ~ spl303_85 ),
    inference(avatar_component_clause,[],[f3550]) ).

thf(f3367,plain,
    ( ! [X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)) )
    | ~ spl303_45 ),
    inference(avatar_component_clause,[],[f3366]) ).

thf(f11149,plain,
    spl303_546,
    inference(avatar_split_clause,[],[f2879,f11147]) ).

thf(f11147,plain,
    ( spl303_546
  <=> ! [X0: secrecy_Secrets,X1: secrecy_Secrets > $o] :
        ( ( $false = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X1)) )
        | ( $true = vAPP(secrecy_Secrets,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_546])]) ).

thf(f2879,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets > $o] :
      ( ( $false = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X1)) )
      | ( $true = vAPP(secrecy_Secrets,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1598]) ).

thf(f1598,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets > $o] : ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X1)) = vAPP(secrecy_Secrets,$o,X1,X0) ),
    inference(cnf_transformation,[],[f838]) ).

thf(f838,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets > $o] : ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X1)) = vAPP(secrecy_Secrets,$o,X1,X0) ),
    inference(rectify,[],[f52]) ).

thf(f52,axiom,
    ! [X46: secrecy_Secrets,X18: secrecy_Secrets > $o] : ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X46),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X18)) = vAPP(secrecy_Secrets,$o,X18,X46) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mem__Collect__eq) ).

thf(f11145,plain,
    spl303_545,
    inference(avatar_split_clause,[],[f2878,f11143]) ).

thf(f11143,plain,
    ( spl303_545
  <=> ! [X0: secrecy_Secrets,X1: secrecy_Secrets > $o] :
        ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X1)) )
        | ( $false = vAPP(secrecy_Secrets,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_545])]) ).

thf(f2878,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets > $o] :
      ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,X1)) )
      | ( $false = vAPP(secrecy_Secrets,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1598]) ).

thf(f11141,plain,
    spl303_544,
    inference(avatar_split_clause,[],[f2877,f11139]) ).

thf(f11139,plain,
    ( spl303_544
  <=> ! [X0: secrecy_Keys,X1: secrecy_Keys > $o] :
        ( ( $false = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X1)) )
        | ( $true = vAPP(secrecy_Keys,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_544])]) ).

thf(f2877,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys > $o] :
      ( ( $false = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X1)) )
      | ( $true = vAPP(secrecy_Keys,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1599]) ).

thf(f1599,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys > $o] : ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X1)) = vAPP(secrecy_Keys,$o,X1,X0) ),
    inference(cnf_transformation,[],[f839]) ).

thf(f839,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys > $o] : ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X1)) = vAPP(secrecy_Keys,$o,X1,X0) ),
    inference(rectify,[],[f54]) ).

thf(f54,axiom,
    ! [X46: secrecy_Keys,X18: secrecy_Keys > $o] : ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X46),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X18)) = vAPP(secrecy_Keys,$o,X18,X46) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_mem__Collect__eq) ).

thf(f11137,plain,
    spl303_543,
    inference(avatar_split_clause,[],[f2876,f11135]) ).

thf(f11135,plain,
    ( spl303_543
  <=> ! [X0: secrecy_Keys,X1: secrecy_Keys > $o] :
        ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X1)) )
        | ( $false = vAPP(secrecy_Keys,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_543])]) ).

thf(f2876,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys > $o] :
      ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,X1)) )
      | ( $false = vAPP(secrecy_Keys,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1599]) ).

thf(f11133,plain,
    spl303_542,
    inference(avatar_split_clause,[],[f2875,f11131]) ).

thf(f11131,plain,
    ( spl303_542
  <=> ! [X0: secrecy_KS,X1: secrecy_KS > $o] :
        ( ( $false = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X1)) )
        | ( $true = vAPP(secrecy_KS,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_542])]) ).

thf(f2875,plain,
    ! [X0: secrecy_KS,X1: secrecy_KS > $o] :
      ( ( $false = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X1)) )
      | ( $true = vAPP(secrecy_KS,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1600]) ).

thf(f1600,plain,
    ! [X0: secrecy_KS,X1: secrecy_KS > $o] : ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X1)) = vAPP(secrecy_KS,$o,X1,X0) ),
    inference(cnf_transformation,[],[f840]) ).

thf(f840,plain,
    ! [X0: secrecy_KS,X1: secrecy_KS > $o] : ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X1)) = vAPP(secrecy_KS,$o,X1,X0) ),
    inference(rectify,[],[f53]) ).

thf(f53,axiom,
    ! [X46: secrecy_KS,X18: secrecy_KS > $o] : ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X46),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X18)) = vAPP(secrecy_KS,$o,X18,X46) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mem__Collect__eq) ).

thf(f11129,plain,
    spl303_541,
    inference(avatar_split_clause,[],[f2874,f11127]) ).

thf(f11127,plain,
    ( spl303_541
  <=> ! [X0: secrecy_KS,X1: secrecy_KS > $o] :
        ( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X1)) )
        | ( $false = vAPP(secrecy_KS,$o,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_541])]) ).

thf(f2874,plain,
    ! [X0: secrecy_KS,X1: secrecy_KS > $o] :
      ( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,X1)) )
      | ( $false = vAPP(secrecy_KS,$o,X1,X0) ) ),
    inference(binary_proxy_clausification,[],[f1600]) ).

thf(f11125,plain,
    spl303_540,
    inference(avatar_split_clause,[],[f2459,f11123]) ).

thf(f11123,plain,
    ( spl303_540
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
        | ( X1 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_540])]) ).

thf(f2459,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2458]) ).

thf(f2458,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2454]) ).

thf(f2454,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1802]) ).

thf(f1802,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X2) ),
    inference(cnf_transformation,[],[f600]) ).

thf(f600,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X2) ),
    inference(fool_elimination,[],[f599]) ).

thf(f599,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f137]) ).

thf(f137,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession,X71: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X71) )
      = ( X31 = X71 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_same__append__eq) ).

thf(f11121,plain,
    spl303_539,
    inference(avatar_split_clause,[],[f2457,f11119]) ).

thf(f2457,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
      | ( X1 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2456]) ).

thf(f2456,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2455]) ).

thf(f2455,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X2)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1802]) ).

thf(f11117,plain,
    spl303_538,
    inference(avatar_split_clause,[],[f2453,f11115]) ).

thf(f11115,plain,
    ( spl303_538
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_538])]) ).

thf(f2453,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2452]) ).

thf(f2452,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2448]) ).

thf(f2448,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1803]) ).

thf(f1803,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X2) ),
    inference(cnf_transformation,[],[f602]) ).

thf(f602,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X2) ),
    inference(fool_elimination,[],[f601]) ).

thf(f601,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
      = ( X0 = X2 ) ),
    inference(rectify,[],[f136]) ).

thf(f136,axiom,
    ! [X31: list_S529945141ession,X28: list_S529945141ession,X71: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X31),X28) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X71),X28) )
      = ( X31 = X71 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_append__same__eq) ).

thf(f11113,plain,
    spl303_537,
    inference(avatar_split_clause,[],[f2451,f11111]) ).

thf(f2451,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
      | ( X0 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2450]) ).

thf(f2450,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2449]) ).

thf(f2449,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X1)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1803]) ).

thf(f11003,plain,
    ( spl303_536
    | ~ spl303_126
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4660,f4646,f3781,f11001]) ).

thf(f11001,plain,
    ( spl303_536
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_536])]) ).

thf(f4660,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) = X0 )
    | ~ spl303_126
    | ~ spl303_192 ),
    inference(superposition,[],[f3782,f4647]) ).

thf(f10999,plain,
    ( spl303_535
    | ~ spl303_29
    | ~ spl303_161 ),
    inference(avatar_split_clause,[],[f4198,f4161,f3294,f10997]) ).

thf(f10997,plain,
    ( spl303_535
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_535])]) ).

thf(f4198,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),X0) )
    | ~ spl303_29
    | ~ spl303_161 ),
    inference(superposition,[],[f4162,f3295]) ).

thf(f10995,plain,
    spl303_534,
    inference(avatar_split_clause,[],[f2839,f10993]) ).

thf(f10993,plain,
    ( spl303_534
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_534])]) ).

thf(f2839,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( nil_Secrecy_KS = X1 ) ),
    inference(equality_proxy_clausification,[],[f2836]) ).

thf(f2836,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) ) ),
    inference(binary_proxy_clausification,[],[f2835]) ).

thf(f2835,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2834]) ).

thf(f2834,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1620]) ).

thf(f1620,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) ),
    inference(cnf_transformation,[],[f450]) ).

thf(f450,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) ),
    inference(fool_elimination,[],[f449]) ).

thf(f449,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
        = ( nil_Secrecy_KS = X1 ) )
      & ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f155]) ).

thf(f155,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X28),X31) )
        = ( nil_Secrecy_KS = X31 ) )
      & ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_split__Nil__iff) ).

thf(f10991,plain,
    ( spl303_533
    | ~ spl303_99
    | ~ spl303_156 ),
    inference(avatar_split_clause,[],[f4142,f4037,f3617,f10989]) ).

thf(f10989,plain,
    ( spl303_533
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,sK40,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_533])]) ).

thf(f4142,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,sK40,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_99
    | ~ spl303_156 ),
    inference(superposition,[],[f3618,f4038]) ).

thf(f10987,plain,
    ( spl303_532
    | ~ spl303_99
    | ~ spl303_155 ),
    inference(avatar_split_clause,[],[f4133,f4033,f3617,f10985]) ).

thf(f10985,plain,
    ( spl303_532
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_532])]) ).

thf(f4133,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_99
    | ~ spl303_155 ),
    inference(superposition,[],[f3618,f4034]) ).

thf(f10983,plain,
    ( spl303_531
    | ~ spl303_96
    | ~ spl303_153 ),
    inference(avatar_split_clause,[],[f4115,f4024,f3605,f10981]) ).

thf(f10981,plain,
    ( spl303_531
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_531])]) ).

thf(f4115,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_96
    | ~ spl303_153 ),
    inference(superposition,[],[f3606,f4025]) ).

thf(f10979,plain,
    ( spl303_530
    | ~ spl303_96
    | ~ spl303_152 ),
    inference(avatar_split_clause,[],[f4108,f4020,f3605,f10977]) ).

thf(f10977,plain,
    ( spl303_530
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_530])]) ).

thf(f4108,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_96
    | ~ spl303_152 ),
    inference(superposition,[],[f3606,f4021]) ).

thf(f10975,plain,
    ( spl303_529
    | ~ spl303_94
    | ~ spl303_98 ),
    inference(avatar_split_clause,[],[f3663,f3613,f3597,f10973]) ).

thf(f10973,plain,
    ( spl303_529
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_529])]) ).

thf(f3663,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_98 ),
    inference(superposition,[],[f3614,f3598]) ).

thf(f10971,plain,
    ( spl303_528
    | ~ spl303_92
    | ~ spl303_95 ),
    inference(avatar_split_clause,[],[f3657,f3601,f3589,f10969]) ).

thf(f10969,plain,
    ( spl303_528
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_528])]) ).

thf(f3589,plain,
    ( spl303_92
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) = X0 )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_92])]) ).

thf(f3657,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_92
    | ~ spl303_95 ),
    inference(superposition,[],[f3602,f3590]) ).

thf(f3590,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_92 ),
    inference(avatar_component_clause,[],[f3589]) ).

thf(f10927,plain,
    ( spl303_527
    | ~ spl303_68
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4062,f4004,f3478,f10925]) ).

thf(f10925,plain,
    ( spl303_527
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) = X0 )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_527])]) ).

thf(f4062,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) = X0 )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_68
    | ~ spl303_148 ),
    inference(superposition,[],[f3479,f4005]) ).

thf(f10923,plain,
    ( spl303_526
    | ~ spl303_37
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4061,f4004,f3326,f10921]) ).

thf(f10921,plain,
    ( spl303_526
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) != vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_526])]) ).

thf(f4061,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) != vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_37
    | ~ spl303_148 ),
    inference(superposition,[],[f3327,f4005]) ).

thf(f10919,plain,
    spl303_525,
    inference(avatar_split_clause,[],[f2838,f10917]) ).

thf(f10917,plain,
    ( spl303_525
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_525])]) ).

thf(f2838,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(equality_proxy_clausification,[],[f2837]) ).

thf(f2837,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f2835]) ).

thf(f10911,plain,
    ( spl303_524
    | ~ spl303_118 ),
    inference(avatar_split_clause,[],[f3895,f3739,f10909]) ).

thf(f10909,plain,
    ( spl303_524
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0)) = X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_524])]) ).

thf(f3895,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0)) = X0 )
        | ( X0 = X1 ) )
    | ~ spl303_118 ),
    inference(equality_proxy_clausification,[],[f3894]) ).

thf(f3894,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0)) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_118 ),
    inference(equality_proxy_clausification,[],[f3893]) ).

thf(f3893,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_118 ),
    inference(equality_proxy_clausification,[],[f3878]) ).

thf(f3878,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_118 ),
    inference(primitive_instantiation,[],[f3740]) ).

thf(f10907,plain,
    ( spl303_523
    | ~ spl303_117 ),
    inference(avatar_split_clause,[],[f3873,f3735,f10905]) ).

thf(f10905,plain,
    ( spl303_523
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0)) = X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_523])]) ).

thf(f3873,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0)) = X0 )
        | ( X0 = X1 ) )
    | ~ spl303_117 ),
    inference(equality_proxy_clausification,[],[f3872]) ).

thf(f3872,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0)) = X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_117 ),
    inference(equality_proxy_clausification,[],[f3871]) ).

thf(f3871,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_117 ),
    inference(equality_proxy_clausification,[],[f3856]) ).

thf(f3856,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),nil_Se901661471ession) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0))) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),X0),X1) ) )
    | ~ spl303_117 ),
    inference(primitive_instantiation,[],[f3736]) ).

thf(f10903,plain,
    ( spl303_522
    | ~ spl303_116 ),
    inference(avatar_split_clause,[],[f3851,f3731,f10901]) ).

thf(f10901,plain,
    ( spl303_522
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0)) = X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_522])]) ).

thf(f3851,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0)) = X0 )
        | ( X0 = X1 ) )
    | ~ spl303_116 ),
    inference(equality_proxy_clausification,[],[f3850]) ).

thf(f3850,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0)) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_116 ),
    inference(equality_proxy_clausification,[],[f3849]) ).

thf(f3849,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_116 ),
    inference(equality_proxy_clausification,[],[f3836]) ).

thf(f3836,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),nil_Secrecy_KS) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_116 ),
    inference(primitive_instantiation,[],[f3732]) ).

thf(f10899,plain,
    ( spl303_521
    | ~ spl303_115 ),
    inference(avatar_split_clause,[],[f3831,f3727,f10897]) ).

thf(f10897,plain,
    ( spl303_521
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0)) = X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_521])]) ).

thf(f3831,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0)) = X0 )
        | ( X0 = X1 ) )
    | ~ spl303_115 ),
    inference(equality_proxy_clausification,[],[f3830]) ).

thf(f3830,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0)) = X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_115 ),
    inference(equality_proxy_clausification,[],[f3829]) ).

thf(f3829,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_115 ),
    inference(equality_proxy_clausification,[],[f3816]) ).

thf(f3816,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),nil_Secrecy_KS) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),X0),X1) ) )
    | ~ spl303_115 ),
    inference(primitive_instantiation,[],[f3728]) ).

thf(f10863,plain,
    spl303_520,
    inference(avatar_split_clause,[],[f2832,f10861]) ).

thf(f2832,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X1 )
      | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2831]) ).

thf(f2831,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X1 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2827]) ).

thf(f2827,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f2821]) ).

thf(f2821,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1621]) ).

thf(f1621,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ),
    inference(cnf_transformation,[],[f452]) ).

thf(f452,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ),
    inference(fool_elimination,[],[f451]) ).

thf(f451,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) )
        = ( nil_Secrecy_KS = X1 ) )
      & ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f141]) ).

thf(f141,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31) )
        = ( nil_Secrecy_KS = X31 ) )
      & ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_append__is__Nil__conv) ).

thf(f10851,plain,
    ( spl303_519
    | ~ spl303_68
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4657,f4646,f3478,f10849]) ).

thf(f10849,plain,
    ( spl303_519
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_519])]) ).

thf(f4657,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))) = X0 )
    | ~ spl303_68
    | ~ spl303_192 ),
    inference(superposition,[],[f3479,f4647]) ).

thf(f10847,plain,
    ( spl303_518
    | ~ spl303_11
    | ~ spl303_29
    | ~ spl303_157 ),
    inference(avatar_split_clause,[],[f4173,f4145,f3294,f3212,f10845]) ).

thf(f10845,plain,
    ( spl303_518
  <=> ! [X0: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),nil_li311616943ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_518])]) ).

thf(f3212,plain,
    ( spl303_11
  <=> ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,nil_li311616943ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_11])]) ).

thf(f4173,plain,
    ( ! [X0: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),nil_li311616943ession)) )
    | ~ spl303_11
    | ~ spl303_29
    | ~ spl303_157 ),
    inference(forward_demodulation,[],[f4166,f3295]) ).

thf(f4166,plain,
    ( ! [X0: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),nil_li311616943ession)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),nil_Se901661471ession) )
    | ~ spl303_11
    | ~ spl303_157 ),
    inference(superposition,[],[f4146,f3214]) ).

thf(f3214,plain,
    ( ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,nil_li311616943ession) )
    | ~ spl303_11 ),
    inference(avatar_component_clause,[],[f3212]) ).

thf(f10843,plain,
    ( spl303_517
    | ~ spl303_11
    | ~ spl303_26
    | ~ spl303_157 ),
    inference(avatar_split_clause,[],[f4172,f4145,f3282,f3212,f10841]) ).

thf(f10841,plain,
    ( spl303_517
  <=> ! [X0: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,nil_li311616943ession),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_517])]) ).

thf(f4172,plain,
    ( ! [X0: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,nil_li311616943ession),X0)) )
    | ~ spl303_11
    | ~ spl303_26
    | ~ spl303_157 ),
    inference(forward_demodulation,[],[f4164,f3283]) ).

thf(f4164,plain,
    ( ! [X0: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,nil_li311616943ession),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) )
    | ~ spl303_11
    | ~ spl303_157 ),
    inference(superposition,[],[f4146,f3214]) ).

thf(f10838,plain,
    ( spl303_516
    | ~ spl303_88
    | ~ spl303_126 ),
    inference(avatar_split_clause,[],[f3784,f3781,f3565,f10836]) ).

thf(f10836,plain,
    ( spl303_516
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_516])]) ).

thf(f3784,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) = X0 )
    | ~ spl303_88
    | ~ spl303_126 ),
    inference(superposition,[],[f3782,f3566]) ).

thf(f10833,plain,
    ( spl303_515
    | ~ spl303_87
    | ~ spl303_122 ),
    inference(avatar_split_clause,[],[f3760,f3757,f3561,f10831]) ).

thf(f10831,plain,
    ( spl303_515
  <=> ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_515])]) ).

thf(f3760,plain,
    ( ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS))) = X0 )
    | ~ spl303_87
    | ~ spl303_122 ),
    inference(superposition,[],[f3758,f3562]) ).

thf(f10793,plain,
    ( spl303_514
    | ~ spl303_36
    | ~ spl303_346 ),
    inference(avatar_split_clause,[],[f6377,f6366,f3322,f10791]) ).

thf(f10791,plain,
    ( spl303_514
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( nil_Se901661471ession != X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_514])]) ).

thf(f6377,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( nil_Se901661471ession != X0 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X1),X0) ) )
    | ~ spl303_36
    | ~ spl303_346 ),
    inference(superposition,[],[f3323,f6367]) ).

thf(f10789,plain,
    spl303_513,
    inference(avatar_split_clause,[],[f2830,f10787]) ).

thf(f2830,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2829]) ).

thf(f2829,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2828]) ).

thf(f2828,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f2821]) ).

thf(f10785,plain,
    ( spl303_512
    | ~ spl303_36
    | ~ spl303_148 ),
    inference(avatar_split_clause,[],[f4060,f4004,f3322,f10783]) ).

thf(f10783,plain,
    ( spl303_512
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_512])]) ).

thf(f4060,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_36
    | ~ spl303_148 ),
    inference(superposition,[],[f3323,f4005]) ).

thf(f10781,plain,
    ( spl303_511
    | ~ spl303_35
    | ~ spl303_146 ),
    inference(avatar_split_clause,[],[f4046,f3996,f3318,f10779]) ).

thf(f10779,plain,
    ( spl303_511
  <=> ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_511])]) ).

thf(f4046,plain,
    ( ! [X0: secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_35
    | ~ spl303_146 ),
    inference(superposition,[],[f3319,f3997]) ).

thf(f10775,plain,
    ( ~ spl303_509
    | spl303_510 ),
    inference(avatar_contradiction_clause,[],[f10774]) ).

thf(f10774,plain,
    ( $false
    | ~ spl303_509
    | spl303_510 ),
    inference(trivial_inequality_removal,[],[f10771]) ).

thf(f10771,plain,
    ( ( $true != $true )
    | ~ spl303_509
    | spl303_510 ),
    inference(superposition,[],[f10735,f10732]) ).

thf(f10732,plain,
    ( ! [X0: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
    | ~ spl303_509 ),
    inference(avatar_component_clause,[],[f10731]) ).

thf(f10731,plain,
    ( spl303_509
  <=> ! [X0: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_509])]) ).

thf(f10735,plain,
    ( ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,distin1076152135ession)) )
    | spl303_510 ),
    inference(avatar_component_clause,[],[f10734]) ).

thf(f10734,plain,
    ( spl303_510
  <=> ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,distin1076152135ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_510])]) ).

thf(f10737,plain,
    ( spl303_509
    | spl303_510
    | ~ spl303_17
    | ~ spl303_117 ),
    inference(avatar_split_clause,[],[f3870,f3735,f3242,f10734,f10731]) ).

thf(f3242,plain,
    ( spl303_17
  <=> ( vAPP(list_S529945141ession,$o,distin1076152135ession,nil_Se901661471ession) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_17])]) ).

thf(f3870,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,distin1076152135ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) ) )
    | ~ spl303_17
    | ~ spl303_117 ),
    inference(trivial_inequality_removal,[],[f3857]) ).

thf(f3857,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,distin1076152135ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) ) )
    | ~ spl303_17
    | ~ spl303_117 ),
    inference(superposition,[],[f3736,f3244]) ).

thf(f3244,plain,
    ( ( vAPP(list_S529945141ession,$o,distin1076152135ession,nil_Se901661471ession) = $true )
    | ~ spl303_17 ),
    inference(avatar_component_clause,[],[f3242]) ).

thf(f10727,plain,
    ( ~ spl303_507
    | spl303_508 ),
    inference(avatar_contradiction_clause,[],[f10726]) ).

thf(f10726,plain,
    ( $false
    | ~ spl303_507
    | spl303_508 ),
    inference(trivial_inequality_removal,[],[f10723]) ).

thf(f10723,plain,
    ( ( $true != $true )
    | ~ spl303_507
    | spl303_508 ),
    inference(superposition,[],[f10687,f10684]) ).

thf(f10684,plain,
    ( ! [X0: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) )
    | ~ spl303_507 ),
    inference(avatar_component_clause,[],[f10683]) ).

thf(f10683,plain,
    ( spl303_507
  <=> ! [X0: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_507])]) ).

thf(f10687,plain,
    ( ( $true != vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,distin1495927511ecy_KS)) )
    | spl303_508 ),
    inference(avatar_component_clause,[],[f10686]) ).

thf(f10686,plain,
    ( spl303_508
  <=> ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,distin1495927511ecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_508])]) ).

thf(f10689,plain,
    ( spl303_507
    | spl303_508
    | ~ spl303_16
    | ~ spl303_115 ),
    inference(avatar_split_clause,[],[f3828,f3727,f3237,f10686,f10683]) ).

thf(f3237,plain,
    ( spl303_16
  <=> ( vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,nil_Secrecy_KS) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_16])]) ).

thf(f3828,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,distin1495927511ecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) ) )
    | ~ spl303_16
    | ~ spl303_115 ),
    inference(trivial_inequality_removal,[],[f3817]) ).

thf(f3817,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,distin1495927511ecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) ) )
    | ~ spl303_16
    | ~ spl303_115 ),
    inference(superposition,[],[f3728,f3239]) ).

thf(f3239,plain,
    ( ( vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,nil_Secrecy_KS) = $true )
    | ~ spl303_16 ),
    inference(avatar_component_clause,[],[f3237]) ).

thf(f10679,plain,
    spl303_506,
    inference(avatar_split_clause,[],[f2804,f10677]) ).

thf(f10677,plain,
    ( spl303_506
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_506])]) ).

thf(f2804,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( nil_Se901661471ession = X1 ) ),
    inference(equality_proxy_clausification,[],[f2801]) ).

thf(f2801,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) ) ),
    inference(binary_proxy_clausification,[],[f2800]) ).

thf(f2800,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2799]) ).

thf(f2799,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1623]) ).

thf(f1623,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) ),
    inference(cnf_transformation,[],[f456]) ).

thf(f456,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) ),
    inference(fool_elimination,[],[f455]) ).

thf(f455,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
        = ( nil_Se901661471ession = X1 ) )
      & ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f154]) ).

thf(f154,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X28),X31) )
        = ( nil_Se901661471ession = X31 ) )
      & ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_split__Nil__iff) ).

thf(f10673,plain,
    ( ~ spl303_505
    | spl303_504
    | ~ spl303_71
    | ~ spl303_181 ),
    inference(avatar_split_clause,[],[f4497,f4441,f3490,f10666,f10670]) ).

thf(f10670,plain,
    ( spl303_505
  <=> ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,distin1076152135ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_505])]) ).

thf(f10666,plain,
    ( spl303_504
  <=> ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_504])]) ).

thf(f3490,plain,
    ( spl303_71
  <=> ! [X0: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_71])]) ).

thf(f4497,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,distin1076152135ession) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_71
    | ~ spl303_181 ),
    inference(trivial_inequality_removal,[],[f4490]) ).

thf(f4490,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,distin1076152135ession) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_71
    | ~ spl303_181 ),
    inference(superposition,[],[f4442,f3491]) ).

thf(f3491,plain,
    ( ! [X0: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_71 ),
    inference(avatar_component_clause,[],[f3490]) ).

thf(f10668,plain,
    ( ~ spl303_503
    | spl303_504
    | ~ spl303_71
    | ~ spl303_180 ),
    inference(avatar_split_clause,[],[f4483,f4437,f3490,f10666,f10662]) ).

thf(f10662,plain,
    ( spl303_503
  <=> ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,distin1076152135ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_503])]) ).

thf(f4483,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,distin1076152135ession) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_71
    | ~ spl303_180 ),
    inference(trivial_inequality_removal,[],[f4476]) ).

thf(f4476,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true != $true )
        | ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
        | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,distin1076152135ession) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_71
    | ~ spl303_180 ),
    inference(superposition,[],[f4438,f3491]) ).

thf(f10660,plain,
    ( ~ spl303_502
    | spl303_501
    | ~ spl303_70
    | ~ spl303_179 ),
    inference(avatar_split_clause,[],[f4469,f4433,f3486,f10653,f10657]) ).

thf(f10657,plain,
    ( spl303_502
  <=> ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,distin1495927511ecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_502])]) ).

thf(f10653,plain,
    ( spl303_501
  <=> ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_501])]) ).

thf(f3486,plain,
    ( spl303_70
  <=> ! [X0: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_70])]) ).

thf(f4469,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,distin1495927511ecy_KS) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_70
    | ~ spl303_179 ),
    inference(trivial_inequality_removal,[],[f4462]) ).

thf(f4462,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,distin1495927511ecy_KS) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_70
    | ~ spl303_179 ),
    inference(superposition,[],[f4434,f3487]) ).

thf(f3487,plain,
    ( ! [X0: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) )
    | ~ spl303_70 ),
    inference(avatar_component_clause,[],[f3486]) ).

thf(f10655,plain,
    ( ~ spl303_500
    | spl303_501
    | ~ spl303_70
    | ~ spl303_178 ),
    inference(avatar_split_clause,[],[f4455,f4429,f3486,f10653,f10649]) ).

thf(f10649,plain,
    ( spl303_500
  <=> ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,distin1495927511ecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_500])]) ).

thf(f4455,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,distin1495927511ecy_KS) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_70
    | ~ spl303_178 ),
    inference(trivial_inequality_removal,[],[f4448]) ).

thf(f4448,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true != $true )
        | ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,X0) )
        | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,distin1495927511ecy_KS) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_70
    | ~ spl303_178 ),
    inference(superposition,[],[f4430,f3487]) ).

thf(f10641,plain,
    ( spl303_499
    | spl303_497
    | ~ spl303_118 ),
    inference(avatar_split_clause,[],[f3896,f3739,f8838,f10638]) ).

thf(f10638,plain,
    ( spl303_499
  <=> ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_499])]) ).

thf(f8838,plain,
    ( spl303_497
  <=> ! [X0: list_S529945141ession] : ( nil_Se901661471ession = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_497])]) ).

thf(f3896,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)) ) )
    | ~ spl303_118 ),
    inference(equality_proxy_clausification,[],[f3875]) ).

thf(f3875,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
        | ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)) ) )
    | ~ spl303_118 ),
    inference(leibniz_equality_elimination,[],[f3740]) ).

thf(f10601,plain,
    ( spl303_75
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_128
    | ~ spl303_168 ),
    inference(avatar_split_clause,[],[f9152,f4272,f3794,f3565,f3282,f3506]) ).

thf(f3506,plain,
    ( spl303_75
  <=> ! [X1: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_75])]) ).

thf(f9152,plain,
    ( ! [X0: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_26
    | ~ spl303_88
    | ~ spl303_128
    | ~ spl303_168 ),
    inference(forward_demodulation,[],[f3797,f4305]) ).

thf(f3797,plain,
    ( ! [X0: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))) )
    | ~ spl303_88
    | ~ spl303_128 ),
    inference(superposition,[],[f3795,f3566]) ).

thf(f10562,plain,
    spl303_498,
    inference(avatar_split_clause,[],[f2803,f10560]) ).

thf(f10560,plain,
    ( spl303_498
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_498])]) ).

thf(f2803,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(equality_proxy_clausification,[],[f2802]) ).

thf(f2802,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f2800]) ).

thf(f9114,plain,
    ( ~ spl303_36
    | ~ spl303_497 ),
    inference(avatar_contradiction_clause,[],[f9113]) ).

thf(f9113,plain,
    ( $false
    | ~ spl303_36
    | ~ spl303_497 ),
    inference(trivial_inequality_removal,[],[f8949]) ).

thf(f8949,plain,
    ( ( nil_Se901661471ession != nil_Se901661471ession )
    | ~ spl303_36
    | ~ spl303_497 ),
    inference(superposition,[],[f3323,f8839]) ).

thf(f8839,plain,
    ( ! [X0: list_S529945141ession] : ( nil_Se901661471ession = X0 )
    | ~ spl303_497 ),
    inference(avatar_component_clause,[],[f8838]) ).

thf(f9112,plain,
    ( ~ spl303_262
    | ~ spl303_497 ),
    inference(avatar_contradiction_clause,[],[f9111]) ).

thf(f9111,plain,
    ( $false
    | ~ spl303_262
    | ~ spl303_497 ),
    inference(trivial_inequality_removal,[],[f9010]) ).

thf(f9010,plain,
    ( ( nil_Se901661471ession != nil_Se901661471ession )
    | ~ spl303_262
    | ~ spl303_497 ),
    inference(superposition,[],[f5452,f8839]) ).

thf(f5452,plain,
    ( ! [X0: secrecy_Expression] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) )
    | ~ spl303_262 ),
    inference(avatar_component_clause,[],[f5451]) ).

thf(f5451,plain,
    ( spl303_262
  <=> ! [X0: secrecy_Expression] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_262])]) ).

thf(f9106,plain,
    ( ~ spl303_476
    | ~ spl303_497 ),
    inference(avatar_contradiction_clause,[],[f9105]) ).

thf(f9105,plain,
    ( $false
    | ~ spl303_476
    | ~ spl303_497 ),
    inference(trivial_inequality_removal,[],[f9032]) ).

thf(f9032,plain,
    ( ( nil_Se901661471ession != nil_Se901661471ession )
    | ~ spl303_476
    | ~ spl303_497 ),
    inference(superposition,[],[f7589,f8839]) ).

thf(f8840,plain,
    ( spl303_496
    | spl303_497
    | ~ spl303_117 ),
    inference(avatar_split_clause,[],[f3874,f3735,f8838,f8834]) ).

thf(f8834,plain,
    ( spl303_496
  <=> ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_496])]) ).

thf(f3874,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)) ) )
    | ~ spl303_117 ),
    inference(equality_proxy_clausification,[],[f3853]) ).

thf(f3853,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
        | ( nil_Se901661471ession = vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)) ) )
    | ~ spl303_117 ),
    inference(leibniz_equality_elimination,[],[f3736]) ).

thf(f8826,plain,
    ( spl303_495
    | spl303_493
    | ~ spl303_116 ),
    inference(avatar_split_clause,[],[f3852,f3731,f7751,f8823]) ).

thf(f8823,plain,
    ( spl303_495
  <=> ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_495])]) ).

thf(f7751,plain,
    ( spl303_493
  <=> ! [X0: list_Secrecy_KS] : ( nil_Secrecy_KS = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_493])]) ).

thf(f3852,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)) ) )
    | ~ spl303_116 ),
    inference(equality_proxy_clausification,[],[f3833]) ).

thf(f3833,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
        | ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)) ) )
    | ~ spl303_116 ),
    inference(leibniz_equality_elimination,[],[f3732]) ).

thf(f8665,plain,
    ( spl303_494
    | ~ spl303_480
    | ~ spl303_482 ),
    inference(avatar_split_clause,[],[f7697,f7650,f7642,f8663]) ).

thf(f8663,plain,
    ( spl303_494
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_494])]) ).

thf(f7642,plain,
    ( spl303_480
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_480])]) ).

thf(f7650,plain,
    ( spl303_482
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_482])]) ).

thf(f7697,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_480
    | ~ spl303_482 ),
    inference(duplicate_literal_removal,[],[f7690]) ).

thf(f7690,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) )
        | ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_480
    | ~ spl303_482 ),
    inference(superposition,[],[f7651,f7643]) ).

thf(f7643,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_480 ),
    inference(avatar_component_clause,[],[f7642]) ).

thf(f7651,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_482 ),
    inference(avatar_component_clause,[],[f7650]) ).

thf(f7954,plain,
    ( ~ spl303_35
    | ~ spl303_493 ),
    inference(avatar_contradiction_clause,[],[f7953]) ).

thf(f7953,plain,
    ( $false
    | ~ spl303_35
    | ~ spl303_493 ),
    inference(trivial_inequality_removal,[],[f7850]) ).

thf(f7850,plain,
    ( ( nil_Secrecy_KS != nil_Secrecy_KS )
    | ~ spl303_35
    | ~ spl303_493 ),
    inference(superposition,[],[f3319,f7752]) ).

thf(f7752,plain,
    ( ! [X0: list_Secrecy_KS] : ( nil_Secrecy_KS = X0 )
    | ~ spl303_493 ),
    inference(avatar_component_clause,[],[f7751]) ).

thf(f7952,plain,
    ( ~ spl303_259
    | ~ spl303_493 ),
    inference(avatar_contradiction_clause,[],[f7951]) ).

thf(f7951,plain,
    ( $false
    | ~ spl303_259
    | ~ spl303_493 ),
    inference(trivial_inequality_removal,[],[f7877]) ).

thf(f7877,plain,
    ( ( nil_Secrecy_KS != nil_Secrecy_KS )
    | ~ spl303_259
    | ~ spl303_493 ),
    inference(superposition,[],[f5416,f7752]) ).

thf(f5416,plain,
    ( ! [X0: secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_259 ),
    inference(avatar_component_clause,[],[f5415]) ).

thf(f5415,plain,
    ( spl303_259
  <=> ! [X0: secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_259])]) ).

thf(f7753,plain,
    ( spl303_492
    | spl303_493
    | ~ spl303_115 ),
    inference(avatar_split_clause,[],[f3832,f3727,f7751,f7747]) ).

thf(f7747,plain,
    ( spl303_492
  <=> ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_492])]) ).

thf(f3832,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)) ) )
    | ~ spl303_115 ),
    inference(equality_proxy_clausification,[],[f3813]) ).

thf(f3813,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
        | ( nil_Secrecy_KS = vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)) ) )
    | ~ spl303_115 ),
    inference(leibniz_equality_elimination,[],[f3728]) ).

thf(f7745,plain,
    spl303_491,
    inference(avatar_split_clause,[],[f2843,f7743]) ).

thf(f7743,plain,
    ( spl303_491
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_491])]) ).

thf(f2843,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(equality_proxy_clausification,[],[f2842]) ).

thf(f2842,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( nil_Secrecy_KS != X1 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(equality_proxy_clausification,[],[f2841]) ).

thf(f2841,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f2840]) ).

thf(f2840,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2833]) ).

thf(f2833,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1620]) ).

thf(f7741,plain,
    spl303_490,
    inference(avatar_split_clause,[],[f2826,f7739]) ).

thf(f7739,plain,
    ( spl303_490
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_490])]) ).

thf(f2826,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(equality_proxy_clausification,[],[f2825]) ).

thf(f2825,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(equality_proxy_clausification,[],[f2824]) ).

thf(f2824,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(equality_proxy_clausification,[],[f2823]) ).

thf(f2823,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f2822]) ).

thf(f2822,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1621]) ).

thf(f7737,plain,
    spl303_489,
    inference(avatar_split_clause,[],[f2808,f7735]) ).

thf(f7735,plain,
    ( spl303_489
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
        | ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_489])]) ).

thf(f2808,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession != X0 ) ),
    inference(equality_proxy_clausification,[],[f2807]) ).

thf(f2807,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( nil_Se901661471ession != X1 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(equality_proxy_clausification,[],[f2806]) ).

thf(f2806,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f2805]) ).

thf(f2805,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2798]) ).

thf(f2798,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1623]) ).

thf(f7733,plain,
    spl303_488,
    inference(avatar_split_clause,[],[f2791,f7731]) ).

thf(f7731,plain,
    ( spl303_488
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) )
        | ( nil_Se901661471ession != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_488])]) ).

thf(f2791,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) )
      | ( nil_Se901661471ession != X0 ) ),
    inference(equality_proxy_clausification,[],[f2790]) ).

thf(f2790,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(equality_proxy_clausification,[],[f2789]) ).

thf(f2789,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(equality_proxy_clausification,[],[f2788]) ).

thf(f2788,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f2787]) ).

thf(f2787,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1624]) ).

thf(f1624,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ),
    inference(cnf_transformation,[],[f458]) ).

thf(f458,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ),
    inference(fool_elimination,[],[f457]) ).

thf(f457,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) )
        = ( nil_Se901661471ession = X1 ) )
      & ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f140]) ).

thf(f140,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31) )
        = ( nil_Se901661471ession = X31 ) )
      & ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_append__is__Nil__conv) ).

thf(f7701,plain,
    ( spl303_487
    | ~ spl303_478
    | ~ spl303_479 ),
    inference(avatar_split_clause,[],[f7681,f7638,f7634,f7699]) ).

thf(f7699,plain,
    ( spl303_487
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_487])]) ).

thf(f7634,plain,
    ( spl303_478
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_478])]) ).

thf(f7638,plain,
    ( spl303_479
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_479])]) ).

thf(f7681,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_478
    | ~ spl303_479 ),
    inference(duplicate_literal_removal,[],[f7676]) ).

thf(f7676,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0) )
        | ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_478
    | ~ spl303_479 ),
    inference(superposition,[],[f7639,f7635]) ).

thf(f7635,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_478 ),
    inference(avatar_component_clause,[],[f7634]) ).

thf(f7639,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_479 ),
    inference(avatar_component_clause,[],[f7638]) ).

thf(f7668,plain,
    ( spl303_486
    | ~ spl303_94
    | ~ spl303_128 ),
    inference(avatar_split_clause,[],[f3799,f3794,f3597,f7666]) ).

thf(f7666,plain,
    ( spl303_486
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_486])]) ).

thf(f3799,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_128 ),
    inference(superposition,[],[f3795,f3598]) ).

thf(f7664,plain,
    ( spl303_485
    | ~ spl303_93
    | ~ spl303_128 ),
    inference(avatar_split_clause,[],[f3798,f3794,f3593,f7662]) ).

thf(f7662,plain,
    ( spl303_485
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_485])]) ).

thf(f3798,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_128 ),
    inference(superposition,[],[f3795,f3594]) ).

thf(f7660,plain,
    ( spl303_484
    | ~ spl303_94
    | ~ spl303_126 ),
    inference(avatar_split_clause,[],[f3786,f3781,f3597,f7658]) ).

thf(f7658,plain,
    ( spl303_484
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,sK38,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_484])]) ).

thf(f3786,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,sK38,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_94
    | ~ spl303_126 ),
    inference(superposition,[],[f3782,f3598]) ).

thf(f7656,plain,
    ( spl303_483
    | ~ spl303_93
    | ~ spl303_126 ),
    inference(avatar_split_clause,[],[f3785,f3781,f3593,f7654]) ).

thf(f7654,plain,
    ( spl303_483
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_483])]) ).

thf(f3785,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_93
    | ~ spl303_126 ),
    inference(superposition,[],[f3782,f3594]) ).

thf(f7652,plain,
    ( spl303_482
    | ~ spl303_92
    | ~ spl303_124 ),
    inference(avatar_split_clause,[],[f3774,f3769,f3589,f7650]) ).

thf(f3774,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_92
    | ~ spl303_124 ),
    inference(superposition,[],[f3770,f3590]) ).

thf(f7648,plain,
    spl303_481,
    inference(avatar_split_clause,[],[f2797,f7646]) ).

thf(f2797,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X1 )
      | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2796]) ).

thf(f2796,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X1 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2792]) ).

thf(f2792,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f2786]) ).

thf(f2786,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1)) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1624]) ).

thf(f7644,plain,
    ( spl303_480
    | ~ spl303_91
    | ~ spl303_124 ),
    inference(avatar_split_clause,[],[f3773,f3769,f3585,f7642]) ).

thf(f3773,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_91
    | ~ spl303_124 ),
    inference(superposition,[],[f3770,f3586]) ).

thf(f7640,plain,
    ( spl303_479
    | ~ spl303_92
    | ~ spl303_122 ),
    inference(avatar_split_clause,[],[f3762,f3757,f3589,f7638]) ).

thf(f3762,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_92
    | ~ spl303_122 ),
    inference(superposition,[],[f3758,f3590]) ).

thf(f7636,plain,
    ( spl303_478
    | ~ spl303_91
    | ~ spl303_122 ),
    inference(avatar_split_clause,[],[f3761,f3757,f3585,f7634]) ).

thf(f3761,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
    | ~ spl303_91
    | ~ spl303_122 ),
    inference(superposition,[],[f3758,f3586]) ).

thf(f7632,plain,
    ( spl303_477
    | ~ spl303_19
    | ~ spl303_85 ),
    inference(avatar_split_clause,[],[f3559,f3550,f3254,f7630]) ).

thf(f7630,plain,
    ( spl303_477
  <=> ! [X0: secrecy_KS,X1: secrecy_Keys] :
        ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) != X0 )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_477])]) ).

thf(f3254,plain,
    ( spl303_19
  <=> ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_19])]) ).

thf(f3559,plain,
    ( ! [X0: secrecy_KS,X1: secrecy_Keys] :
        ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) != X0 )
        | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) )
    | ~ spl303_19
    | ~ spl303_85 ),
    inference(superposition,[],[f3255,f3551]) ).

thf(f3255,plain,
    ( ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) )
    | ~ spl303_19 ),
    inference(avatar_component_clause,[],[f3254]) ).

thf(f7590,plain,
    ( spl303_476
    | ~ spl303_36
    | ~ spl303_192 ),
    inference(avatar_split_clause,[],[f4655,f4646,f3322,f7588]) ).

thf(f4655,plain,
    ( ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
    | ~ spl303_36
    | ~ spl303_192 ),
    inference(superposition,[],[f3323,f4647]) ).

thf(f7586,plain,
    ( spl303_475
    | ~ spl303_68
    | ~ spl303_88 ),
    inference(avatar_split_clause,[],[f3580,f3565,f3478,f7584]) ).

thf(f7584,plain,
    ( spl303_475
  <=> ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_475])]) ).

thf(f3580,plain,
    ( ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) = X0 )
    | ~ spl303_68
    | ~ spl303_88 ),
    inference(superposition,[],[f3479,f3566]) ).

thf(f7582,plain,
    ( spl303_474
    | ~ spl303_69
    | ~ spl303_88 ),
    inference(avatar_split_clause,[],[f3579,f3565,f3482,f7580]) ).

thf(f7580,plain,
    ( spl303_474
  <=> ! [X0: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_474])]) ).

thf(f3579,plain,
    ( ! [X0: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) )
    | ~ spl303_69
    | ~ spl303_88 ),
    inference(superposition,[],[f3483,f3566]) ).

thf(f7578,plain,
    spl303_473,
    inference(avatar_split_clause,[],[f2795,f7576]) ).

thf(f2795,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2794]) ).

thf(f2794,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2793]) ).

thf(f2793,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f2786]) ).

thf(f7468,plain,
    ( spl303_472
    | ~ spl303_36
    | ~ spl303_328 ),
    inference(avatar_split_clause,[],[f6211,f6155,f3322,f7466]) ).

thf(f7466,plain,
    ( spl303_472
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_472])]) ).

thf(f6211,plain,
    ( ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) )
    | ~ spl303_36
    | ~ spl303_328 ),
    inference(superposition,[],[f3323,f6156]) ).

thf(f7464,plain,
    ( spl303_471
    | ~ spl303_35
    | ~ spl303_327 ),
    inference(avatar_split_clause,[],[f6200,f6151,f3318,f7462]) ).

thf(f7462,plain,
    ( spl303_471
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_471])]) ).

thf(f6200,plain,
    ( ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) )
    | ~ spl303_35
    | ~ spl303_327 ),
    inference(superposition,[],[f3319,f6152]) ).

thf(f7460,plain,
    ( spl303_470
    | ~ spl303_3
    | ~ spl303_53 ),
    inference(avatar_split_clause,[],[f3412,f3402,f3143,f7458]) ).

thf(f7458,plain,
    ( spl303_470
  <=> ! [X0: list_S529945141ession,X1: $o] :
        ( ( $true = X1 )
        | ( $false = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_470])]) ).

thf(f3402,plain,
    ( spl303_53
  <=> ! [X0: $o,X1: list_S529945141ession] :
        ( ( $true = X0 )
        | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_53])]) ).

thf(f3412,plain,
    ( ! [X0: list_S529945141ession,X1: $o] :
        ( ( $true = X1 )
        | ( $false = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_53 ),
    inference(trivial_inequality_removal,[],[f3411]) ).

thf(f3411,plain,
    ( ! [X0: list_S529945141ession,X1: $o] :
        ( ( $true != $true )
        | ( $true = X1 )
        | ( $false = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_53 ),
    inference(superposition,[],[f3403,f3144]) ).

thf(f3403,plain,
    ( ! [X0: $o,X1: list_S529945141ession] :
        ( ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) )
        | ( $true = X0 ) )
    | ~ spl303_53 ),
    inference(avatar_component_clause,[],[f3402]) ).

thf(f7456,plain,
    ( spl303_469
    | ~ spl303_3
    | ~ spl303_52 ),
    inference(avatar_split_clause,[],[f3410,f3398,f3143,f7454]) ).

thf(f7454,plain,
    ( spl303_469
  <=> ! [X0: list_S529945141ession,X1: $o] :
        ( ( nil_Se901661471ession = X0 )
        | ( $false = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_469])]) ).

thf(f3398,plain,
    ( spl303_52
  <=> ! [X0: $o,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = X1 )
        | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_52])]) ).

thf(f3410,plain,
    ( ! [X0: list_S529945141ession,X1: $o] :
        ( ( nil_Se901661471ession = X0 )
        | ( $false = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_52 ),
    inference(trivial_inequality_removal,[],[f3409]) ).

thf(f3409,plain,
    ( ! [X0: list_S529945141ession,X1: $o] :
        ( ( $true != $true )
        | ( nil_Se901661471ession = X0 )
        | ( $false = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_52 ),
    inference(superposition,[],[f3399,f3144]) ).

thf(f3399,plain,
    ( ! [X0: $o,X1: list_S529945141ession] :
        ( ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) )
        | ( nil_Se901661471ession = X1 ) )
    | ~ spl303_52 ),
    inference(avatar_component_clause,[],[f3398]) ).

thf(f7452,plain,
    ( spl303_468
    | ~ spl303_3
    | ~ spl303_51 ),
    inference(avatar_split_clause,[],[f3408,f3394,f3143,f7450]) ).

thf(f7450,plain,
    ( spl303_468
  <=> ! [X0: list_Secrecy_KS,X1: $o] :
        ( ( $true = X1 )
        | ( $false = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_468])]) ).

thf(f3394,plain,
    ( spl303_51
  <=> ! [X0: $o,X1: list_Secrecy_KS] :
        ( ( $true = X0 )
        | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_51])]) ).

thf(f3408,plain,
    ( ! [X0: list_Secrecy_KS,X1: $o] :
        ( ( $true = X1 )
        | ( $false = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_51 ),
    inference(trivial_inequality_removal,[],[f3407]) ).

thf(f3407,plain,
    ( ! [X0: list_Secrecy_KS,X1: $o] :
        ( ( $true != $true )
        | ( $true = X1 )
        | ( $false = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_51 ),
    inference(superposition,[],[f3395,f3144]) ).

thf(f3395,plain,
    ( ! [X0: $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) )
        | ( $true = X0 ) )
    | ~ spl303_51 ),
    inference(avatar_component_clause,[],[f3394]) ).

thf(f7448,plain,
    ( spl303_467
    | ~ spl303_3
    | ~ spl303_50 ),
    inference(avatar_split_clause,[],[f3406,f3390,f3143,f7446]) ).

thf(f7446,plain,
    ( spl303_467
  <=> ! [X0: list_Secrecy_KS,X1: $o] :
        ( ( nil_Secrecy_KS = X0 )
        | ( $false = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_467])]) ).

thf(f3390,plain,
    ( spl303_50
  <=> ! [X0: $o,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_50])]) ).

thf(f3406,plain,
    ( ! [X0: list_Secrecy_KS,X1: $o] :
        ( ( nil_Secrecy_KS = X0 )
        | ( $false = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_50 ),
    inference(trivial_inequality_removal,[],[f3405]) ).

thf(f3405,plain,
    ( ! [X0: list_Secrecy_KS,X1: $o] :
        ( ( $true != $true )
        | ( nil_Secrecy_KS = X0 )
        | ( $false = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X0),X1) ) )
    | ~ spl303_3
    | ~ spl303_50 ),
    inference(superposition,[],[f3391,f3144]) ).

thf(f3391,plain,
    ( ! [X0: $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) )
        | ( nil_Secrecy_KS = X1 ) )
    | ~ spl303_50 ),
    inference(avatar_component_clause,[],[f3390]) ).

thf(f7444,plain,
    spl303_466,
    inference(avatar_split_clause,[],[f2773,f7442]) ).

thf(f7442,plain,
    ( spl303_466
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_466])]) ).

thf(f2773,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) != X1 ) ),
    inference(equality_proxy_clausification,[],[f2772]) ).

thf(f2772,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X1) ) ),
    inference(equality_proxy_clausification,[],[f2768]) ).

thf(f2768,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X1) ) ),
    inference(binary_proxy_clausification,[],[f1626]) ).

thf(f1626,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X1) ),
    inference(cnf_transformation,[],[f462]) ).

thf(f462,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X1) ),
    inference(fool_elimination,[],[f461]) ).

thf(f461,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) = X1 )
      = ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f147]) ).

thf(f147,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31) = X31 )
      = ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_append__self__conv2) ).

thf(f7440,plain,
    spl303_465,
    inference(avatar_split_clause,[],[f2771,f7438]) ).

thf(f7438,plain,
    ( spl303_465
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_465])]) ).

thf(f2771,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) = X1 ) ),
    inference(equality_proxy_clausification,[],[f2770]) ).

thf(f2770,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X1) ) ),
    inference(equality_proxy_clausification,[],[f2769]) ).

thf(f2769,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X1) ) ),
    inference(binary_proxy_clausification,[],[f1626]) ).

thf(f7432,plain,
    spl303_464,
    inference(avatar_split_clause,[],[f1503,f7429]) ).

thf(f7429,plain,
    ( spl303_464
  <=> ( lexord1123423577ession = 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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_464])]) ).

thf(f1503,plain,
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    inference(cnf_transformation,[],[f378]) ).

thf(f378,plain,
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ression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)),bCOMB,vNOT))),cCOMB)))))))))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)),bCOMB,vNOT))))))))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),bCOMB,cCOMB),lexord1123423577ession))))))),
    inference(fool_elimination,[],[f377]) ).

thf(f377,plain,
    ( lexord1123423577ession
    = ( ^ [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
          ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession,X6: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X5),X6)
              & ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X3)
              & ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
          | ? [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession,X10: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 ) )
          | ? [X11: list_S529945141ession] :
              ( ( X2 = X11 )
              & ( nil_Se901661471ession = X1 ) ) ) ) ),
    inference(rectify,[],[f120]) ).

thf(f120,axiom,
    ( lexord1123423577ession
    = ( ^ [X67: secrecy_Expression > secrecy_Expression > $o,X62: list_S529945141ession,X63: list_S529945141ession] :
          ( ? [X47: secrecy_Expression,X29: secrecy_Expression,X64: list_S529945141ession,X30: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X67),X64),X30)
              & ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X67,X29),X47)
              & ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X67,X47),X29)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X29),X30) = X63 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X47),X64) = X62 ) )
          | ? [X47: secrecy_Expression,X29: secrecy_Expression,X64: list_S529945141ession,X30: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X67,X47),X29)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X29),X30) = X63 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X47),X64) = X62 ) )
          | ? [X30: list_S529945141ession] :
              ( ( X30 = X63 )
              & ( nil_Se901661471ession = X62 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ord_Olexordp__eq_Osimps) ).

thf(f7427,plain,
    spl303_463,
    inference(avatar_split_clause,[],[f1501,f7424]) ).

thf(f7424,plain,
    ( spl303_463
  <=> ( lexord948960489ecy_KS = vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vOR))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),$o),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),bCOMB,vSIGMA(list_Secrecy_KS))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),vAPP(sTfun(sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vAND),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS))))),vEQ(list_Secrecy_KS))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),$o),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),bCOMB,vSIGMA(list_Secrecy_KS)))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),$o),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),bCOMB,vSIGMA(list_Secrecy_KS))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))))),bCOMB,vAPP(sTfun(sTfun(list_Secrec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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_463])]) ).

thf(f1501,plain,
    lexord948960489ecy_KS = 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un($o,$o))),bCOMB,vAND)))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),vAPP(sTfun(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun($o,$o)),sTfun($o,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),bCOMB,vNOT))),cCOMB)))))))))),vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),bCOMB,vNOT))))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,cCOMB),lexord948960489ecy_KS))))))),
    inference(cnf_transformation,[],[f374]) ).

thf(f374,plain,
    lexord948960489ecy_KS = 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un($o,$o))),bCOMB,vAND)))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),vAPP(sTfun(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun($o,$o)),sTfun($o,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),bCOMB,vNOT))),cCOMB)))))))))),vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,$o)),bCOMB,vNOT))))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,cCOMB),lexord948960489ecy_KS))))))),
    inference(fool_elimination,[],[f373]) ).

thf(f373,plain,
    ( lexord948960489ecy_KS
    = ( ^ [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
          ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS,X6: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X5),X6)
              & ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X3)
              & ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
          | ? [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS,X10: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 ) )
          | ? [X11: list_Secrecy_KS] :
              ( ( X2 = X11 )
              & ( nil_Secrecy_KS = X1 ) ) ) ) ),
    inference(rectify,[],[f119]) ).

thf(f119,axiom,
    ( lexord948960489ecy_KS
    = ( ^ [X67: secrecy_KS > secrecy_KS > $o,X62: list_Secrecy_KS,X63: list_Secrecy_KS] :
          ( ? [X47: secrecy_KS,X29: secrecy_KS,X64: list_Secrecy_KS,X30: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X67),X64),X30)
              & ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X67,X29),X47)
              & ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X67,X47),X29)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X29),X30) = X63 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X47),X64) = X62 ) )
          | ? [X47: secrecy_KS,X29: secrecy_KS,X64: list_Secrecy_KS,X30: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X67,X47),X29)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X29),X30) = X63 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X47),X64) = X62 ) )
          | ? [X30: list_Secrecy_KS] :
              ( ( X30 = X63 )
              & ( nil_Secrecy_KS = X62 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_ord_Olexordp__eq_Osimps) ).

thf(f7418,plain,
    spl303_462,
    inference(avatar_split_clause,[],[f1500,f7415]) ).

thf(f7415,plain,
    ( spl303_462
  <=> ( listre84909707ession = 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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_462])]) ).

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pression,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),bCOMB,cCOMB),listre84909707ession))))))),
    inference(cnf_transformation,[],[f372]) ).

thf(f372,plain,
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pression,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),bCOMB,cCOMB),listre84909707ession))))))),
    inference(fool_elimination,[],[f371]) ).

thf(f371,plain,
    ( listre84909707ession
    = ( ^ [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
          ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession,X6: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6)
              & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
          | ( ( nil_Se901661471ession = X2 )
            & ( nil_Se901661471ession = X1 ) ) ) ) ),
    inference(rectify,[],[f101]) ).

thf(f101,axiom,
    ( listre84909707ession
    = ( ^ [X61: secrecy_Expression > secrecy_Expression > $o,X62: list_S529945141ession,X63: list_S529945141ession] :
          ( ? [X47: secrecy_Expression,X29: secrecy_Expression,X64: list_S529945141ession,X30: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X61),X64),X30)
              & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X61,X47),X29)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X29),X30) = X63 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X47),X64) = X62 ) )
          | ( ( nil_Se901661471ession = X63 )
            & ( nil_Se901661471ession = X62 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_listrelp_Osimps) ).

thf(f7413,plain,
    spl303_461,
    inference(avatar_split_clause,[],[f1499,f7410]) ).

thf(f7410,plain,
    ( spl303_461
  <=> ( listre565996059ecy_KS = vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun($o,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(list_Secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun($o,$o)),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_S529945141ession,sTfun($o,$o)),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,bCOMB),vAPP(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),bCOMB,vAND),vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)))),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),$o),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),bCOMB,vSIGMA(list_Secrecy_KS)))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)))),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)))),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secr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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_461])]) ).

thf(f1499,plain,
    listre565996059ecy_KS = 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fun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)))),bCOMB,cCOMB),listre565996059ecy_KS))))))),
    inference(cnf_transformation,[],[f370]) ).

thf(f370,plain,
    listre565996059ecy_KS = 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y_KS,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vAND)))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),vAPP(sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))))),vAPP(sTfun(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))))),sTfun(sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))))),bCOMB,bCOMB),vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),vAPP(sTfun(sTfun(sTfun(secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),sTfun(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(list_S529945141ession,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))))),bCOMB,bCOMB),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(list_S529945141ession,sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_Expression,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun($o,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun($o,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)))),bCOMB,cCOMB),listre565996059ecy_KS))))))),
    inference(fool_elimination,[],[f369]) ).

thf(f369,plain,
    ( listre565996059ecy_KS
    = ( ^ [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
          ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession,X6: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6)
              & vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
          | ( ( nil_Secrecy_KS = X2 )
            & ( nil_Se901661471ession = X1 ) ) ) ) ),
    inference(rectify,[],[f100]) ).

thf(f100,axiom,
    ( listre565996059ecy_KS
    = ( ^ [X61: secrecy_Expression > secrecy_KS > $o,X62: list_S529945141ession,X63: list_Secrecy_KS] :
          ( ? [X47: secrecy_Expression,X29: secrecy_KS,X64: list_S529945141ession,X30: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X61),X64),X30)
              & vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X61,X47),X29)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X29),X30) = X63 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X47),X64) = X62 ) )
          | ( ( nil_Secrecy_KS = X63 )
            & ( nil_Se901661471ession = X62 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_listrelp_Osimps) ).

thf(f7408,plain,
    spl303_460,
    inference(avatar_split_clause,[],[f2761,f7406]) ).

thf(f7406,plain,
    ( spl303_460
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_460])]) ).

thf(f2761,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) != X0 ) ),
    inference(equality_proxy_clausification,[],[f2760]) ).

thf(f2760,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X1 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X0) ) ),
    inference(equality_proxy_clausification,[],[f2756]) ).

thf(f2756,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X0) ) ),
    inference(binary_proxy_clausification,[],[f1628]) ).

thf(f1628,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X0) ),
    inference(cnf_transformation,[],[f466]) ).

thf(f466,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X0) ),
    inference(fool_elimination,[],[f465]) ).

thf(f465,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) = X0 )
      = ( nil_Secrecy_KS = X1 ) ),
    inference(rectify,[],[f149]) ).

thf(f149,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31) = X28 )
      = ( nil_Secrecy_KS = X31 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_self__append__conv) ).

thf(f7404,plain,
    spl303_459,
    inference(avatar_split_clause,[],[f1498,f7401]) ).

thf(f7401,plain,
    ( spl303_459
  <=> ( listre1601064475ession = vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun($o,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(list_S529945141ession,$o),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o)))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vAND),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)))),vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession)))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(list_S529945141ession,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vSIGMA(list_S529945141ession)))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))))),bCOMB,vAPP(sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTf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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_459])]) ).

thf(f1498,plain,
    listre1601064475ession = 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sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun($o,$o)),sTfun($o,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)))),bCOMB,cCOMB),listre1601064475ession))))))),
    inference(cnf_transformation,[],[f368]) ).

thf(f368,plain,
    listre1601064475ession = 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COMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(secrecy_Expression,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND)))))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))))),vAPP(sTfun(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(sTfun(sTfun(secrecy_Expression,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))),sTfun(sTfun(secrecy_Expression,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun(secrecy_KS,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun($o,$o)),sTfun($o,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession))),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)))),bCOMB,cCOMB),listre1601064475ession))))))),
    inference(fool_elimination,[],[f367]) ).

thf(f367,plain,
    ( listre1601064475ession
    = ( ^ [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
          ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS,X6: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6)
              & vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
          | ( ( nil_Se901661471ession = X2 )
            & ( nil_Secrecy_KS = X1 ) ) ) ) ),
    inference(rectify,[],[f99]) ).

thf(f99,axiom,
    ( listre1601064475ession
    = ( ^ [X61: secrecy_KS > secrecy_Expression > $o,X62: list_Secrecy_KS,X63: list_S529945141ession] :
          ( ? [X47: secrecy_KS,X29: secrecy_Expression,X64: list_Secrecy_KS,X30: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X61),X64),X30)
              & vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X61,X47),X29)
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X29),X30) = X63 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X47),X64) = X62 ) )
          | ( ( nil_Se901661471ession = X63 )
            & ( nil_Secrecy_KS = X62 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_listrelp_Osimps) ).

thf(f7399,plain,
    spl303_458,
    inference(avatar_split_clause,[],[f1497,f7396]) ).

thf(f7396,plain,
    ( spl303_458
  <=> ( listre788412843ecy_KS = vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,$o)),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,$o)))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_Secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun($o,$o))),bCOMB,vAND),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)))),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS)))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),$o),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),bCOMB,vSIGMA(list_Secrecy_KS)))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vAPP(sTfun(sTfun(list_Secrecy_KS,$o),$o),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),bCOMB,vSIGMA(list_Secrecy_KS))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_458])]) ).

thf(f1497,plain,
    listre788412843ecy_KS = 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st_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),vAPP(sTfun(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun($o,$o)),sTfun($o,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,cCOMB),listre788412843ecy_KS))))))),
    inference(cnf_transformation,[],[f366]) ).

thf(f366,plain,
    listre788412843ecy_KS = 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st_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),vAPP(sTfun(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),vAPP(sTfun(sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))))),bCOMB,bCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))))),bCOMB,vAPP(sTfun(sTfun($o,sTfun(secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun(secrecy_KS,$o))))),bCOMB,bCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,sTfun($o,$o)),sTfun($o,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))),sTfun(list_Secrecy_KS,sTfun($o,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_KS,$o),sTfun(secrecy_KS,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)))),bCOMB,cCOMB),vAPP(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS))),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS))))))))))))),cCOMB))))))))),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),vAPP(sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o))),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)))),bCOMB,cCOMB),listre788412843ecy_KS))))))),
    inference(fool_elimination,[],[f365]) ).

thf(f365,plain,
    ( listre788412843ecy_KS
    = ( ^ [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
          ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS,X6: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6)
              & vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
          | ( ( nil_Secrecy_KS = X2 )
            & ( nil_Secrecy_KS = X1 ) ) ) ) ),
    inference(rectify,[],[f98]) ).

thf(f98,axiom,
    ( listre788412843ecy_KS
    = ( ^ [X61: secrecy_KS > secrecy_KS > $o,X62: list_Secrecy_KS,X63: list_Secrecy_KS] :
          ( ? [X47: secrecy_KS,X29: secrecy_KS,X64: list_Secrecy_KS,X30: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X61),X64),X30)
              & vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X61,X47),X29)
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X29),X30) = X63 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X47),X64) = X62 ) )
          | ( ( nil_Secrecy_KS = X63 )
            & ( nil_Secrecy_KS = X62 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_listrelp_Osimps) ).

thf(f7390,plain,
    spl303_457,
    inference(avatar_split_clause,[],[f1494,f7387]) ).

thf(f7387,plain,
    ( spl303_457
  <=> ( knowle1268625169orrect = vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vEQ($o))),eout))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Keys,$o),$o),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,$o)),bCOMB,vSIGMA(secrecy_Keys))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)))),bCOMB,vAPP(sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),cCOMB,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o))),bCOMB,vEQ(secrecy_Expression)),secrecy_kE)))))),vAPP(sTfun(secrecy_specID,set_Secrecy_Keys),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_Keys),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_Keys,$o)),sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),cCOMB,member_Secrecy_Keys)),specKeys)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Secrets,$o),$o),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,$o)),bCOMB,vSIGMA(secrecy_Secrets))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)))),bCOMB,vAPP(sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),cCOMB,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o))),bCOMB,vEQ(secrecy_Expression)),secrecy_sE)))))),vAPP(sTfun(secrecy_specID,set_Secrecy_Secrets),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_Secrets),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o)),sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),cCOMB,member2138796287ecrets)),specSecrets))))))),vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o)))),bCOMB,bCOMB),knowle731562421_knows)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_457])]) ).

thf(f1494,plain,
    knowle1268625169orrect = vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vEQ($o))),eout))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Keys,$o),$o),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,$o)),bCOMB,vSIGMA(secrecy_Keys))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)))),bCOMB,vAPP(sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),cCOMB,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o))),bCOMB,vEQ(secrecy_Expression)),secrecy_kE)))))),vAPP(sTfun(secrecy_specID,set_Secrecy_Keys),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_Keys),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_Keys,$o)),sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),cCOMB,member_Secrecy_Keys)),specKeys)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Secrets,$o),$o),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,$o)),bCOMB,vSIGMA(secrecy_Secrets))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)))),bCOMB,vAPP(sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),cCOMB,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o))),bCOMB,vEQ(secrecy_Expression)),secrecy_sE)))))),vAPP(sTfun(secrecy_specID,set_Secrecy_Secrets),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_Secrets),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o)),sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),cCOMB,member2138796287ecrets)),specSecrets))))))),vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o)))),bCOMB,bCOMB),knowle731562421_knows)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession)))),
    inference(cnf_transformation,[],[f360]) ).

thf(f360,plain,
    knowle1268625169orrect = vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vEQ($o))),eout))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(secrecy_Expression,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Expression,$o),sTfun(secrecy_Expression,sTfun($o,$o))),bCOMB,vOR)),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Keys,$o),$o),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,$o)),bCOMB,vSIGMA(secrecy_Keys))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)))),bCOMB,vAPP(sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o))),cCOMB,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(secrecy_Expression,$o))),bCOMB,vEQ(secrecy_Expression)),secrecy_kE)))))),vAPP(sTfun(secrecy_specID,set_Secrecy_Keys),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_Keys),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_Keys,$o)),sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),cCOMB,member_Secrecy_Keys)),specKeys)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Secrets,$o),$o),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,$o)),bCOMB,vSIGMA(secrecy_Secrets))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)))),bCOMB,vAPP(sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o))),cCOMB,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(secrecy_Expression,$o))),bCOMB,vEQ(secrecy_Expression)),secrecy_sE)))))),vAPP(sTfun(secrecy_specID,set_Secrecy_Secrets),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_Secrets),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o)),sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),cCOMB,member2138796287ecrets)),specSecrets))))))),vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_specID,sTfun(secrecy_Expression,$o))),cCOMB,vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,$o)))),bCOMB,bCOMB),knowle731562421_knows)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession)))),
    inference(fool_elimination,[],[f359]) ).

thf(f359,plain,
    ( knowle1268625169orrect
    = ( ^ [X0: secrecy_specID,X1: secrecy_Expression] :
          ( ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
          | ? [X2: secrecy_Secrets] :
              ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X2),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0))
              & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2) = X1 ) )
          | ? [X3: secrecy_Keys] :
              ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0))
              & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = X1 ) ) ) ) ),
    inference(rectify,[],[f78]) ).

thf(f78,axiom,
    ( knowle1268625169orrect
    = ( ^ [X52: secrecy_specID,X53: secrecy_Expression] :
          ( ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X52),X53) = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X52),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X53),nil_Se901661471ession)) )
          | ? [X55: secrecy_Secrets] :
              ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X55),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X52))
              & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X55) = X53 ) )
          | ? [X54: secrecy_Keys] :
              ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X54),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X52))
              & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X54) = X53 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_eoutKnowsECorrect__def) ).

thf(f7385,plain,
    spl303_456,
    inference(avatar_split_clause,[],[f1495,f7382]) ).

thf(f7382,plain,
    ( spl303_456
  <=> ( notSpe1586871396tsExpr = vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Keys,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vPI(secrecy_Keys))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Keys,$o),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o))),bCOMB,mem_Se1967555118ession),secrecy_kE)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)),bCOMB,vNOT)),vAPP(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(set_Secrecy_KS,sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_KS),sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o)),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Keys,secrecy_KS),sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o))),bCOMB,member_Secrecy_KS2),secrecy_kKS))),specKeysSecrets))))))),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Secrets,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vPI(secrecy_Secrets))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Secrets,$o),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o))),bCOMB,mem_Se1967555118ession),secrecy_sE)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)),bCOMB,vNOT)),vAPP(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(set_Secrecy_KS,sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_KS),sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o)),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_KS),sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o))),bCOMB,member_Secrecy_KS2),secrecy_sKS))),specKeysSecrets))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_456])]) ).

thf(f1495,plain,
    notSpe1586871396tsExpr = vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Keys,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vPI(secrecy_Keys))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Keys,$o),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o))),bCOMB,mem_Se1967555118ession),secrecy_kE)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)),bCOMB,vNOT)),vAPP(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(set_Secrecy_KS,sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_KS),sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o)),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Keys,secrecy_KS),sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o))),bCOMB,member_Secrecy_KS2),secrecy_kKS))),specKeysSecrets))))))),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Secrets,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vPI(secrecy_Secrets))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Secrets,$o),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o))),bCOMB,mem_Se1967555118ession),secrecy_sE)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)),bCOMB,vNOT)),vAPP(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(set_Secrecy_KS,sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_KS),sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o)),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_KS),sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o))),bCOMB,member_Secrecy_KS2),secrecy_sKS))),specKeysSecrets))))),
    inference(cnf_transformation,[],[f362]) ).

thf(f362,plain,
    notSpe1586871396tsExpr = vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),sCOMB,vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),vAPP(sTfun(sTfun(list_S529945141ession,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(secrecy_specID,sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,$o)))),bCOMB,sCOMB),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o))),vAPP(sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list_S529945141ession,$o),sTfun(list_S529945141ession,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Keys,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vPI(secrecy_Keys))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(secrecy_Keys,$o),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),vAPP(sTfun(sTfun(secrecy_Keys,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Keys,secrecy_Expression),sTfun(secrecy_Keys,sTfun(list_S529945141ession,$o))),bCOMB,mem_Se1967555118ession),secrecy_kE)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Keys,$o),sTfun(secrecy_Keys,$o)),bCOMB,vNOT)),vAPP(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o)),vAPP(sTfun(set_Secrecy_KS,sTfun(secrecy_Keys,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Keys,$o))),bCOMB,vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_Keys,$o)),cCOMB,vAPP(sTfun(secrecy_Keys,secrecy_KS),sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o)),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Keys,secrecy_KS),sTfun(secrecy_Keys,sTfun(set_Secrecy_KS,$o))),bCOMB,member_Secrecy_KS2),secrecy_kKS))),specKeysSecrets))))))),vAPP(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o)),vAPP(sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(secrecy_specID,sTfun(list_S529945141ession,$o))),bCOMB,vAPP(sTfun(sTfun(secrecy_Secrets,$o),$o),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,$o)),bCOMB,vPI(secrecy_Secrets))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)))),bCOMB,vAPP(sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(secrecy_Secrets,$o),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o))),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)))),bCOMB,sCOMB),vAPP(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o))),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),sTfun(sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o)),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_Expression),sTfun(secrecy_Secrets,sTfun(list_S529945141ession,$o))),bCOMB,mem_Se1967555118ession),secrecy_sE)))))),vAPP(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(secrecy_Secrets,$o),sTfun(secrecy_Secrets,$o)),bCOMB,vNOT)),vAPP(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o)),vAPP(sTfun(set_Secrecy_KS,sTfun(secrecy_Secrets,$o)),sTfun(sTfun(secrecy_specID,set_Secrecy_KS),sTfun(secrecy_specID,sTfun(secrecy_Secrets,$o))),bCOMB,vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_Secrets,$o)),cCOMB,vAPP(sTfun(secrecy_Secrets,secrecy_KS),sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o)),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Secrets,secrecy_KS),sTfun(secrecy_Secrets,sTfun(set_Secrecy_KS,$o))),bCOMB,member_Secrecy_KS2),secrecy_sKS))),specKeysSecrets))))),
    inference(fool_elimination,[],[f361]) ).

thf(f361,plain,
    ( notSpe1586871396tsExpr
    = ( ^ [X0: secrecy_specID,X1: list_S529945141ession] :
          ( ! [X2: secrecy_Secrets] :
              ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2)),X1)
             => ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X2)),vAPP(secrecy_specID,set_Secrecy_KS,specKeysSecrets,X0)) )
          & ! [X3: secrecy_Keys] :
              ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3)),X1)
             => ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3)),vAPP(secrecy_specID,set_Secrecy_KS,specKeysSecrets,X0)) ) ) ) ),
    inference(rectify,[],[f212]) ).

thf(f212,axiom,
    ( notSpe1586871396tsExpr
    = ( ^ [X90: secrecy_specID,X53: list_S529945141ession] :
          ( ! [X29: secrecy_Secrets] :
              ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X29)),X53)
             => ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X29)),vAPP(secrecy_specID,set_Secrecy_KS,specKeysSecrets,X90)) )
          & ! [X47: secrecy_Keys] :
              ( vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X47)),X53)
             => ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X47)),vAPP(secrecy_specID,set_Secrecy_KS,specKeysSecrets,X90)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_notSpecKeysSecretsExpr__def) ).

thf(f7372,plain,
    spl303_455,
    inference(avatar_split_clause,[],[f1949,f7370]) ).

thf(f7370,plain,
    ( spl303_455
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK251,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) )
        | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_455])]) ).

thf(f1949,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK251,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) )
      | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1441]) ).

thf(f1441,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK251,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) = X1 ) )
      | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK250,sK251,sK252])],[f1439,f1440]) ).

thf(f1440,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),X4),X3),X0),X5) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK251,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1439,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),X4),X3),X0),X5) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(rectify,[],[f1190]) ).

thf(f1190,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),X8),X7),X0),X9) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 ) )
      | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1123,f1189,f1188]) ).

thf(f1188,plain,
    ! [X9: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X7: secrecy_Expression,X8: secrecy_Expression,X2: list_S529945141ession] :
      ( ? [X10: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),X8),X7),X0),X9) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1189,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression] :
          ( ? [X5: secrecy_Expression] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) )
              & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 ) )
          & ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1123,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
          ( ? [X10: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) )
              & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7) )
              & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 ) )
      | ? [X3: secrecy_Expression] :
          ( ? [X5: secrecy_Expression] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) )
              & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 ) )
          & ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(flattening,[],[f1122]) ).

thf(f1122,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
          ( ? [X10: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) )
              & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7) )
              & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 ) )
      | ? [X3: secrecy_Expression] :
          ( ? [X5: secrecy_Expression] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) )
              & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 ) )
          & ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f915]) ).

thf(f915,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) )
     => ( ( nil_Se901661471ession != X1 )
       => ( ! [X3: secrecy_Expression] :
              ( ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 )
             => ! [X5: secrecy_Expression] :
                  ( ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 )
                 => ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) ) ) )
         => ~ ! [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 )
               => ! [X10: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 )
                   => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8) )
                     => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7) )
                       => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) ) ) ) ) ) ) ) ),
    inference(flattening,[],[f696]) ).

thf(f696,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) )
     => ( ( nil_Se901661471ession != X1 )
       => ( ! [X3: secrecy_Expression] :
              ( ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 )
             => ! [X5: secrecy_Expression] :
                  ( ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 )
                 => ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) ) ) )
         => ~ ! [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 )
               => ! [X10: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 )
                   => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8) )
                     => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7) )
                       => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f695]) ).

thf(f695,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2)
     => ( ( nil_Se901661471ession != X1 )
       => ( ! [X3: secrecy_Expression] :
              ( ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 )
             => ! [X5: secrecy_Expression] :
                  ( ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 )
                 => ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) ) )
         => ~ ! [X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X9) = X1 )
               => ! [X10: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 )
                   => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8)
                     => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7)
                       => ~ vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) ) ) ) ) ) ) ),
    inference(rectify,[],[f118]) ).

thf(f118,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X36: list_S529945141ession,X40: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X36),X40)
     => ( ( nil_Se901661471ession != X36 )
       => ( ! [X20: secrecy_Expression] :
              ( ? [X32: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32) = X36 )
             => ! [X33: secrecy_Expression] :
                  ( ? [X34: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34) = X40 )
                 => ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X20),X33) ) )
         => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32) = X36 )
               => ! [X34: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34) = X40 )
                   => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X20),X33)
                     => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X33),X20)
                       => ~ vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X32),X34) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_ord_Olexordp__eq_Ocases) ).

thf(f7368,plain,
    spl303_454,
    inference(avatar_split_clause,[],[f1922,f7366]) ).

thf(f7366,plain,
    ( spl303_454
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK231,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) )
        | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_454])]) ).

thf(f1922,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK231,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) )
      | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1412]) ).

thf(f1412,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK231,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) = X1 ) )
      | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK230,sK231,sK232])],[f1410,f1411]) ).

thf(f1411,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),X4),X3),X0),X5) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK231,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1410,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),X4),X3),X0),X5) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(rectify,[],[f1181]) ).

thf(f1181,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),X8),X7),X0),X9) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 ) )
      | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1115,f1180,f1179]) ).

thf(f1179,plain,
    ! [X9: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X7: secrecy_KS,X8: secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X10: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),X8),X7),X0),X9) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1180,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS] :
          ( ? [X5: secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) )
              & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 ) )
          & ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1115,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
          ( ? [X10: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) )
              & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7) )
              & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 ) )
      | ? [X3: secrecy_KS] :
          ( ? [X5: secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) )
              & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 ) )
          & ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(flattening,[],[f1114]) ).

thf(f1114,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
          ( ? [X10: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) )
              & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7) )
              & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 ) )
      | ? [X3: secrecy_KS] :
          ( ? [X5: secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) )
              & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 ) )
          & ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f911]) ).

thf(f911,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) )
     => ( ( nil_Secrecy_KS != X1 )
       => ( ! [X3: secrecy_KS] :
              ( ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 )
             => ! [X5: secrecy_KS] :
                  ( ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 )
                 => ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) ) ) )
         => ~ ! [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 )
               => ! [X10: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 )
                   => ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8) )
                     => ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7) )
                       => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) ) ) ) ) ) ) ) ),
    inference(flattening,[],[f688]) ).

thf(f688,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) )
     => ( ( nil_Secrecy_KS != X1 )
       => ( ! [X3: secrecy_KS] :
              ( ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 )
             => ! [X5: secrecy_KS] :
                  ( ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 )
                 => ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) ) ) )
         => ~ ! [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 )
               => ! [X10: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 )
                   => ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8) )
                     => ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7) )
                       => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f687]) ).

thf(f687,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2)
     => ( ( nil_Secrecy_KS != X1 )
       => ( ! [X3: secrecy_KS] :
              ( ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 )
             => ! [X5: secrecy_KS] :
                  ( ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 )
                 => ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) ) )
         => ~ ! [X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X9) = X1 )
               => ! [X10: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 )
                   => ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8)
                     => ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7)
                       => ~ vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) ) ) ) ) ) ) ),
    inference(rectify,[],[f117]) ).

thf(f117,axiom,
    ! [X58: secrecy_KS > secrecy_KS > $o,X36: list_Secrecy_KS,X40: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),X36),X40)
     => ( ( nil_Secrecy_KS != X36 )
       => ( ! [X20: secrecy_KS] :
              ( ? [X32: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32) = X36 )
             => ! [X33: secrecy_KS] :
                  ( ? [X34: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34) = X40 )
                 => ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X58,X20),X33) ) )
         => ~ ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32) = X36 )
               => ! [X34: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34) = X40 )
                   => ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X58,X20),X33)
                     => ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X58,X33),X20)
                       => ~ vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),X32),X34) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_ord_Olexordp__eq_Ocases) ).

thf(f7364,plain,
    spl303_453,
    inference(avatar_split_clause,[],[f2759,f7362]) ).

thf(f7362,plain,
    ( spl303_453
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_453])]) ).

thf(f2759,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1) = X0 ) ),
    inference(equality_proxy_clausification,[],[f2758]) ).

thf(f2758,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X1 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X0) ) ),
    inference(equality_proxy_clausification,[],[f2757]) ).

thf(f2757,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)),X0) ) ),
    inference(binary_proxy_clausification,[],[f1628]) ).

thf(f7348,plain,
    spl303_452,
    inference(avatar_split_clause,[],[f2012,f7346]) ).

thf(f7346,plain,
    ( spl303_452
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK300,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK301,X3),X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK302,X3)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_452])]) ).

thf(f2012,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK300,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK301,X3),X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK302,X3)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1477]) ).

thf(f1477,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK300,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK301,X3),X0))) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK302,X3)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK298,sK299,sK300,sK301,sK302])],[f1474,f1476,f1475]) ).

thf(f1475,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK300,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK301,X3),X0))) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1476,plain,
    ! [X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X8) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK302,X3)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1474,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
      | ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
      | ? [X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X8) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(rectify,[],[f1194]) ).

thf(f1194,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
      | ? [X5: secrecy_Expression,X6: secrecy_Expression,X7: list_S529945141ession,X8: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),X8)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X5),X6) ) )
      | ? [X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1149,f1193]) ).

thf(f1193,plain,
    ! [X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o] :
      ( ? [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10) ) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1149,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ? [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10) ) )
      | ? [X5: secrecy_Expression,X6: secrecy_Expression,X7: list_S529945141ession,X8: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),X8)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X5),X6) ) )
      | ? [X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(flattening,[],[f1148]) ).

thf(f1148,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ? [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10) ) )
      | ? [X5: secrecy_Expression,X6: secrecy_Expression,X7: list_S529945141ession,X8: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),X8)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X5),X6) ) )
      | ? [X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f922]) ).

thf(f922,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) )
     => ( ! [X4: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X4) )
       => ( ! [X5: secrecy_Expression,X6: secrecy_Expression,X7: list_S529945141ession,X8: list_S529945141ession] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X5),X6) )
             => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),X8)) ) )
         => ( ! [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
                ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10) )
               => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9) )
                 => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12) )
                   => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12) )
                     => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) ) ) ) ) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ) ) ),
    inference(flattening,[],[f752]) ).

thf(f752,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) )
     => ( ! [X4: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X4) )
       => ( ! [X5: secrecy_Expression,X6: secrecy_Expression,X7: list_S529945141ession,X8: list_S529945141ession] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X5),X6) )
             => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),X8)) ) )
         => ( ! [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
                ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10) )
               => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9) )
                 => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12) )
                   => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12) )
                     => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) ) ) ) ) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f751]) ).

thf(f751,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2)
     => ( ! [X4: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),X4)
       => ( ! [X5: secrecy_Expression,X6: secrecy_Expression,X7: list_S529945141ession,X8: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X5),X6)
             => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),X8)) )
         => ( ! [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
                ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10)
               => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9)
                 => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12)
                   => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12)
                     => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) ) ) ) )
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ) ),
    inference(rectify,[],[f122]) ).

thf(f122,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X12: list_S529945141ession,X0: list_S529945141ession,X18: list_S529945141ession > list_S529945141ession > $o] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X12),X0)
     => ( ! [X37: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,nil_Se901661471ession),X37)
       => ( ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession,X34: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X20),X33)
             => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) )
         => ( ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession,X34: list_S529945141ession] :
                ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X20),X33)
               => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X33),X20)
                 => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X32),X34)
                   => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X32),X34)
                     => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) ) ) ) )
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X12),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_ord_Olexordp__eq_Oinducts) ).

thf(f7344,plain,
    spl303_451,
    inference(avatar_split_clause,[],[f1993,f7342]) ).

thf(f7342,plain,
    ( spl303_451
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK279,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK280,X3),X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK281,X3)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_451])]) ).

thf(f1993,plain,
    ! [X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK279,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK280,X3),X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK281,X3)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1463]) ).

thf(f1463,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK279,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK280,X3),X0))) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK281,X3)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK277,sK278,sK279,sK280,sK281])],[f1460,f1462,f1461]) ).

thf(f1461,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK279,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK280,X3),X0))) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1462,plain,
    ! [X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X8) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK281,X3)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1460,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
      | ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
      | ? [X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X8) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(rectify,[],[f1192]) ).

thf(f1192,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
      | ? [X5: secrecy_KS,X6: secrecy_KS,X7: list_Secrecy_KS,X8: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),X8)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X5),X6) ) )
      | ? [X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X4) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1141,f1191]) ).

thf(f1191,plain,
    ! [X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o] :
      ( ? [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10) ) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1141,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ? [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10) ) )
      | ? [X5: secrecy_KS,X6: secrecy_KS,X7: list_Secrecy_KS,X8: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),X8)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X5),X6) ) )
      | ? [X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X4) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(flattening,[],[f1140]) ).

thf(f1140,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ? [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10) ) )
      | ? [X5: secrecy_KS,X6: secrecy_KS,X7: list_Secrecy_KS,X8: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),X8)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X5),X6) ) )
      | ? [X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X4) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f921]) ).

thf(f921,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) )
     => ( ! [X4: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X4) )
       => ( ! [X5: secrecy_KS,X6: secrecy_KS,X7: list_Secrecy_KS,X8: list_Secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X5),X6) )
             => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),X8)) ) )
         => ( ! [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
                ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10) )
               => ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9) )
                 => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12) )
                   => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12) )
                     => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) ) ) ) ) )
           => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ) ) ),
    inference(flattening,[],[f744]) ).

thf(f744,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) )
     => ( ! [X4: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X4) )
       => ( ! [X5: secrecy_KS,X6: secrecy_KS,X7: list_Secrecy_KS,X8: list_Secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X5),X6) )
             => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),X8)) ) )
         => ( ! [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
                ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10) )
               => ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9) )
                 => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12) )
                   => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12) )
                     => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) ) ) ) ) )
           => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f743]) ).

thf(f743,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2)
     => ( ! [X4: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),X4)
       => ( ! [X5: secrecy_KS,X6: secrecy_KS,X7: list_Secrecy_KS,X8: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X5),X6)
             => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),X8)) )
         => ( ! [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
                ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10)
               => ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9)
                 => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12)
                   => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12)
                     => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) ) ) ) )
           => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ) ),
    inference(rectify,[],[f121]) ).

thf(f121,axiom,
    ! [X58: secrecy_KS > secrecy_KS > $o,X12: list_Secrecy_KS,X0: list_Secrecy_KS,X18: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),X12),X0)
     => ( ! [X37: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,nil_Secrecy_KS),X37)
       => ( ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS,X34: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X58,X20),X33)
             => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) )
         => ( ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS,X34: list_Secrecy_KS] :
                ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X58,X20),X33)
               => ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X58,X33),X20)
                 => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),X32),X34)
                   => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X32),X34)
                     => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) ) ) ) )
           => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X12),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_ord_Olexordp__eq_Oinducts) ).

thf(f7270,plain,
    spl303_450,
    inference(avatar_split_clause,[],[f3100,f7268]) ).

thf(f7268,plain,
    ( spl303_450
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK130,X1)),nil_Se901661471ession) = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0))) = X1 )
        | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_450])]) ).

thf(f3100,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK130,X1)),nil_Se901661471ession) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0))) = X1 )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)) ) ),
    inference(forward_demodulation,[],[f2080,f1527]) ).

thf(f2080,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0))) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK130,X1)),nil_Se901661471ession) = X1 )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)) ) ),
    inference(equality_resolution,[],[f1836]) ).

thf(f1836,plain,
    ! [X2: $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,X2),X1),X0))) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK130,X1)),nil_Se901661471ession) = X1 )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1317]) ).

thf(f1317,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0))),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,X2),X1),X0))))) != X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,X2),X1),X0))) = X1 ) )
      | ( ( $true = X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK130,X1)),nil_Se901661471ession) = X1 ) )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK127,sK128,sK129,sK130])],[f1314,f1316,f1315]) ).

thf(f1315,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)))) != X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X1 ) )
     => ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0))),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,X2),X1),X0))))) != X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,X2),X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1316,plain,
    ! [X1: list_S529945141ession] :
      ( ? [X6: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),nil_Se901661471ession) = X1 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK130,X1)),nil_Se901661471ession) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1314,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)))) != X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X6: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X6),nil_Se901661471ession) = X1 ) )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(rectify,[],[f1170]) ).

thf(f1170,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)))) != X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X3: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession) = X1 ) )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(definition_folding,[],[f1062,f1169]) ).

thf(f1169,plain,
    ! [X2: $o,X1: list_S529945141ession] :
      ( ( ( $true = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1062,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)))) != X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X3: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession) = X1 ) )
      | ( ( $true = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(flattening,[],[f1061]) ).

thf(f1061,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)))) != X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X3: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession) = X1 ) )
      | ( ( $true = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(ennf_transformation,[],[f907]) ).

thf(f907,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) = X2 )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( $true != X2 ) )
       => ( ( ? [X3: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession) = X1 )
           => ( $true != X2 ) )
         => ~ ! [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) = X1 )
               => ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)))) = X2 ) ) ) ) ),
    inference(flattening,[],[f624]) ).

thf(f624,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) = X2 )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( $true != X2 ) )
       => ( ( ? [X3: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession) = X1 )
           => ( $true != X2 ) )
         => ~ ! [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) = X1 )
               => ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5)),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)))) = X2 ) ) ) ) ),
    inference(fool_elimination,[],[f623]) ).

thf(f623,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: $o] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) = X2 )
     => ( ( ( nil_Se901661471ession = X1 )
         => ~ X2 )
       => ( ( ? [X3: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession) = X1 )
           => ~ X2 )
         => ~ ! [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) = X1 )
               => ( X2
                  = ( ~ ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6))
                        & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) ) ) ) ) ) ) ),
    inference(rectify,[],[f328]) ).

thf(f328,axiom,
    ! [X39: secrecy_Expression > secrecy_Expression > $o,X56: list_S529945141ession,X15: $o] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X39),X56) = X15 )
     => ( ( ( nil_Se901661471ession = X56 )
         => ~ X15 )
       => ( ( ? [X20: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession) = X56 )
           => ~ X15 )
         => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32)) = X56 )
               => ( X15
                  = ( ~ ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))
                        & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X39,X20),X33) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_successively_Oelims_I1_J) ).

thf(f7266,plain,
    spl303_449,
    inference(avatar_split_clause,[],[f3097,f7264]) ).

thf(f7264,plain,
    ( spl303_449
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK126,X1)),nil_Secrecy_KS) = X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0))) = X1 )
        | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_449])]) ).

thf(f3097,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK126,X1)),nil_Secrecy_KS) = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0))) = X1 )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)) ) ),
    inference(forward_demodulation,[],[f2076,f1526]) ).

thf(f2076,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0))) = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK126,X1)),nil_Secrecy_KS) = X1 )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)) ) ),
    inference(equality_resolution,[],[f1830]) ).

thf(f1830,plain,
    ! [X2: $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,X2),X1),X0))) = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK126,X1)),nil_Secrecy_KS) = X1 )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1311]) ).

thf(f1311,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0))),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,X2),X1),X0))))) != X2 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,X2),X1),X0))) = X1 ) )
      | ( ( $true = X2 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK126,X1)),nil_Secrecy_KS) = X1 ) )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK123,sK124,sK125,sK126])],[f1308,f1310,f1309]) ).

thf(f1309,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)))) != X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X1 ) )
     => ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0))),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,X2),X1),X0))))) != X2 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,X2),X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1310,plain,
    ! [X1: list_Secrecy_KS] :
      ( ? [X6: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),nil_Secrecy_KS) = X1 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK126,X1)),nil_Secrecy_KS) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1308,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)))) != X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X6: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X6),nil_Secrecy_KS) = X1 ) )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(rectify,[],[f1168]) ).

thf(f1168,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)))) != X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X3: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS) = X1 ) )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(definition_folding,[],[f1060,f1167]) ).

thf(f1167,plain,
    ! [X2: $o,X1: list_Secrecy_KS] :
      ( ( ( $true = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1060,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)))) != X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X3: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS) = X1 ) )
      | ( ( $true = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(flattening,[],[f1059]) ).

thf(f1059,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)))) != X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) = X1 ) )
      | ( ( $true = X2 )
        & ? [X3: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS) = X1 ) )
      | ( ( $true = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(ennf_transformation,[],[f906]) ).

thf(f906,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) = X2 )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( $true != X2 ) )
       => ( ( ? [X3: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS) = X1 )
           => ( $true != X2 ) )
         => ~ ! [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) = X1 )
               => ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)))) = X2 ) ) ) ) ),
    inference(flattening,[],[f622]) ).

thf(f622,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) = X2 )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( $true != X2 ) )
       => ( ( ? [X3: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS) = X1 )
           => ( $true != X2 ) )
         => ~ ! [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) = X1 )
               => ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5)),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)))) = X2 ) ) ) ) ),
    inference(fool_elimination,[],[f621]) ).

thf(f621,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: $o] :
      ( ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) = X2 )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ~ X2 )
       => ( ( ? [X3: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS) = X1 )
           => ~ X2 )
         => ~ ! [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) = X1 )
               => ( X2
                  = ( ~ ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6))
                        & vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) ) ) ) ) ) ) ),
    inference(rectify,[],[f327]) ).

thf(f327,axiom,
    ! [X39: secrecy_KS > secrecy_KS > $o,X56: list_Secrecy_KS,X15: $o] :
      ( ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X39),X56) = X15 )
     => ( ( ( nil_Secrecy_KS = X56 )
         => ~ X15 )
       => ( ( ? [X20: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS) = X56 )
           => ~ X15 )
         => ~ ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32)) = X56 )
               => ( X15
                  = ( ~ ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X39),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32))
                        & vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X39,X20),X33) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_successively_Oelims_I1_J) ).

thf(f7262,plain,
    spl303_448,
    inference(avatar_split_clause,[],[f2749,f7260]) ).

thf(f7260,plain,
    ( spl303_448
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_448])]) ).

thf(f2749,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != X1 ) ),
    inference(equality_proxy_clausification,[],[f2748]) ).

thf(f2748,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X1) ) ),
    inference(equality_proxy_clausification,[],[f2744]) ).

thf(f2744,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X1) ) ),
    inference(binary_proxy_clausification,[],[f1630]) ).

thf(f1630,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X1) ),
    inference(cnf_transformation,[],[f470]) ).

thf(f470,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X1) ),
    inference(fool_elimination,[],[f469]) ).

thf(f469,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = X1 )
      = ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f146]) ).

thf(f146,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31) = X31 )
      = ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_append__self__conv2) ).

thf(f7258,plain,
    spl303_447,
    inference(avatar_split_clause,[],[f2079,f7256]) ).

thf(f7256,plain,
    ( spl303_447
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0))) = X1 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_447])]) ).

thf(f2079,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)),X1),X0))) = X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)) ) ),
    inference(equality_resolution,[],[f1837]) ).

thf(f1837,plain,
    ! [X2: $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK127,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK128,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP($o,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK129,X2),X1),X0))) = X1 )
      | ( $true = X2 )
      | ( $true = vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) )
      | ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1317]) ).

thf(f7254,plain,
    spl303_446,
    inference(avatar_split_clause,[],[f2075,f7252]) ).

thf(f7252,plain,
    ( spl303_446
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0))) = X1 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
        | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_446])]) ).

thf(f2075,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)),X1),X0))) = X1 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)) ) ),
    inference(equality_resolution,[],[f1831]) ).

thf(f1831,plain,
    ! [X2: $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK123,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK124,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP($o,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK125,X2),X1),X0))) = X1 )
      | ( $true = X2 )
      | ( $true = vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) )
      | ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1311]) ).

thf(f7246,plain,
    spl303_445,
    inference(avatar_split_clause,[],[f3108,f7244]) ).

thf(f7244,plain,
    ( spl303_445
  <=> ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK163,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0)))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_445])]) ).

thf(f3108,plain,
    ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK163,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0)))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1862,f1527]) ).

thf(f1862,plain,
    ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK163,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0)))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1349]) ).

thf(f1349,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK163,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0)))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0))) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK162,sK163,sK164,sK165,sK166,sK167,sK168])],[f1345,f1348,f1347,f1346]) ).

thf(f1346,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o] :
      ( ? [X3: secrecy_Expression > secrecy_Expression > $o,X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6))) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK163,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0)))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1347,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o] :
      ( ? [X7: secrecy_Expression > secrecy_Expression > $o,X8: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X7),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),nil_Se901661471ession)) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1348,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o] :
      ( ? [X9: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X9),nil_Se901661471ession) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ),
    introduced(choice_axiom,[]) ).

thf(f1345,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X3: secrecy_Expression > secrecy_Expression > $o,X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6))) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) ) )
      | ? [X7: secrecy_Expression > secrecy_Expression > $o,X8: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X7),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),nil_Se901661471ession)) )
      | ? [X9: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X9),nil_Se901661471ession) ) ),
    inference(rectify,[],[f1086]) ).

thf(f1086,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X6: secrecy_Expression > secrecy_Expression > $o,X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9))) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9)) ) )
      | ? [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
      | ? [X3: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession) ) ),
    inference(flattening,[],[f1085]) ).

thf(f1085,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X6: secrecy_Expression > secrecy_Expression > $o,X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9))) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9)) ) )
      | ? [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
      | ? [X3: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f648]) ).

thf(f648,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ! [X3: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession) )
     => ( ! [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
       => ( ! [X6: secrecy_Expression > secrecy_Expression > $o,X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9)) )
             => ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9))) ) )
         => ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f647]) ).

thf(f647,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ! [X3: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession)
     => ( ! [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession))
       => ( ! [X6: secrecy_Expression > secrecy_Expression > $o,X7: secrecy_Expression,X8: secrecy_Expression,X9: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9))
             => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X9))) )
         => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ),
    inference(rectify,[],[f45]) ).

thf(f45,axiom,
    ! [X18: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X35: secrecy_Expression > secrecy_Expression > $o,X36: list_S529945141ession] :
      ( ! [X45: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),nil_Se901661471ession)
     => ( ! [X45: secrecy_Expression > secrecy_Expression > $o,X20: secrecy_Expression] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))
       => ( ! [X45: secrecy_Expression > secrecy_Expression > $o,X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))
             => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))) )
         => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X35),X36) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_successively_Oinduct) ).

thf(f7242,plain,
    spl303_444,
    inference(avatar_split_clause,[],[f3106,f7240]) ).

thf(f7240,plain,
    ( spl303_444
  <=> ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK152,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0)))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_444])]) ).

thf(f3106,plain,
    ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK152,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0)))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1858,f1526]) ).

thf(f1858,plain,
    ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK152,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0)))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1340]) ).

thf(f1340,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK152,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0)))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0))) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK151,sK152,sK153,sK154,sK155,sK156,sK157])],[f1336,f1339,f1338,f1337]) ).

thf(f1337,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o] :
      ( ? [X3: secrecy_KS > secrecy_KS > $o,X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK152,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0)))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1338,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o] :
      ( ? [X7: secrecy_KS > secrecy_KS > $o,X8: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X7),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),nil_Secrecy_KS)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1339,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o] :
      ( ? [X9: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X9),nil_Secrecy_KS) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ),
    introduced(choice_axiom,[]) ).

thf(f1336,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X3: secrecy_KS > secrecy_KS > $o,X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) ) )
      | ? [X7: secrecy_KS > secrecy_KS > $o,X8: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X7),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),nil_Secrecy_KS)) )
      | ? [X9: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X9),nil_Secrecy_KS) ) ),
    inference(rectify,[],[f1082]) ).

thf(f1082,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X6: secrecy_KS > secrecy_KS > $o,X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9)) ) )
      | ? [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
      | ? [X3: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1081]) ).

thf(f1081,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X6: secrecy_KS > secrecy_KS > $o,X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9)) ) )
      | ? [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
      | ? [X3: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f644]) ).

thf(f644,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ! [X3: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS) )
     => ( ! [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
       => ( ! [X6: secrecy_KS > secrecy_KS > $o,X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9)) )
             => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9))) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f643]) ).

thf(f643,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ! [X3: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS)
     => ( ! [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS))
       => ( ! [X6: secrecy_KS > secrecy_KS > $o,X7: secrecy_KS,X8: secrecy_KS,X9: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9))
             => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X9))) )
         => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ),
    inference(rectify,[],[f44]) ).

thf(f44,axiom,
    ! [X18: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X35: secrecy_KS > secrecy_KS > $o,X36: list_Secrecy_KS] :
      ( ! [X45: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),nil_Secrecy_KS)
     => ( ! [X45: secrecy_KS > secrecy_KS > $o,X20: secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))
       => ( ! [X45: secrecy_KS > secrecy_KS > $o,X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32))
             => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32))) )
         => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X35),X36) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_successively_Oinduct) ).

thf(f7219,plain,
    spl303_443,
    inference(avatar_split_clause,[],[f2085,f7217]) ).

thf(f7217,plain,
    ( spl303_443
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0))),X2)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_443])]) ).

thf(f2085,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0))),X2)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) ),
    inference(equality_resolution,[],[f1976]) ).

thf(f1976,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0))),X2)) = X3 )
      | ( X2 = X3 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1445]) ).

thf(f1445,plain,
    ! [X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0))),X2)) = X3 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)) = X1 ) )
      | ( ( X2 = X3 )
        & ( nil_Se901661471ession = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK255,sK256])],[f1131,f1444]) ).

thf(f1444,plain,
    ! [X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ? [X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X4)),X2)) = X3 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
     => ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0))),X2)) = X3 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1131,plain,
    ! [X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ? [X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X4)),X2)) = X3 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
      | ( ( X2 = X3 )
        & ( nil_Se901661471ession = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(flattening,[],[f1130]) ).

thf(f1130,plain,
    ! [X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ? [X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X4)),X2)) = X3 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
      | ( ( X2 = X3 )
        & ( nil_Se901661471ession = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(ennf_transformation,[],[f920]) ).

thf(f920,plain,
    ! [X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X3 )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( X2 != X3 ) )
       => ~ ! [X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X4)),X2)) != X3 ) ) ) ),
    inference(rectify,[],[f87]) ).

thf(f87,axiom,
    ! [X39: secrecy_Expression > secrecy_Expression,X56: list_S529945141ession,X57: list_S529945141ession,X15: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X39),X56),X57) = X15 )
     => ( ( ( nil_Se901661471ession = X56 )
         => ( X15 != X57 ) )
       => ~ ! [X42: secrecy_Expression,X43: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X42),X43) = X56 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X39),X43),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X39,X42)),X57)) != X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_map__tailrec__rev_Oelims) ).

thf(f7215,plain,
    spl303_442,
    inference(avatar_split_clause,[],[f2081,f7213]) ).

thf(f7213,plain,
    ( spl303_442
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0))),X2)) )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_442])]) ).

thf(f2081,plain,
    ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0))),X2)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) ),
    inference(equality_resolution,[],[f1972]) ).

thf(f1972,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0))),X2)) = X3 )
      | ( X2 = X3 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1443]) ).

thf(f1443,plain,
    ! [X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0))),X2)) = X3 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)) = X1 ) )
      | ( ( X2 = X3 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK253,sK254])],[f1129,f1442]) ).

thf(f1442,plain,
    ! [X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ? [X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,X4)),X2)) = X3 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
     => ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0))),X2)) = X3 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1129,plain,
    ! [X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ? [X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,X4)),X2)) = X3 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
      | ( ( X2 = X3 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(flattening,[],[f1128]) ).

thf(f1128,plain,
    ! [X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ? [X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,X4)),X2)) = X3 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
      | ( ( X2 = X3 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(ennf_transformation,[],[f919]) ).

thf(f919,plain,
    ! [X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X3 )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( X2 != X3 ) )
       => ~ ! [X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X5),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,X4)),X2)) != X3 ) ) ) ),
    inference(rectify,[],[f86]) ).

thf(f86,axiom,
    ! [X39: secrecy_KS > secrecy_Expression,X56: list_Secrecy_KS,X57: list_S529945141ession,X15: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X39),X56),X57) = X15 )
     => ( ( ( nil_Secrecy_KS = X56 )
         => ( X15 != X57 ) )
       => ~ ! [X42: secrecy_KS,X43: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X42),X43) = X56 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X39),X43),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X39,X42)),X57)) != X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_map__tailrec__rev_Oelims) ).

thf(f7211,plain,
    spl303_441,
    inference(avatar_split_clause,[],[f2747,f7209]) ).

thf(f7209,plain,
    ( spl303_441
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_441])]) ).

thf(f2747,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = X1 ) ),
    inference(equality_proxy_clausification,[],[f2746]) ).

thf(f2746,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X1) ) ),
    inference(equality_proxy_clausification,[],[f2745]) ).

thf(f2745,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X1) ) ),
    inference(binary_proxy_clausification,[],[f1630]) ).

thf(f7203,plain,
    spl303_440,
    inference(avatar_split_clause,[],[f1979,f7201]) ).

thf(f7201,plain,
    ( spl303_440
  <=> ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X3: list_S529945141ession,X2: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK267,X0)),nil_Se901661471ession),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK268,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_440])]) ).

thf(f1979,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK267,X0)),nil_Se901661471ession),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK268,X0)) ) ),
    inference(cnf_transformation,[],[f1453]) ).

thf(f1453,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0))) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK267,X0)),nil_Se901661471ession),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK268,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK263,sK264,sK265,sK266,sK267,sK268])],[f1450,f1452,f1451]) ).

thf(f1451,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X4: secrecy_Expression > secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X4,X5)),X7)) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1452,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X8: secrecy_Expression > secrecy_Expression,X9: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X8),nil_Se901661471ession),X9) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK267,X0)),nil_Se901661471ession),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK268,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1450,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ? [X4: secrecy_Expression > secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X4,X5)),X7)) ) )
      | ? [X8: secrecy_Expression > secrecy_Expression,X9: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X8),nil_Se901661471ession),X9) ) ),
    inference(rectify,[],[f1135]) ).

thf(f1135,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ? [X6: secrecy_Expression > secrecy_Expression,X7: secrecy_Expression,X8: list_S529945141ession,X9: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),X9) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X6,X7)),X9)) ) )
      | ? [X4: secrecy_Expression > secrecy_Expression,X5: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),nil_Se901661471ession),X5) ) ),
    inference(flattening,[],[f1134]) ).

thf(f1134,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ? [X6: secrecy_Expression > secrecy_Expression,X7: secrecy_Expression,X8: list_S529945141ession,X9: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),X9) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X6,X7)),X9)) ) )
      | ? [X4: secrecy_Expression > secrecy_Expression,X5: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),nil_Se901661471ession),X5) ) ),
    inference(ennf_transformation,[],[f736]) ).

thf(f736,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ! [X4: secrecy_Expression > secrecy_Expression,X5: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),nil_Se901661471ession),X5) )
     => ( ! [X6: secrecy_Expression > secrecy_Expression,X7: secrecy_Expression,X8: list_S529945141ession,X9: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X6,X7)),X9)) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),X9) ) )
       => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) ) ) ),
    inference(fool_elimination,[],[f735]) ).

thf(f735,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] :
      ( ! [X4: secrecy_Expression > secrecy_Expression,X5: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X4),nil_Se901661471ession),X5)
     => ( ! [X6: secrecy_Expression > secrecy_Expression,X7: secrecy_Expression,X8: list_S529945141ession,X9: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X6,X7)),X9))
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),X9) )
       => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) ) ),
    inference(rectify,[],[f41]) ).

thf(f41,axiom,
    ! [X18: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X35: secrecy_Expression > secrecy_Expression,X36: list_S529945141ession,X40: list_S529945141ession] :
      ( ! [X41: secrecy_Expression > secrecy_Expression,X37: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X18,X41),nil_Se901661471ession),X37)
     => ( ! [X41: secrecy_Expression > secrecy_Expression,X42: secrecy_Expression,X43: list_S529945141ession,X44: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X18,X41),X43),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X41,X42)),X44))
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X18,X41),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X42),X43)),X44) )
       => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X18,X35),X36),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_map__tailrec__rev_Oinduct) ).

thf(f7199,plain,
    spl303_439,
    inference(avatar_split_clause,[],[f1977,f7197]) ).

thf(f7197,plain,
    ( spl303_439
  <=> ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X3: list_S529945141ession,X2: list_Secrecy_KS,X1: secrecy_KS > secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK261,X0)),nil_Secrecy_KS),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK262,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_439])]) ).

thf(f1977,plain,
    ! [X2: list_Secrecy_KS,X3: list_S529945141ession,X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK261,X0)),nil_Secrecy_KS),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK262,X0)) ) ),
    inference(cnf_transformation,[],[f1449]) ).

thf(f1449,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression,X2: list_Secrecy_KS,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0))) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK261,X0)),nil_Secrecy_KS),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK262,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK257,sK258,sK259,sK260,sK261,sK262])],[f1446,f1448,f1447]) ).

thf(f1447,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o] :
      ( ? [X4: secrecy_KS > secrecy_Expression,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X4,X5)),X7)) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1448,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o] :
      ( ? [X8: secrecy_KS > secrecy_Expression,X9: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X8),nil_Secrecy_KS),X9) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK261,X0)),nil_Secrecy_KS),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK262,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1446,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression,X2: list_Secrecy_KS,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ? [X4: secrecy_KS > secrecy_Expression,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X4,X5)),X7)) ) )
      | ? [X8: secrecy_KS > secrecy_Expression,X9: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X8),nil_Secrecy_KS),X9) ) ),
    inference(rectify,[],[f1133]) ).

thf(f1133,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression,X2: list_Secrecy_KS,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ? [X6: secrecy_KS > secrecy_Expression,X7: secrecy_KS,X8: list_Secrecy_KS,X9: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),X9) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X6,X7)),X9)) ) )
      | ? [X4: secrecy_KS > secrecy_Expression,X5: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),nil_Secrecy_KS),X5) ) ),
    inference(flattening,[],[f1132]) ).

thf(f1132,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression,X2: list_Secrecy_KS,X3: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ? [X6: secrecy_KS > secrecy_Expression,X7: secrecy_KS,X8: list_Secrecy_KS,X9: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),X9) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X6,X7)),X9)) ) )
      | ? [X4: secrecy_KS > secrecy_Expression,X5: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),nil_Secrecy_KS),X5) ) ),
    inference(ennf_transformation,[],[f734]) ).

thf(f734,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression,X2: list_Secrecy_KS,X3: list_S529945141ession] :
      ( ! [X4: secrecy_KS > secrecy_Expression,X5: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),nil_Secrecy_KS),X5) )
     => ( ! [X6: secrecy_KS > secrecy_Expression,X7: secrecy_KS,X8: list_Secrecy_KS,X9: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X6,X7)),X9)) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),X9) ) )
       => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) ) ) ),
    inference(fool_elimination,[],[f733]) ).

thf(f733,plain,
    ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression,X2: list_Secrecy_KS,X3: list_S529945141ession] :
      ( ! [X4: secrecy_KS > secrecy_Expression,X5: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X4),nil_Secrecy_KS),X5)
     => ( ! [X6: secrecy_KS > secrecy_Expression,X7: secrecy_KS,X8: list_Secrecy_KS,X9: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),X8),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X6,X7)),X9))
           => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),X9) )
       => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) ) ),
    inference(rectify,[],[f40]) ).

thf(f40,axiom,
    ! [X18: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X35: secrecy_KS > secrecy_Expression,X36: list_Secrecy_KS,X40: list_S529945141ession] :
      ( ! [X41: secrecy_KS > secrecy_Expression,X37: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X18,X41),nil_Secrecy_KS),X37)
     => ( ! [X41: secrecy_KS > secrecy_Expression,X42: secrecy_KS,X43: list_Secrecy_KS,X44: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X18,X41),X43),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X41,X42)),X44))
           => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X18,X41),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X42),X43)),X44) )
       => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X18,X35),X36),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_map__tailrec__rev_Oinduct) ).

thf(f7159,plain,
    spl303_438,
    inference(avatar_split_clause,[],[f2743,f7157]) ).

thf(f7157,plain,
    ( spl303_438
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_438])]) ).

thf(f2743,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) != X0 ) ),
    inference(equality_proxy_clausification,[],[f2742]) ).

thf(f2742,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X1 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X0) ) ),
    inference(equality_proxy_clausification,[],[f2738]) ).

thf(f2738,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X0) ) ),
    inference(binary_proxy_clausification,[],[f1631]) ).

thf(f1631,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X0) ),
    inference(cnf_transformation,[],[f472]) ).

thf(f472,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X0) ),
    inference(fool_elimination,[],[f471]) ).

thf(f471,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = X0 )
      = ( nil_Se901661471ession = X1 ) ),
    inference(rectify,[],[f150]) ).

thf(f150,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31) = X28 )
      = ( nil_Se901661471ession = X31 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_append__self__conv) ).

thf(f7146,plain,
    spl303_437,
    inference(avatar_split_clause,[],[f3109,f7144]) ).

thf(f7144,plain,
    ( spl303_437
  <=> ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_437])]) ).

thf(f3109,plain,
    ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1861,f1527]) ).

thf(f1861,plain,
    ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK162,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK164,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK165,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK166,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK167,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK168,X0)),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1349]) ).

thf(f7142,plain,
    spl303_436,
    inference(avatar_split_clause,[],[f3107,f7140]) ).

thf(f7140,plain,
    ( spl303_436
  <=> ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_436])]) ).

thf(f3107,plain,
    ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1857,f1526]) ).

thf(f1857,plain,
    ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK151,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK153,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK154,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK155,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK156,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK157,X0)),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1340]) ).

thf(f7138,plain,
    spl303_435,
    inference(avatar_split_clause,[],[f2086,f7136]) ).

thf(f7136,plain,
    ( spl303_435
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0))),X2)) )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_435])]) ).

thf(f2086,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0))),X2)) )
      | ( nil_Se901661471ession = X1 ) ),
    inference(equality_resolution,[],[f1975]) ).

thf(f1975,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0))),X2)) = X3 )
      | ( nil_Se901661471ession = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1445]) ).

thf(f7134,plain,
    spl303_434,
    inference(avatar_split_clause,[],[f2082,f7132]) ).

thf(f7132,plain,
    ( spl303_434
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0))),X2)) )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_434])]) ).

thf(f2082,plain,
    ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0))),X2)) )
      | ( nil_Secrecy_KS = X1 ) ),
    inference(equality_resolution,[],[f1971]) ).

thf(f1971,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_KS,secrecy_Expression,X0,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0))),X2)) = X3 )
      | ( nil_Secrecy_KS = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1443]) ).

thf(f7130,plain,
    spl303_433,
    inference(avatar_split_clause,[],[f2005,f7128]) ).

thf(f7128,plain,
    ( spl303_433
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_433])]) ).

thf(f2005,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1469]) ).

thf(f1469,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK290,sK291,sK292,sK293])],[f1147,f1468]) ).

thf(f1468,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X6),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X6),X7) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1147,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X6),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X6),X7) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(flattening,[],[f1146]) ).

thf(f1146,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ? [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X6),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X6),X7) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f750]) ).

thf(f750,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
       => ( ! [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5) )
             => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X6),X7) )
               => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X6),X7) )
                 => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) ) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f749]) ).

thf(f749,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2)
     => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession)
       => ( ! [X4: secrecy_Expression,X5: secrecy_Expression,X6: list_S529945141ession,X7: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X4),X5)
             => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X6),X7)
               => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X6),X7)
                 => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) ) ) )
         => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ),
    inference(rectify,[],[f97]) ).

thf(f97,axiom,
    ! [X60: secrecy_Expression > secrecy_Expression > $o,X12: list_S529945141ession,X0: list_S529945141ession,X18: list_S529945141ession > list_S529945141ession > $o] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),X12),X0)
     => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,nil_Se901661471ession),nil_Se901661471ession)
       => ( ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession,X34: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X60,X20),X33)
             => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),X32),X34)
               => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X32),X34)
                 => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) ) ) )
         => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X12),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_listrelp_Oinducts) ).

thf(f7126,plain,
    spl303_432,
    inference(avatar_split_clause,[],[f2001,f7124]) ).

thf(f7124,plain,
    ( spl303_432
  <=> ! [X0: secrecy_KS > secrecy_Expression > $o,X3: list_Secrecy_KS > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_432])]) ).

thf(f2001,plain,
    ! [X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1467]) ).

thf(f1467,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK286,sK287,sK288,sK289])],[f1145,f1466]) ).

thf(f1466,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X3: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ? [X4: secrecy_KS,X5: secrecy_Expression,X6: list_Secrecy_KS,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X6),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X6),X7) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1145,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ? [X4: secrecy_KS,X5: secrecy_Expression,X6: list_Secrecy_KS,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X6),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X6),X7) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(flattening,[],[f1144]) ).

thf(f1144,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ? [X4: secrecy_KS,X5: secrecy_Expression,X6: list_Secrecy_KS,X7: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X6),X7) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X6),X7) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f748]) ).

thf(f748,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
       => ( ! [X4: secrecy_KS,X5: secrecy_Expression,X6: list_Secrecy_KS,X7: list_S529945141ession] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X4),X5) )
             => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X6),X7) )
               => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X6),X7) )
                 => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) ) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f747]) ).

thf(f747,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2)
     => ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession)
       => ( ! [X4: secrecy_KS,X5: secrecy_Expression,X6: list_Secrecy_KS,X7: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X4),X5)
             => ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X6),X7)
               => ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X6),X7)
                 => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X7)) ) ) )
         => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) ) ) ),
    inference(rectify,[],[f95]) ).

thf(f95,axiom,
    ! [X60: secrecy_KS > secrecy_Expression > $o,X12: list_Secrecy_KS,X0: list_S529945141ession,X18: list_Secrecy_KS > list_S529945141ession > $o] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X60),X12),X0)
     => ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,nil_Secrecy_KS),nil_Se901661471ession)
       => ( ! [X20: secrecy_KS,X33: secrecy_Expression,X32: list_Secrecy_KS,X34: list_S529945141ession] :
              ( vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X60,X20),X33)
             => ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X60),X32),X34)
               => ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,X32),X34)
                 => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) ) ) )
         => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,X12),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_listrelp_Oinducts) ).

thf(f7122,plain,
    spl303_431,
    inference(avatar_split_clause,[],[f1997,f7120]) ).

thf(f7120,plain,
    ( spl303_431
  <=> ! [X0: secrecy_Expression > secrecy_KS > $o,X3: list_S529945141ession > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_431])]) ).

thf(f1997,plain,
    ! [X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1465]) ).

thf(f1465,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK282,sK283,sK284,sK285])],[f1143,f1464]) ).

thf(f1464,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X3: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ? [X4: secrecy_Expression,X5: secrecy_KS,X6: list_S529945141ession,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X6),X7) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1143,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ? [X4: secrecy_Expression,X5: secrecy_KS,X6: list_S529945141ession,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X6),X7) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(flattening,[],[f1142]) ).

thf(f1142,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ? [X4: secrecy_Expression,X5: secrecy_KS,X6: list_S529945141ession,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X6),X7) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f746]) ).

thf(f746,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
       => ( ! [X4: secrecy_Expression,X5: secrecy_KS,X6: list_S529945141ession,X7: list_Secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X4),X5) )
             => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X6),X7) )
               => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
                 => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) ) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f745]) ).

thf(f745,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2)
     => ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS)
       => ( ! [X4: secrecy_Expression,X5: secrecy_KS,X6: list_S529945141ession,X7: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X4),X5)
             => ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X6),X7)
               => ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X6),X7)
                 => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) ) ) )
         => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ),
    inference(rectify,[],[f96]) ).

thf(f96,axiom,
    ! [X60: secrecy_Expression > secrecy_KS > $o,X12: list_S529945141ession,X0: list_Secrecy_KS,X18: list_S529945141ession > list_Secrecy_KS > $o] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X60),X12),X0)
     => ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,nil_Se901661471ession),nil_Secrecy_KS)
       => ( ! [X20: secrecy_Expression,X33: secrecy_KS,X32: list_S529945141ession,X34: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X60,X20),X33)
             => ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X60),X32),X34)
               => ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,X32),X34)
                 => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) ) ) )
         => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,X12),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_listrelp_Oinducts) ).

thf(f7118,plain,
    spl303_430,
    inference(avatar_split_clause,[],[f1986,f7116]) ).

thf(f7116,plain,
    ( spl303_430
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_430])]) ).

thf(f1986,plain,
    ! [X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1455]) ).

thf(f1455,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK269,sK270,sK271,sK272])],[f1139,f1454]) ).

thf(f1454,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X6),X7) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1139,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X6),X7) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(flattening,[],[f1138]) ).

thf(f1138,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ? [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X6),X7) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f742]) ).

thf(f742,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
       => ( ! [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5) )
             => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X6),X7) )
               => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X6),X7) )
                 => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) ) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f741]) ).

thf(f741,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2)
     => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS)
       => ( ! [X4: secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS,X7: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X4),X5)
             => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X6),X7)
               => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X6),X7)
                 => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X7)) ) ) )
         => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) ) ) ),
    inference(rectify,[],[f94]) ).

thf(f94,axiom,
    ! [X60: secrecy_KS > secrecy_KS > $o,X12: list_Secrecy_KS,X0: list_Secrecy_KS,X18: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X60),X12),X0)
     => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,nil_Secrecy_KS),nil_Secrecy_KS)
       => ( ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS,X34: list_Secrecy_KS] :
              ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X60,X20),X33)
             => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X60),X32),X34)
               => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X32),X34)
                 => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) ) ) )
         => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X12),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_listrelp_Oinducts) ).

thf(f7114,plain,
    spl303_429,
    inference(avatar_split_clause,[],[f2741,f7112]) ).

thf(f7112,plain,
    ( spl303_429
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( nil_Se901661471ession != X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_429])]) ).

thf(f2741,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1) = X0 ) ),
    inference(equality_proxy_clausification,[],[f2740]) ).

thf(f2740,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X0) ) ),
    inference(equality_proxy_clausification,[],[f2739]) ).

thf(f2739,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X0) ) ),
    inference(binary_proxy_clausification,[],[f1631]) ).

thf(f7088,plain,
    spl303_428,
    inference(avatar_split_clause,[],[f1872,f7086]) ).

thf(f7086,plain,
    ( spl303_428
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK197,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK199,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK201,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK202,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK203,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK204,X0))),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_428])]) ).

thf(f1872,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK197,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK199,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK201,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK202,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK203,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK204,X0))),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1373]) ).

thf(f1373,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK197,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK199,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK201,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK202,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK203,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK204,X0))),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK197,sK198,sK199,sK200,sK201,sK202,sK203,sK204])],[f1369,f1372,f1371,f1370]) ).

thf(f1370,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),X6) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK197,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK199,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1371,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X7: secrecy_Expression,X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK201,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK202,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1372,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X9: secrecy_Expression,X10: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)),nil_Se901661471ession) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK203,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK204,X0))),nil_Se901661471ession) ) ),
    introduced(choice_axiom,[]) ).

thf(f1369,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),X6) ) )
      | ? [X7: secrecy_Expression,X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
      | ? [X9: secrecy_Expression,X10: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ),
    inference(rectify,[],[f1096]) ).

thf(f1096,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_Expression,X10: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_Expression,X6: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ),
    inference(flattening,[],[f1095]) ).

thf(f1095,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_Expression,X10: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_Expression,X6: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f658]) ).

thf(f658,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) )
     => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Se901661471ession) )
       => ( ! [X5: secrecy_Expression,X6: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
         => ( ! [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_Expression,X10: list_S529945141ession] :
                ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X8),X10) )
               => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) ) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f657]) ).

thf(f657,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession)
     => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Se901661471ession)
       => ( ! [X5: secrecy_Expression,X6: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6))
         => ( ! [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_Expression,X10: list_S529945141ession] :
                ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X8),X10)
               => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) )
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ) ),
    inference(rectify,[],[f34]) ).

thf(f34,axiom,
    ! [X18: list_S529945141ession > list_S529945141ession > $o,X28: list_S529945141ession,X31: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,nil_Se901661471ession),nil_Se901661471ession)
     => ( ! [X20: secrecy_Expression,X32: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),nil_Se901661471ession)
       => ( ! [X33: secrecy_Expression,X34: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34))
         => ( ! [X20: secrecy_Expression,X32: list_S529945141ession,X33: secrecy_Expression,X34: list_S529945141ession] :
                ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X32),X34)
               => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) )
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X28),X31) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_list__induct2_H) ).

thf(f7084,plain,
    spl303_427,
    inference(avatar_split_clause,[],[f1870,f7082]) ).

thf(f7082,plain,
    ( spl303_427
  <=> ! [X2: list_S529945141ession,X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK189,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK191,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK193,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK194,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK195,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK196,X0))),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_427])]) ).

thf(f1870,plain,
    ! [X2: list_S529945141ession,X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK189,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK191,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK193,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK194,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK195,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK196,X0))),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1368]) ).

thf(f1368,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK189,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK191,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK193,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK194,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK195,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK196,X0))),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK189,sK190,sK191,sK192,sK193,sK194,sK195,sK196])],[f1364,f1367,f1366,f1365]) ).

thf(f1365,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X4),X6) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK189,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK191,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1366,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ? [X7: secrecy_Expression,X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK193,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK194,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1367,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o] :
      ( ? [X9: secrecy_KS,X10: list_Secrecy_KS] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)),nil_Se901661471ession) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK195,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK196,X0))),nil_Se901661471ession) ) ),
    introduced(choice_axiom,[]) ).

thf(f1364,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X4),X6) ) )
      | ? [X7: secrecy_Expression,X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
      | ? [X9: secrecy_KS,X10: list_Secrecy_KS] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ),
    inference(rectify,[],[f1094]) ).

thf(f1094,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_Expression,X10: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_Expression,X6: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ),
    inference(flattening,[],[f1093]) ).

thf(f1093,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_Expression,X10: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_Expression,X6: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f656]) ).

thf(f656,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) )
     => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Se901661471ession) )
       => ( ! [X5: secrecy_Expression,X6: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
         => ( ! [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_Expression,X10: list_S529945141ession] :
                ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X8),X10) )
               => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) ) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f655]) ).

thf(f655,plain,
    ! [X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession)
     => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Se901661471ession)
       => ( ! [X5: secrecy_Expression,X6: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6))
         => ( ! [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_Expression,X10: list_S529945141ession] :
                ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X8),X10)
               => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)) )
           => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ) ),
    inference(rectify,[],[f32]) ).

thf(f32,axiom,
    ! [X18: list_Secrecy_KS > list_S529945141ession > $o,X28: list_Secrecy_KS,X31: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,nil_Secrecy_KS),nil_Se901661471ession)
     => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),nil_Se901661471ession)
       => ( ! [X33: secrecy_Expression,X34: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34))
         => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS,X33: secrecy_Expression,X34: list_S529945141ession] :
                ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,X32),X34)
               => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) )
           => vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X18,X28),X31) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_list__induct2_H) ).

thf(f7080,plain,
    spl303_426,
    inference(avatar_split_clause,[],[f1868,f7078]) ).

thf(f7078,plain,
    ( spl303_426
  <=> ! [X2: list_Secrecy_KS,X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK181,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK183,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK185,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK186,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK187,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK188,X0))),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_426])]) ).

thf(f1868,plain,
    ! [X2: list_Secrecy_KS,X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK181,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK183,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK185,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK186,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK187,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK188,X0))),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1363]) ).

thf(f1363,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK181,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK183,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK185,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK186,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK187,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK188,X0))),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK181,sK182,sK183,sK184,sK185,sK186,sK187,sK188])],[f1359,f1362,f1361,f1360]) ).

thf(f1360,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X4),X6) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK181,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK183,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1361,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ? [X7: secrecy_KS,X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK185,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK186,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1362,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o] :
      ( ? [X9: secrecy_Expression,X10: list_S529945141ession] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)),nil_Secrecy_KS) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK187,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK188,X0))),nil_Secrecy_KS) ) ),
    introduced(choice_axiom,[]) ).

thf(f1359,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X4),X6) ) )
      | ? [X7: secrecy_KS,X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
      | ? [X9: secrecy_Expression,X10: list_S529945141ession] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ),
    inference(rectify,[],[f1092]) ).

thf(f1092,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_KS,X10: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_KS,X6: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1091]) ).

thf(f1091,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_KS,X10: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_KS,X6: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f654]) ).

thf(f654,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) )
     => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Secrecy_KS) )
       => ( ! [X5: secrecy_KS,X6: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
         => ( ! [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_KS,X10: list_Secrecy_KS] :
                ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X8),X10) )
               => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) ) )
           => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f653]) ).

thf(f653,plain,
    ! [X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS)
     => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] : vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),nil_Secrecy_KS)
       => ( ! [X5: secrecy_KS,X6: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6))
         => ( ! [X7: secrecy_Expression,X8: list_S529945141ession,X9: secrecy_KS,X10: list_Secrecy_KS] :
                ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X8),X10)
               => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) )
           => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ) ),
    inference(rectify,[],[f33]) ).

thf(f33,axiom,
    ! [X18: list_S529945141ession > list_Secrecy_KS > $o,X28: list_S529945141ession,X31: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,nil_Se901661471ession),nil_Secrecy_KS)
     => ( ! [X20: secrecy_Expression,X32: list_S529945141ession] : vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),nil_Secrecy_KS)
       => ( ! [X33: secrecy_KS,X34: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34))
         => ( ! [X20: secrecy_Expression,X32: list_S529945141ession,X33: secrecy_KS,X34: list_Secrecy_KS] :
                ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,X32),X34)
               => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) )
           => vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X18,X28),X31) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_list__induct2_H) ).

thf(f7076,plain,
    spl303_425,
    inference(avatar_split_clause,[],[f1866,f7074]) ).

thf(f7074,plain,
    ( spl303_425
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK173,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK175,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK177,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK178,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK179,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK180,X0))),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_425])]) ).

thf(f1866,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK173,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK175,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK177,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK178,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK179,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK180,X0))),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1358]) ).

thf(f1358,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK173,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK175,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK177,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK178,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK179,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK180,X0))),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK173,sK174,sK175,sK176,sK177,sK178,sK179,sK180])],[f1354,f1357,f1356,f1355]) ).

thf(f1355,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),X6) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK173,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK175,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1356,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X7: secrecy_KS,X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK177,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK178,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1357,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X9: secrecy_KS,X10: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)),nil_Secrecy_KS) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK179,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK180,X0))),nil_Secrecy_KS) ) ),
    introduced(choice_axiom,[]) ).

thf(f1354,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),X6) ) )
      | ? [X7: secrecy_KS,X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
      | ? [X9: secrecy_KS,X10: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    inference(rectify,[],[f1090]) ).

thf(f1090,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_KS,X10: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_KS,X6: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1089]) ).

thf(f1089,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_KS,X10: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X8),X10) ) )
      | ? [X5: secrecy_KS,X6: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f652]) ).

thf(f652,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) )
     => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Secrecy_KS) )
       => ( ! [X5: secrecy_KS,X6: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
         => ( ! [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_KS,X10: list_Secrecy_KS] :
                ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X8),X10) )
               => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) ) )
           => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ) ) ),
    inference(fool_elimination,[],[f651]) ).

thf(f651,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS)
     => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),nil_Secrecy_KS)
       => ( ! [X5: secrecy_KS,X6: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6))
         => ( ! [X7: secrecy_KS,X8: list_Secrecy_KS,X9: secrecy_KS,X10: list_Secrecy_KS] :
                ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X8),X10)
               => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10)) )
           => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ) ),
    inference(rectify,[],[f31]) ).

thf(f31,axiom,
    ! [X18: list_Secrecy_KS > list_Secrecy_KS > $o,X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,nil_Secrecy_KS),nil_Secrecy_KS)
     => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),nil_Secrecy_KS)
       => ( ! [X33: secrecy_KS,X34: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34))
         => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS,X33: secrecy_KS,X34: list_Secrecy_KS] :
                ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X32),X34)
               => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) )
           => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X28),X31) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_list__induct2_H) ).

thf(f7063,plain,
    spl303_424,
    inference(avatar_split_clause,[],[f1980,f7061]) ).

thf(f7061,plain,
    ( spl303_424
  <=> ! [X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X3: list_S529945141ession,X2: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK267,X0)),nil_Se901661471ession),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK268,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_424])]) ).

thf(f1980,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK263,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),secrecy_Expression,sK264,X0)),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK265,X0))),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK266,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),sTfun(secrecy_Expression,secrecy_Expression),sK267,X0)),nil_Se901661471ession),vAPP(sTfun(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK268,X0)) ) ),
    inference(cnf_transformation,[],[f1453]) ).

thf(f7059,plain,
    spl303_423,
    inference(avatar_split_clause,[],[f1978,f7057]) ).

thf(f7057,plain,
    ( spl303_423
  <=> ! [X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X3: list_S529945141ession,X2: list_Secrecy_KS,X1: secrecy_KS > secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK261,X0)),nil_Secrecy_KS),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK262,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_423])]) ).

thf(f1978,plain,
    ! [X2: list_Secrecy_KS,X3: list_S529945141ession,X0: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,X1: secrecy_KS > secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,X1),X2),X3) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK257,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),secrecy_KS,sK258,X0)),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_Secrecy_KS,sK259,X0))),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK260,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),X0,vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),sTfun(secrecy_KS,secrecy_Expression),sK261,X0)),nil_Secrecy_KS),vAPP(sTfun(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o))),list_S529945141ession,sK262,X0)) ) ),
    inference(cnf_transformation,[],[f1449]) ).

thf(f7027,plain,
    spl303_422,
    inference(avatar_split_clause,[],[f2087,f7025]) ).

thf(f2087,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) = X2 ) ),
    inference(equality_resolution,[],[f1974]) ).

thf(f1974,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)) = X1 )
      | ( X2 = X3 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1445]) ).

thf(f7023,plain,
    spl303_421,
    inference(avatar_split_clause,[],[f2083,f7021]) ).

thf(f2083,plain,
    ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) = X2 ) ),
    inference(equality_resolution,[],[f1970]) ).

thf(f1970,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)) = X1 )
      | ( X2 = X3 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1443]) ).

thf(f7011,plain,
    spl303_420,
    inference(avatar_split_clause,[],[f2010,f7009]) ).

thf(f7009,plain,
    ( spl303_420
  <=> ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0))) )
        | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_420])]) ).

thf(f2010,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0))) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(cnf_transformation,[],[f1473]) ).

thf(f1473,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)) ) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK294,sK295,sK296,sK297])],[f1471,f1472]) ).

thf(f1472,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),X5) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X4),X5) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1471,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),X5) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X4),X5) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) ) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(rectify,[],[f1470]) ).

thf(f1470,plain,
    ! [X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o] :
      ( ? [X9: secrecy_Expression,X10: secrecy_Expression,X11: list_S529945141ession,X12: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X11)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X12)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X11),X12) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X11),X12) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X9),X10) ) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) ) ),
    inference(nnf_transformation,[],[f1193]) ).

thf(f7007,plain,
    spl303_419,
    inference(avatar_split_clause,[],[f1991,f7005]) ).

thf(f7005,plain,
    ( spl303_419
  <=> ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0))) )
        | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_419])]) ).

thf(f1991,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0))) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(cnf_transformation,[],[f1459]) ).

thf(f1459,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)) ) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK273,sK274,sK275,sK276])],[f1457,f1458]) ).

thf(f1458,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),X5) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X4),X5) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1457,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),X5) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X4),X5) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) ) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(rectify,[],[f1456]) ).

thf(f1456,plain,
    ! [X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o] :
      ( ? [X9: secrecy_KS,X10: secrecy_KS,X11: list_Secrecy_KS,X12: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X11)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),X12)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X11),X12) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X11),X12) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X10),X9) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X9),X10) ) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) ) ),
    inference(nnf_transformation,[],[f1191]) ).

thf(f6988,plain,
    spl303_418,
    inference(avatar_split_clause,[],[f2011,f6986]) ).

thf(f6986,plain,
    ( spl303_418
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK302,X3)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_418])]) ).

thf(f2011,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X0),X3) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK298,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK299,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK302,X3)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1477]) ).

thf(f6984,plain,
    spl303_417,
    inference(avatar_split_clause,[],[f1992,f6982]) ).

thf(f6982,plain,
    ( spl303_417
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK281,X3)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_417])]) ).

thf(f1992,plain,
    ! [X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X0),X3) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK277,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK278,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK281,X3)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1463]) ).

thf(f6976,plain,
    spl303_416,
    inference(avatar_split_clause,[],[f1947,f6974]) ).

thf(f6974,plain,
    ( spl303_416
  <=> ! [X4: list_S529945141ession,X0: list_S529945141ession,X3: secrecy_Expression,X2: secrecy_Expression,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_416])]) ).

thf(f1947,plain,
    ! [X2: secrecy_Expression,X3: secrecy_Expression,X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1438]) ).

thf(f1438,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) = X4 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK249])],[f1436,f1437]) ).

thf(f1437,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
      ( ? [X5: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),X5) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X4 ) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
        & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) = X4 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1436,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
      ( ? [X5: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),X0),X5) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X4 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ),
    inference(rectify,[],[f1435]) ).

thf(f1435,plain,
    ! [X9: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X7: secrecy_Expression,X8: secrecy_Expression,X2: list_S529945141ession] :
      ( ? [X10: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X9),X10) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X8),X7) )
          & ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X7),X8) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X8),X10) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X2),X8),X7),X0),X9) ) ),
    inference(nnf_transformation,[],[f1188]) ).

thf(f6972,plain,
    spl303_415,
    inference(avatar_split_clause,[],[f1920,f6970]) ).

thf(f6970,plain,
    ( spl303_415
  <=> ! [X4: list_Secrecy_KS,X0: list_Secrecy_KS,X3: secrecy_KS,X2: secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_415])]) ).

thf(f1920,plain,
    ! [X2: secrecy_KS,X3: secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X4: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1409]) ).

thf(f1409,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
      ( ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) = X4 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK229])],[f1407,f1408]) ).

thf(f1408,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
      ( ? [X5: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),X5) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X4 ) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
        & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) = X4 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1407,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
      ( ? [X5: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),X0),X5) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X4 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ),
    inference(rectify,[],[f1406]) ).

thf(f1406,plain,
    ! [X9: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X7: secrecy_KS,X8: secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X10: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X9),X10) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X8),X7) )
          & ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X7),X8) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X8),X10) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X2),X8),X7),X0),X9) ) ),
    inference(nnf_transformation,[],[f1179]) ).

thf(f6960,plain,
    ( spl303_414
    | ~ spl303_3
    | ~ spl303_48 ),
    inference(avatar_split_clause,[],[f3388,f3378,f3143,f6958]) ).

thf(f6958,plain,
    ( spl303_414
  <=> ! [X0: secrecy_Expression > $o] : ( $false = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_414])]) ).

thf(f3378,plain,
    ( spl303_48
  <=> ! [X0: secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_48])]) ).

thf(f3388,plain,
    ( ! [X0: secrecy_Expression > $o] : ( $false = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) )
    | ~ spl303_3
    | ~ spl303_48 ),
    inference(trivial_inequality_removal,[],[f3387]) ).

thf(f3387,plain,
    ( ! [X0: secrecy_Expression > $o] :
        ( ( $true != $true )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_48 ),
    inference(superposition,[],[f3379,f3144]) ).

thf(f3379,plain,
    ( ! [X0: secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) )
    | ~ spl303_48 ),
    inference(avatar_component_clause,[],[f3378]) ).

thf(f6956,plain,
    spl303_413,
    inference(avatar_split_clause,[],[f1948,f6954]) ).

thf(f6954,plain,
    ( spl303_413
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) = X1 )
        | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_413])]) ).

thf(f1948,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK250,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK252,X2),X1),X0)) = X1 )
      | ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1441]) ).

thf(f6952,plain,
    spl303_412,
    inference(avatar_split_clause,[],[f1921,f6950]) ).

thf(f6950,plain,
    ( spl303_412
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) = X1 )
        | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_412])]) ).

thf(f1921,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK230,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK232,X2),X1),X0)) = X1 )
      | ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1412]) ).

thf(f6926,plain,
    spl303_411,
    inference(avatar_split_clause,[],[f1871,f6924]) ).

thf(f6924,plain,
    ( spl303_411
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK201,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK202,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK203,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK204,X0))),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_411])]) ).

thf(f1871,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK198,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK200,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK201,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK202,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK203,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK204,X0))),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1373]) ).

thf(f6922,plain,
    spl303_410,
    inference(avatar_split_clause,[],[f1869,f6920]) ).

thf(f6920,plain,
    ( spl303_410
  <=> ! [X2: list_S529945141ession,X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK193,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK194,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK195,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK196,X0))),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_410])]) ).

thf(f1869,plain,
    ! [X2: list_S529945141ession,X0: list_Secrecy_KS > list_S529945141ession > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK190,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK192,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK193,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK194,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),secrecy_KS,sK195,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),list_Secrecy_KS,sK196,X0))),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X0,nil_Secrecy_KS),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1368]) ).

thf(f6918,plain,
    spl303_409,
    inference(avatar_split_clause,[],[f1867,f6916]) ).

thf(f6916,plain,
    ( spl303_409
  <=> ! [X2: list_Secrecy_KS,X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK185,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK186,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK187,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK188,X0))),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_409])]) ).

thf(f1867,plain,
    ! [X2: list_Secrecy_KS,X0: list_S529945141ession > list_Secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK182,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK184,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK185,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK186,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),secrecy_Expression,sK187,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),list_S529945141ession,sK188,X0))),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X0,nil_Se901661471ession),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1363]) ).

thf(f6914,plain,
    spl303_408,
    inference(avatar_split_clause,[],[f1865,f6912]) ).

thf(f6912,plain,
    ( spl303_408
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK177,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK178,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK179,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK180,X0))),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_408])]) ).

thf(f1865,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK174,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK176,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK177,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK178,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK179,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK180,X0))),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1358]) ).

thf(f6910,plain,
    ( spl303_407
    | ~ spl303_3
    | ~ spl303_47 ),
    inference(avatar_split_clause,[],[f3386,f3374,f3143,f6908]) ).

thf(f6908,plain,
    ( spl303_407
  <=> ! [X0: secrecy_KS > $o] : ( $false = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_407])]) ).

thf(f3374,plain,
    ( spl303_47
  <=> ! [X0: secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_47])]) ).

thf(f3386,plain,
    ( ! [X0: secrecy_KS > $o] : ( $false = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_3
    | ~ spl303_47 ),
    inference(trivial_inequality_removal,[],[f3385]) ).

thf(f3385,plain,
    ( ! [X0: secrecy_KS > $o] :
        ( ( $true != $true )
        | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_47 ),
    inference(superposition,[],[f3375,f3144]) ).

thf(f3375,plain,
    ( ! [X0: secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_47 ),
    inference(avatar_component_clause,[],[f3374]) ).

thf(f6904,plain,
    spl303_406,
    inference(avatar_split_clause,[],[f1726,f6902]) ).

thf(f6902,plain,
    ( spl303_406
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_406])]) ).

thf(f1726,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(cnf_transformation,[],[f1252]) ).

thf(f1252,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) )
          | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)) ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) = X1 ) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65,sK66])],[f1006,f1251]) ).

thf(f1251,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
            | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 ) )
     => ( ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) )
          | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)) ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1006,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
            | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 ) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(ennf_transformation,[],[f885]) ).

thf(f885,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
     => ~ ! [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
            ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 )
           => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) ) ) ) ),
    inference(flattening,[],[f528]) ).

thf(f528,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
     => ~ ! [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
            ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 )
           => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) ) ) ) ),
    inference(fool_elimination,[],[f527]) ).

thf(f527,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ~ vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)
     => ~ ! [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
            ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 )
           => ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))
              & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) ) ) ),
    inference(rectify,[],[f334]) ).

thf(f334,axiom,
    ! [X39: secrecy_Expression > secrecy_Expression > $o,X56: list_S529945141ession] :
      ( ~ vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X39),X56)
     => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
            ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32)) = X56 )
           => ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))
              & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X39,X20),X33) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_successively_Oelims_I3_J) ).

thf(f6868,plain,
    spl303_405,
    inference(avatar_split_clause,[],[f2088,f6866]) ).

thf(f6866,plain,
    ( spl303_405
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)) = X1 )
        | ( nil_Se901661471ession = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_405])]) ).

thf(f2088,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2)),X2),X1),X0)) = X1 )
      | ( nil_Se901661471ession = X1 ) ),
    inference(equality_resolution,[],[f1973]) ).

thf(f1973,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),secrecy_Expression))),sK255,X3),X2),X1),X0)),vAPP(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,secrecy_Expression),list_S529945141ession))),sK256,X3),X2),X1),X0)) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1445]) ).

thf(f6864,plain,
    spl303_404,
    inference(avatar_split_clause,[],[f2084,f6862]) ).

thf(f6862,plain,
    ( spl303_404
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)) = X1 )
        | ( nil_Secrecy_KS = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_404])]) ).

thf(f2084,plain,
    ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2)),X2),X1),X0)) = X1 )
      | ( nil_Secrecy_KS = X1 ) ),
    inference(equality_resolution,[],[f1969]) ).

thf(f1969,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_KS > secrecy_Expression,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),secrecy_KS))),sK253,X3),X2),X1),X0)),vAPP(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS)),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,secrecy_Expression),list_Secrecy_KS))),sK254,X3),X2),X1),X0)) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_KS,secrecy_Expression),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,list_S529945141ession)),map_ta623472337ession,X0),X1),X2) != X3 ) ),
    inference(cnf_transformation,[],[f1443]) ).

thf(f6860,plain,
    spl303_403,
    inference(avatar_split_clause,[],[f1944,f6858]) ).

thf(f6858,plain,
    ( spl303_403
  <=> ! [X2: secrecy_Expression,X4: list_S529945141ession,X0: list_S529945141ession,X3: secrecy_Expression,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) = X4 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_403])]) ).

thf(f1944,plain,
    ! [X2: secrecy_Expression,X3: secrecy_Expression,X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X4: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,list_S529945141ession)))),sK249,X4),X3),X2),X1),X0)) = X4 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1438]) ).

thf(f6856,plain,
    spl303_402,
    inference(avatar_split_clause,[],[f1917,f6854]) ).

thf(f6854,plain,
    ( spl303_402
  <=> ! [X2: secrecy_KS,X4: list_Secrecy_KS,X0: list_Secrecy_KS,X3: secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) = X4 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_402])]) ).

thf(f1917,plain,
    ! [X2: secrecy_KS,X3: secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X4: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,list_Secrecy_KS)))),sK229,X4),X3),X2),X1),X0)) = X4 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1409]) ).

thf(f6816,plain,
    spl303_401,
    inference(avatar_split_clause,[],[f1825,f6814]) ).

thf(f6814,plain,
    ( spl303_401
  <=> ! [X2: list_S529945141ession,X0: list_l425507653ession,X1: list_S529945141ession] :
        ( ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0)),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0))),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X0 )
        | ( nil_li311616943ession = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_401])]) ).

thf(f1825,plain,
    ! [X2: list_S529945141ession,X0: list_l425507653ession,X1: list_S529945141ession] :
      ( ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0)),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0))),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X0 )
      | ( nil_li311616943ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ),
    inference(cnf_transformation,[],[f1305]) ).

thf(f1305,plain,
    ! [X0: list_l425507653ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0))),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)) = X1 )
        & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0)),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0))),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X0 ) )
      | ( nil_li311616943ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK119,sK120,sK121,sK122])],[f1058,f1304]) ).

thf(f1304,plain,
    ! [X0: list_l425507653ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: list_l425507653ession,X4: list_S529945141ession,X5: list_S529945141ession,X6: list_l425507653ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X5),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X6)) = X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X3)),X4) = X1 )
          & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X3),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),X5)),X6)) = X0 ) )
     => ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0))),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)) = X1 )
        & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0)),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0))),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1058,plain,
    ! [X0: list_l425507653ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: list_l425507653ession,X4: list_S529945141ession,X5: list_S529945141ession,X6: list_l425507653ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X5),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X6)) = X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X3)),X4) = X1 )
          & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X3),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),X5)),X6)) = X0 ) )
      | ( nil_li311616943ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ),
    inference(flattening,[],[f1057]) ).

thf(f1057,plain,
    ! [X0: list_l425507653ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: list_l425507653ession,X4: list_S529945141ession,X5: list_S529945141ession,X6: list_l425507653ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X5),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X6)) = X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X3)),X4) = X1 )
          & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X3),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),X5)),X6)) = X0 ) )
      | ( nil_li311616943ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ),
    inference(ennf_transformation,[],[f905]) ).

thf(f905,plain,
    ! [X0: list_l425507653ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) )
     => ( ( nil_li311616943ession != X0 )
       => ? [X3: list_l425507653ession,X4: list_S529945141ession,X5: list_S529945141ession,X6: list_l425507653ession] :
            ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X5),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X6)) = X2 )
            & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X3)),X4) = X1 )
            & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X3),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),X5)),X6)) = X0 ) ) ) ),
    inference(rectify,[],[f207]) ).

thf(f207,axiom,
    ! [X83: list_l425507653ession,X31: list_S529945141ession,X71: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X31),X71) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X83) )
     => ( ( nil_li311616943ession != X83 )
       => ? [X87: list_l425507653ession,X32: list_S529945141ession,X88: list_S529945141ession,X89: list_l425507653ession] :
            ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X88),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X89)) = X71 )
            & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X87)),X32) = X31 )
            & ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X87),vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X32),X88)),X89)) = X83 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_concat__eq__appendD) ).

thf(f6786,plain,
    spl303_400,
    inference(avatar_split_clause,[],[f2003,f6784]) ).

thf(f6784,plain,
    ( spl303_400
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_400])]) ).

thf(f2003,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1469]) ).

thf(f6782,plain,
    spl303_399,
    inference(avatar_split_clause,[],[f1999,f6780]) ).

thf(f6780,plain,
    ( spl303_399
  <=> ! [X0: secrecy_KS > secrecy_Expression > $o,X3: list_Secrecy_KS > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_399])]) ).

thf(f1999,plain,
    ! [X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1467]) ).

thf(f6763,plain,
    spl303_398,
    inference(avatar_split_clause,[],[f1995,f6761]) ).

thf(f6761,plain,
    ( spl303_398
  <=> ! [X0: secrecy_Expression > secrecy_KS > $o,X3: list_S529945141ession > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_398])]) ).

thf(f1995,plain,
    ! [X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1465]) ).

thf(f6759,plain,
    spl303_397,
    inference(avatar_split_clause,[],[f1984,f6757]) ).

thf(f6757,plain,
    ( spl303_397
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_397])]) ).

thf(f1984,plain,
    ! [X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1455]) ).

thf(f6755,plain,
    spl303_396,
    inference(avatar_split_clause,[],[f1854,f6753]) ).

thf(f6753,plain,
    ( spl303_396
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_396])]) ).

thf(f1854,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ),
    inference(cnf_transformation,[],[f1331]) ).

thf(f1331,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK141,sK142,sK143,sK144,sK145,sK146])],[f1327,f1330,f1329,f1328]) ).

thf(f1328,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),X6) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1329,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X7: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X7),nil_Se901661471ession) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) ) ),
    introduced(choice_axiom,[]) ).

thf(f1330,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X8) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1327,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),X6) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) ) )
      | ? [X7: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X7),nil_Se901661471ession) )
      | ? [X8: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X8) ) ),
    inference(rectify,[],[f1078]) ).

thf(f1078,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X5: secrecy_Expression,X6: list_S529945141ession,X7: secrecy_Expression,X8: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),X8) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) ) )
      | ? [X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),nil_Se901661471ession) )
      | ? [X3: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3) ) ),
    inference(flattening,[],[f1077]) ).

thf(f1077,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X5: secrecy_Expression,X6: list_S529945141ession,X7: secrecy_Expression,X8: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),X8) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) ) )
      | ? [X4: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),nil_Se901661471ession) )
      | ? [X3: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3) ) ),
    inference(ennf_transformation,[],[f640]) ).

thf(f640,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ! [X3: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3) )
     => ( ! [X4: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),nil_Se901661471ession) )
       => ( ! [X5: secrecy_Expression,X6: list_S529945141ession,X7: secrecy_Expression,X8: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) )
             => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),X8) )
               => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f639]) ).

thf(f639,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ! [X3: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3)
     => ( ! [X4: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X4),nil_Se901661471ession)
       => ( ! [X5: secrecy_Expression,X6: list_S529945141ession,X7: secrecy_Expression,X8: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8))
             => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),X8)
               => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8)) ) )
         => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ),
    inference(rectify,[],[f61]) ).

thf(f61,axiom,
    ! [X18: list_S529945141ession > list_S529945141ession > $o,X35: list_S529945141ession,X36: list_S529945141ession] :
      ( ! [X37: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,nil_Se901661471ession),X37)
     => ( ! [X32: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X32),nil_Se901661471ession)
       => ( ! [X20: secrecy_Expression,X32: list_S529945141ession,X33: secrecy_Expression,X34: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X32),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34))
             => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),X34)
               => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34)) ) )
         => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X35),X36) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_shuffles_Oinduct) ).

thf(f6751,plain,
    spl303_395,
    inference(avatar_split_clause,[],[f1849,f6749]) ).

thf(f6749,plain,
    ( spl303_395
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_395])]) ).

thf(f1849,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ),
    inference(cnf_transformation,[],[f1322]) ).

thf(f1322,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK131,sK132,sK133,sK134,sK135,sK136])],[f1318,f1321,f1320,f1319]) ).

thf(f1319,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),X6) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1320,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X7: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X7),nil_Secrecy_KS) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) ) ),
    introduced(choice_axiom,[]) ).

thf(f1321,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X8) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1318,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),X6) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) ) )
      | ? [X7: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X7),nil_Secrecy_KS) )
      | ? [X8: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X8) ) ),
    inference(rectify,[],[f1074]) ).

thf(f1074,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X5: secrecy_KS,X6: list_Secrecy_KS,X7: secrecy_KS,X8: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),X8) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) ) )
      | ? [X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),nil_Secrecy_KS) )
      | ? [X3: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3) ) ),
    inference(flattening,[],[f1073]) ).

thf(f1073,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X5: secrecy_KS,X6: list_Secrecy_KS,X7: secrecy_KS,X8: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),X8) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) ) )
      | ? [X4: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),nil_Secrecy_KS) )
      | ? [X3: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3) ) ),
    inference(ennf_transformation,[],[f636]) ).

thf(f636,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ! [X3: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3) )
     => ( ! [X4: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),nil_Secrecy_KS) )
       => ( ! [X5: secrecy_KS,X6: list_Secrecy_KS,X7: secrecy_KS,X8: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) )
             => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),X8) )
               => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f635]) ).

thf(f635,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ! [X3: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3)
     => ( ! [X4: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X4),nil_Secrecy_KS)
       => ( ! [X5: secrecy_KS,X6: list_Secrecy_KS,X7: secrecy_KS,X8: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8))
             => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),X8)
               => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8)) ) )
         => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ),
    inference(rectify,[],[f60]) ).

thf(f60,axiom,
    ! [X18: list_Secrecy_KS > list_Secrecy_KS > $o,X35: list_Secrecy_KS,X36: list_Secrecy_KS] :
      ( ! [X37: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,nil_Secrecy_KS),X37)
     => ( ! [X32: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X32),nil_Secrecy_KS)
       => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS,X33: secrecy_KS,X34: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X32),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34))
             => ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),X34)
               => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34)) ) )
         => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X35),X36) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_shuffles_Oinduct) ).

thf(f6739,plain,
    spl303_394,
    inference(avatar_split_clause,[],[f1938,f6737]) ).

thf(f6737,plain,
    ( spl303_394
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_394])]) ).

thf(f1938,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1427]) ).

thf(f1427,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK241,sK242,sK243,sK244])],[f1424,f1426,f1425]) ).

thf(f1425,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X2 ) )
     => ( ? [X6: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)),X6) )
            & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)) )
            & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)),X6) = X1 ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1426,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X6: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)),X6) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)),X6) = X1 ) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1424,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ),
    inference(rectify,[],[f1423]) ).

thf(f1423,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) ) ),
    inference(nnf_transformation,[],[f1186]) ).

thf(f1186,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6735,plain,
    spl303_393,
    inference(avatar_split_clause,[],[f1932,f6733]) ).

thf(f6733,plain,
    ( spl303_393
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_393])]) ).

thf(f1932,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1422]) ).

thf(f1422,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK237,sK238,sK239,sK240])],[f1419,f1421,f1420]) ).

thf(f1420,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X2 ) )
     => ( ? [X6: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)),X6) )
            & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)) )
            & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)),X6) = X1 ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1421,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ? [X6: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)),X6) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)),X6) = X1 ) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1419,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ),
    inference(rectify,[],[f1418]) ).

thf(f1418,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X2: list_S529945141ession,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) ) ),
    inference(nnf_transformation,[],[f1184]) ).

thf(f1184,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X2: list_S529945141ession,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6730,plain,
    spl303_392,
    inference(avatar_split_clause,[],[f1926,f6728]) ).

thf(f6728,plain,
    ( spl303_392
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_392])]) ).

thf(f1926,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1417]) ).

thf(f1417,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK233,sK234,sK235,sK236])],[f1414,f1416,f1415]) ).

thf(f1415,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X2 ) )
     => ( ? [X6: list_Secrecy_KS] :
            ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)),X6) )
            & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)) )
            & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)),X6) = X1 ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1416,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ? [X6: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)),X6) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)),X6) = X1 ) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1414,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ),
    inference(rectify,[],[f1413]) ).

thf(f1413,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) ) ),
    inference(nnf_transformation,[],[f1182]) ).

thf(f1182,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6726,plain,
    spl303_391,
    inference(avatar_split_clause,[],[f1911,f6724]) ).

thf(f6724,plain,
    ( spl303_391
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_391])]) ).

thf(f1911,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1398]) ).

thf(f1398,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK221,sK222,sK223,sK224])],[f1395,f1397,f1396]) ).

thf(f1396,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X2 ) )
     => ( ? [X6: list_Secrecy_KS] :
            ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)),X6) )
            & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)) )
            & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)),X6) = X1 ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1397,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X6: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)),X6) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)),X6) = X1 ) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1395,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ),
    inference(rectify,[],[f1394]) ).

thf(f1394,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) ) ),
    inference(nnf_transformation,[],[f1177]) ).

thf(f1177,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6718,plain,
    spl303_390,
    inference(avatar_split_clause,[],[f1864,f6716]) ).

thf(f6716,plain,
    ( spl303_390
  <=> ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK170,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK172,X0)),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_390])]) ).

thf(f1864,plain,
    ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK170,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK172,X0)),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1353]) ).

thf(f1353,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK170,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK172,X0)),nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK169,sK170,sK171,sK172])],[f1350,f1352,f1351]) ).

thf(f1351,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o] :
      ( ? [X3: secrecy_Expression > secrecy_Expression > $o,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),X5) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),secrecy_Expression,sK170,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1352,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o] :
      ( ? [X6: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),nil_Se901661471ession) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK172,X0)),nil_Se901661471ession) ) ),
    introduced(choice_axiom,[]) ).

thf(f1350,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X3: secrecy_Expression > secrecy_Expression > $o,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),X5) ) )
      | ? [X6: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X6),nil_Se901661471ession) ) ),
    inference(rectify,[],[f1088]) ).

thf(f1088,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),X6) ) )
      | ? [X3: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession) ) ),
    inference(flattening,[],[f1087]) ).

thf(f1087,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),X6) ) )
      | ? [X3: secrecy_Expression > secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f650]) ).

thf(f650,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ! [X3: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession) )
     => ( ! [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression,X6: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),X6) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) ) )
       => ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f649]) ).

thf(f649,plain,
    ! [X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession] :
      ( ! [X3: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X3),nil_Se901661471ession)
     => ( ! [X4: secrecy_Expression > secrecy_Expression > $o,X5: secrecy_Expression,X6: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),X6)
           => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6)) )
       => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f49]) ).

thf(f49,axiom,
    ! [X18: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X35: secrecy_Expression > secrecy_Expression > $o,X36: list_S529945141ession] :
      ( ! [X45: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),nil_Se901661471ession)
     => ( ! [X45: secrecy_Expression > secrecy_Expression > $o,X20: secrecy_Expression,X34: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),X34)
           => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X45),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X34)) )
       => vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X18,X35),X36) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_sorted__wrt_Oinduct) ).

thf(f6714,plain,
    spl303_389,
    inference(avatar_split_clause,[],[f1860,f6712]) ).

thf(f6712,plain,
    ( spl303_389
  <=> ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK159,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK161,X0)),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_389])]) ).

thf(f1860,plain,
    ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK159,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK161,X0)),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1344]) ).

thf(f1344,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK159,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK161,X0)),nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK158,sK159,sK160,sK161])],[f1341,f1343,f1342]) ).

thf(f1342,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o] :
      ( ? [X3: secrecy_KS > secrecy_KS > $o,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),X5) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK159,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1343,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o] :
      ( ? [X6: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),nil_Secrecy_KS) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK161,X0)),nil_Secrecy_KS) ) ),
    introduced(choice_axiom,[]) ).

thf(f1341,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X3: secrecy_KS > secrecy_KS > $o,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),X5) ) )
      | ? [X6: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X6),nil_Secrecy_KS) ) ),
    inference(rectify,[],[f1084]) ).

thf(f1084,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),X6) ) )
      | ? [X3: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1083]) ).

thf(f1083,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),X6) ) )
      | ? [X3: secrecy_KS > secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f646]) ).

thf(f646,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ! [X3: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS) )
     => ( ! [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS,X6: list_Secrecy_KS] :
            ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),X6) )
           => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) ) )
       => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f645]) ).

thf(f645,plain,
    ! [X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS] :
      ( ! [X3: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X3),nil_Secrecy_KS)
     => ( ! [X4: secrecy_KS > secrecy_KS > $o,X5: secrecy_KS,X6: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),X6)
           => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6)) )
       => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f48]) ).

thf(f48,axiom,
    ! [X18: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X35: secrecy_KS > secrecy_KS > $o,X36: list_Secrecy_KS] :
      ( ! [X45: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),nil_Secrecy_KS)
     => ( ! [X45: secrecy_KS > secrecy_KS > $o,X20: secrecy_KS,X34: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),X34)
           => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X45),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X34)) )
       => vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X18,X35),X36) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_sorted__wrt_Oinduct) ).

thf(f6700,plain,
    spl303_388,
    inference(avatar_split_clause,[],[f3075,f6698]) ).

thf(f6698,plain,
    ( spl303_388
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) = X1 )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_388])]) ).

thf(f3075,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(forward_demodulation,[],[f1767,f1527]) ).

thf(f1767,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(cnf_transformation,[],[f1291]) ).

thf(f1291,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) = X1 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100,sK101,sK102])],[f1288,f1290,f1289]) ).

thf(f1289,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 ) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) )
        & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1290,plain,
    ! [X1: list_S529945141ession] :
      ( ? [X5: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession) = X1 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1288,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X3) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 ) )
      | ? [X5: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(rectify,[],[f1048]) ).

thf(f1048,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X1 ) )
      | ? [X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(flattening,[],[f1047]) ).

thf(f1047,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
          & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X1 ) )
      | ? [X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(ennf_transformation,[],[f576]) ).

thf(f576,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) )
     => ( ( nil_Se901661471ession != X1 )
       => ( ! [X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) != X1 )
         => ~ ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X1 )
               => ~ ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
                    & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) ) ) ) ) ) ),
    inference(fool_elimination,[],[f575]) ).

thf(f575,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1)
     => ( ( nil_Se901661471ession != X1 )
       => ( ! [X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) != X1 )
         => ~ ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X1 )
               => ~ ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))
                    & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) ) ) ) ) ),
    inference(rectify,[],[f330]) ).

thf(f330,axiom,
    ! [X39: secrecy_Expression > secrecy_Expression > $o,X56: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X39),X56)
     => ( ( nil_Se901661471ession != X56 )
       => ( ! [X20: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession) != X56 )
         => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32)) = X56 )
               => ~ ( vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))
                    & vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X39,X20),X33) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_successively_Oelims_I2_J) ).

thf(f6696,plain,
    spl303_387,
    inference(avatar_split_clause,[],[f3072,f6694]) ).

thf(f6694,plain,
    ( spl303_387
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) = X1 )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_387])]) ).

thf(f3072,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(forward_demodulation,[],[f1761,f1526]) ).

thf(f1761,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f1287,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) = X1 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK95,sK96,sK97,sK98])],[f1284,f1286,f1285]) ).

thf(f1285,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X2),X3) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) = X1 ) )
     => ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1286,plain,
    ! [X1: list_Secrecy_KS] :
      ( ? [X5: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS) = X1 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1284,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X2),X3) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) = X1 ) )
      | ? [X5: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(rectify,[],[f1043]) ).

thf(f1043,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X1 ) )
      | ? [X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(flattening,[],[f1042]) ).

thf(f1042,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
          & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X1 ) )
      | ? [X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(ennf_transformation,[],[f568]) ).

thf(f568,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) )
     => ( ( nil_Secrecy_KS != X1 )
       => ( ! [X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) != X1 )
         => ~ ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X1 )
               => ~ ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
                    & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) ) ) ) ) ) ),
    inference(fool_elimination,[],[f567]) ).

thf(f567,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1)
     => ( ( nil_Secrecy_KS != X1 )
       => ( ! [X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) != X1 )
         => ~ ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X1 )
               => ~ ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))
                    & vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) ) ) ) ) ),
    inference(rectify,[],[f329]) ).

thf(f329,axiom,
    ! [X39: secrecy_KS > secrecy_KS > $o,X56: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X39),X56)
     => ( ( nil_Secrecy_KS != X56 )
       => ( ! [X20: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS) != X56 )
         => ~ ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32)) = X56 )
               => ~ ( vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X39),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32))
                    & vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X39,X20),X33) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_successively_Oelims_I2_J) ).

thf(f6665,plain,
    spl303_386,
    inference(avatar_split_clause,[],[f2004,f6663]) ).

thf(f6663,plain,
    ( spl303_386
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_386])]) ).

thf(f2004,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK292,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK293,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1469]) ).

thf(f6661,plain,
    spl303_385,
    inference(avatar_split_clause,[],[f2002,f6659]) ).

thf(f6659,plain,
    ( spl303_385
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_385])]) ).

thf(f2002,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession > list_S529945141ession > $o,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK290,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK291,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X3,nil_Se901661471ession),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1469]) ).

thf(f6656,plain,
    spl303_384,
    inference(avatar_split_clause,[],[f2000,f6654]) ).

thf(f6654,plain,
    ( spl303_384
  <=> ! [X0: secrecy_KS > secrecy_Expression > $o,X3: list_Secrecy_KS > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_384])]) ).

thf(f2000,plain,
    ! [X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),sK288,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK289,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1467]) ).

thf(f6652,plain,
    spl303_383,
    inference(avatar_split_clause,[],[f1998,f6650]) ).

thf(f6650,plain,
    ( spl303_383
  <=> ! [X0: secrecy_KS > secrecy_Expression > $o,X3: list_Secrecy_KS > list_S529945141ession > $o,X2: list_S529945141ession,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_383])]) ).

thf(f1998,plain,
    ! [X2: list_S529945141ession,X3: list_Secrecy_KS > list_S529945141ession > $o,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,X1),X2) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),sK286,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK287,X3),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),X3,nil_Secrecy_KS),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1467]) ).

thf(f6648,plain,
    spl303_382,
    inference(avatar_split_clause,[],[f1996,f6646]) ).

thf(f6646,plain,
    ( spl303_382
  <=> ! [X0: secrecy_Expression > secrecy_KS > $o,X3: list_S529945141ession > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_382])]) ).

thf(f1996,plain,
    ! [X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),sK284,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK285,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1465]) ).

thf(f6644,plain,
    spl303_381,
    inference(avatar_split_clause,[],[f1994,f6642]) ).

thf(f6642,plain,
    ( spl303_381
  <=> ! [X0: secrecy_Expression > secrecy_KS > $o,X3: list_S529945141ession > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_381])]) ).

thf(f1994,plain,
    ! [X2: list_Secrecy_KS,X3: list_S529945141ession > list_Secrecy_KS > $o,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),sK282,X3),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),sK283,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),X3,nil_Se901661471ession),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1465]) ).

thf(f6640,plain,
    spl303_380,
    inference(avatar_split_clause,[],[f1985,f6638]) ).

thf(f6638,plain,
    ( spl303_380
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_380])]) ).

thf(f1985,plain,
    ! [X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK271,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK272,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1455]) ).

thf(f6636,plain,
    spl303_379,
    inference(avatar_split_clause,[],[f1983,f6634]) ).

thf(f6634,plain,
    ( spl303_379
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_379])]) ).

thf(f1983,plain,
    ! [X2: list_Secrecy_KS,X3: list_Secrecy_KS > list_Secrecy_KS > $o,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,X1),X2) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK269,X3),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK270,X3),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X3,nil_Secrecy_KS),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1455]) ).

thf(f6594,plain,
    spl303_378,
    inference(avatar_split_clause,[],[f1943,f6592]) ).

thf(f6592,plain,
    ( spl303_378
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_378])]) ).

thf(f1943,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1434]) ).

thf(f1434,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK247,X2),X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK248,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK245,sK246,sK247,sK248])],[f1429,f1433,f1432,f1431,f1430]) ).

thf(f1430,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression] :
          ( ? [X4: secrecy_Expression] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ? [X5: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
          & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X6) = X2 ) )
     => ( ? [X4: secrecy_Expression] :
            ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),X4) )
            & ? [X5: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
        & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),X6) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1431,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X4: secrecy_Expression] :
          ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),X4) )
          & ? [X5: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
     => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)) )
        & ? [X5: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)),X5) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1432,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X5: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)),X5) = X1 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK247,X2),X1),X0)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1433,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),X6) = X2 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK248,X2),X1),X0)) = X2 ) ),
    introduced(choice_axiom,[]) ).

thf(f1429,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression] :
          ( ? [X4: secrecy_Expression] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ? [X5: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5) = X1 ) )
          & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X6) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ),
    inference(rectify,[],[f1428]) ).

thf(f1428,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X2: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression] :
          ( ? [X5: secrecy_Expression] :
              ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X5) )
              & ? [X6: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X2 ) )
          & ? [X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X1),X2),X0) ) ),
    inference(nnf_transformation,[],[f1189]) ).

thf(f6590,plain,
    spl303_377,
    inference(avatar_split_clause,[],[f1942,f6588]) ).

thf(f6588,plain,
    ( spl303_377
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK247,X2),X1),X0)) = X1 )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_377])]) ).

thf(f1942,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK246,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK247,X2),X1),X0)) = X1 )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1434]) ).

thf(f6586,plain,
    spl303_376,
    inference(avatar_split_clause,[],[f1941,f6584]) ).

thf(f6584,plain,
    ( spl303_376
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK248,X2),X1),X0)) = X2 )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_376])]) ).

thf(f1941,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK245,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK248,X2),X1),X0)) = X2 )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP15,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1434]) ).

thf(f6582,plain,
    spl303_375,
    inference(avatar_split_clause,[],[f1937,f6580]) ).

thf(f6580,plain,
    ( spl303_375
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_375])]) ).

thf(f1937,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1427]) ).

thf(f6578,plain,
    spl303_374,
    inference(avatar_split_clause,[],[f1936,f6576]) ).

thf(f6576,plain,
    ( spl303_374
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) = X1 )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_374])]) ).

thf(f1936,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK242,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK244,X2),X1),X0)) = X1 )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1427]) ).

thf(f6574,plain,
    spl303_373,
    inference(avatar_split_clause,[],[f1935,f6572]) ).

thf(f6572,plain,
    ( spl303_373
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)) = X2 )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_373])]) ).

thf(f1935,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK241,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK243,X2),X1),X0)) = X2 )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1427]) ).

thf(f6569,plain,
    spl303_372,
    inference(avatar_split_clause,[],[f1931,f6567]) ).

thf(f6567,plain,
    ( spl303_372
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_372])]) ).

thf(f1931,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1422]) ).

thf(f6565,plain,
    spl303_371,
    inference(avatar_split_clause,[],[f1930,f6563]) ).

thf(f6563,plain,
    ( spl303_371
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) = X1 )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_371])]) ).

thf(f1930,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_Expression)),sK238,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_S529945141ession)),sK240,X2),X1),X0)) = X1 )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1422]) ).

thf(f6561,plain,
    spl303_370,
    inference(avatar_split_clause,[],[f1929,f6559]) ).

thf(f6559,plain,
    ( spl303_370
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)) = X2 )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_370])]) ).

thf(f1929,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),secrecy_KS)),sK237,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),list_Secrecy_KS)),sK239,X2),X1),X0)) = X2 )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1422]) ).

thf(f6557,plain,
    spl303_369,
    inference(avatar_split_clause,[],[f1925,f6555]) ).

thf(f6555,plain,
    ( spl303_369
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_369])]) ).

thf(f1925,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1417]) ).

thf(f6553,plain,
    spl303_368,
    inference(avatar_split_clause,[],[f1924,f6551]) ).

thf(f6551,plain,
    ( spl303_368
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) = X1 )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_368])]) ).

thf(f1924,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_KS)),sK234,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK236,X2),X1),X0)) = X1 )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1417]) ).

thf(f6549,plain,
    spl303_367,
    inference(avatar_split_clause,[],[f1923,f6547]) ).

thf(f6547,plain,
    ( spl303_367
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)) = X2 )
        | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_367])]) ).

thf(f1923,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),secrecy_Expression)),sK233,X2),X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),list_S529945141ession)),sK235,X2),X1),X0)) = X2 )
      | ( $true != vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1417]) ).

thf(f6545,plain,
    spl303_366,
    inference(avatar_split_clause,[],[f1916,f6543]) ).

thf(f6543,plain,
    ( spl303_366
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_366])]) ).

thf(f1916,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1405]) ).

thf(f1405,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK227,X2),X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK228,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK225,sK226,sK227,sK228])],[f1400,f1404,f1403,f1402,f1401]) ).

thf(f1401,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS] :
          ( ? [X4: secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ? [X5: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
          & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X6) = X2 ) )
     => ( ? [X4: secrecy_KS] :
            ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),X4) )
            & ? [X5: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
        & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),X6) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1402,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X4: secrecy_KS] :
          ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),X4) )
          & ? [X5: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
     => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)) )
        & ? [X5: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)),X5) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1403,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X5: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)),X5) = X1 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK227,X2),X1),X0)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1404,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),X6) = X2 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK228,X2),X1),X0)) = X2 ) ),
    introduced(choice_axiom,[]) ).

thf(f1400,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS] :
          ( ? [X4: secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ? [X5: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5) = X1 ) )
          & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X6) = X2 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ),
    inference(rectify,[],[f1399]) ).

thf(f1399,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X2: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS] :
          ( ? [X5: secrecy_KS] :
              ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X5) )
              & ? [X6: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X2 ) )
          & ? [X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X1),X2),X0) ) ),
    inference(nnf_transformation,[],[f1180]) ).

thf(f6541,plain,
    spl303_365,
    inference(avatar_split_clause,[],[f1915,f6539]) ).

thf(f6539,plain,
    ( spl303_365
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK227,X2),X1),X0)) = X1 )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_365])]) ).

thf(f1915,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK226,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK227,X2),X1),X0)) = X1 )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1405]) ).

thf(f6537,plain,
    spl303_364,
    inference(avatar_split_clause,[],[f1914,f6535]) ).

thf(f6535,plain,
    ( spl303_364
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK228,X2),X1),X0)) = X2 )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_364])]) ).

thf(f1914,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK225,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK228,X2),X1),X0)) = X2 )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP10,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1405]) ).

thf(f6533,plain,
    spl303_363,
    inference(avatar_split_clause,[],[f1910,f6531]) ).

thf(f6531,plain,
    ( spl303_363
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)) )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_363])]) ).

thf(f1910,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)) )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1398]) ).

thf(f6528,plain,
    spl303_362,
    inference(avatar_split_clause,[],[f1909,f6526]) ).

thf(f6526,plain,
    ( spl303_362
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) = X1 )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_362])]) ).

thf(f1909,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK222,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK224,X2),X1),X0)) = X1 )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1398]) ).

thf(f6524,plain,
    spl303_361,
    inference(avatar_split_clause,[],[f1908,f6522]) ).

thf(f6522,plain,
    ( spl303_361
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)) = X2 )
        | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_361])]) ).

thf(f1908,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS)),sK221,X2),X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS)),sK223,X2),X1),X0)) = X2 )
      | ( $true != vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1398]) ).

thf(f6518,plain,
    spl303_360,
    inference(avatar_split_clause,[],[f3064,f6516]) ).

thf(f6516,plain,
    ( spl303_360
  <=> ! [X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
        | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
        | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_360])]) ).

thf(f3064,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(forward_demodulation,[],[f1756,f1527]) ).

thf(f1756,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f1283,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
        & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 ) )
      | ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
        & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 ) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94])],[f1035,f1282,f1281]) ).

thf(f1281,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ? [X2: secrecy_Secrets] :
          ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X2),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
          & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2) = X1 ) )
     => ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
        & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1282,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ? [X3: secrecy_Keys] :
          ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
          & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = X1 ) )
     => ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
        & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1035,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ? [X2: secrecy_Secrets] :
          ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X2),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
          & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2) = X1 ) )
      | ? [X3: secrecy_Keys] :
          ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
          & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = X1 ) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(flattening,[],[f1034]) ).

thf(f1034,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ? [X2: secrecy_Secrets] :
          ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X2),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
          & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2) = X1 ) )
      | ? [X3: secrecy_Keys] :
          ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
          & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = X1 ) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(ennf_transformation,[],[f558]) ).

thf(f558,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) )
     => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
       => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
          | ? [X2: secrecy_Secrets] :
              ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X2),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
              & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2) = X1 ) )
          | ? [X3: secrecy_Keys] :
              ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
              & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = X1 ) ) ) ) ),
    inference(fool_elimination,[],[f557]) ).

thf(f557,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1)
     => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1)
       => ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))
          | ? [X2: secrecy_Secrets] :
              ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X2),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0))
              & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X2) = X1 ) )
          | ? [X3: secrecy_Keys] :
              ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0))
              & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = X1 ) ) ) ) ),
    inference(rectify,[],[f77]) ).

thf(f77,axiom,
    ! [X4: secrecy_specID,X9: secrecy_Expression] :
      ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X4),X9)
     => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X4),X9)
       => ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),nil_Se901661471ession))
          | ? [X51: secrecy_Secrets] :
              ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X51),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X4))
              & ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X51) = X9 ) )
          | ? [X50: secrecy_Keys] :
              ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X50),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X4))
              & ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X50) = X9 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_eoutKnowsECorrect__L1) ).

thf(f6471,plain,
    spl303_359,
    inference(avatar_split_clause,[],[f2064,f6469]) ).

thf(f6469,plain,
    ( spl303_359
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0))) )
        | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_359])]) ).

thf(f2064,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0))) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) ),
    inference(equality_resolution,[],[f1819]) ).

thf(f1819,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0))) = X2 )
      | ( X1 = X2 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f1301,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0))) = X2 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0)) = X0 ) )
      | ( ( X1 = X2 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK115,sK116])],[f1053,f1300]) ).

thf(f1300,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),X4)) = X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X0 ) )
     => ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0))) = X2 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1053,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),X4)) = X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X0 ) )
      | ( ( X1 = X2 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(flattening,[],[f1052]) ).

thf(f1052,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),X4)) = X2 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X0 ) )
      | ( ( X1 = X2 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(ennf_transformation,[],[f902]) ).

thf(f902,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X2 )
     => ( ( ( nil_Secrecy_KS = X0 )
         => ( X1 != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X0 )
             => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),X4)) != X2 ) ) ) ),
    inference(rectify,[],[f131]) ).

thf(f131,axiom,
    ! [X39: list_Secrecy_KS,X56: list_Secrecy_KS,X15: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X39),X56) = X15 )
     => ( ( ( nil_Secrecy_KS = X39 )
         => ( X15 != X56 ) )
       => ~ ! [X20: secrecy_KS,X32: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32) = X39 )
             => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X56),X32)) != X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_splice_Oelims) ).

thf(f6466,plain,
    spl303_358,
    inference(avatar_split_clause,[],[f1853,f6464]) ).

thf(f6464,plain,
    ( spl303_358
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_358])]) ).

thf(f1853,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK141,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ),
    inference(cnf_transformation,[],[f1331]) ).

thf(f6462,plain,
    spl303_357,
    inference(avatar_split_clause,[],[f1852,f6460]) ).

thf(f6460,plain,
    ( spl303_357
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_357])]) ).

thf(f1852,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK142,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK143,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK144,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK145,X0)),nil_Se901661471ession) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK146,X0)) ) ),
    inference(cnf_transformation,[],[f1331]) ).

thf(f6458,plain,
    spl303_356,
    inference(avatar_split_clause,[],[f1848,f6456]) ).

thf(f6456,plain,
    ( spl303_356
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_356])]) ).

thf(f1848,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK131,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ),
    inference(cnf_transformation,[],[f1322]) ).

thf(f6454,plain,
    spl303_355,
    inference(avatar_split_clause,[],[f1847,f6452]) ).

thf(f6452,plain,
    ( spl303_355
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_355])]) ).

thf(f1847,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK132,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK133,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK134,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK135,X0)),nil_Secrecy_KS) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK136,X0)) ) ),
    inference(cnf_transformation,[],[f1322]) ).

thf(f6440,plain,
    spl303_354,
    inference(avatar_split_clause,[],[f3073,f6438]) ).

thf(f6438,plain,
    ( spl303_354
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_354])]) ).

thf(f3073,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(forward_demodulation,[],[f1769,f1527]) ).

thf(f1769,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK101,X1),X0))) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(cnf_transformation,[],[f1291]) ).

thf(f6436,plain,
    spl303_353,
    inference(avatar_split_clause,[],[f3070,f6434]) ).

thf(f6434,plain,
    ( spl303_353
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_353])]) ).

thf(f3070,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(forward_demodulation,[],[f1763,f1526]) ).

thf(f1763,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),list_Secrecy_KS),sK97,X1),X0))) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f6425,plain,
    spl303_352,
    inference(avatar_split_clause,[],[f2018,f6423]) ).

thf(f6423,plain,
    ( spl303_352
  <=> ! [X4: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession,X2: secrecy_Expression,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4) )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1) )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_352])]) ).

thf(f2018,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(cnf_transformation,[],[f1159]) ).

thf(f1159,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(flattening,[],[f1158]) ).

thf(f1158,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(ennf_transformation,[],[f925]) ).

thf(f925,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) )
     => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1) )
       => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4) )
         => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ) ) ) ),
    inference(flattening,[],[f760]) ).

thf(f760,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) )
     => ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1) )
       => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4) )
         => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ) ) ) ),
    inference(fool_elimination,[],[f759]) ).

thf(f759,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2)
     => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X2),X1)
       => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X3),X4)
         => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ) ) ),
    inference(rectify,[],[f108]) ).

thf(f108,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X39: secrecy_Expression,X15: secrecy_Expression,X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X39),X15)
     => ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X15),X39)
       => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X28),X31)
         => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_ord_Olexordp__eq_OCons__eq) ).

thf(f6421,plain,
    ( spl303_351
    | ~ spl303_68
    | ~ spl303_94 ),
    inference(avatar_split_clause,[],[f3652,f3597,f3478,f6419]) ).

thf(f6419,plain,
    ( spl303_351
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,sK38,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_351])]) ).

thf(f3652,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,sK38,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_68
    | ~ spl303_94 ),
    inference(superposition,[],[f3479,f3598]) ).

thf(f6409,plain,
    spl303_350,
    inference(avatar_split_clause,[],[f1863,f6407]) ).

thf(f6407,plain,
    ( spl303_350
  <=> ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK172,X0)),nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_350])]) ).

thf(f1863,plain,
    ! [X2: list_S529945141ession,X0: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK169,X0)),vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),list_S529945141ession,sK171,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sK172,X0)),nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1353]) ).

thf(f6405,plain,
    spl303_349,
    inference(avatar_split_clause,[],[f1859,f6403]) ).

thf(f6403,plain,
    ( spl303_349
  <=> ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK161,X0)),nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_349])]) ).

thf(f1859,plain,
    ! [X2: list_Secrecy_KS,X0: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK158,X0)),vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK160,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sK161,X0)),nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1344]) ).

thf(f6376,plain,
    spl303_348,
    inference(avatar_split_clause,[],[f2008,f6374]) ).

thf(f6374,plain,
    ( spl303_348
  <=> ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
        | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_348])]) ).

thf(f2008,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X1),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(cnf_transformation,[],[f1473]) ).

thf(f6372,plain,
    spl303_347,
    inference(avatar_split_clause,[],[f1989,f6370]) ).

thf(f6370,plain,
    ( spl303_347
  <=> ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
        | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_347])]) ).

thf(f1989,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X1),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(cnf_transformation,[],[f1459]) ).

thf(f6368,plain,
    spl303_346,
    inference(avatar_split_clause,[],[f1725,f6366]) ).

thf(f1725,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK64,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK65,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),list_S529945141ession),sK66,X1),X0))) = X1 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(cnf_transformation,[],[f1252]) ).

thf(f6364,plain,
    ( spl303_345
    | ~ spl303_69
    | ~ spl303_94 ),
    inference(avatar_split_clause,[],[f3651,f3597,f3482,f6362]) ).

thf(f6362,plain,
    ( spl303_345
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_345])]) ).

thf(f3651,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_69
    | ~ spl303_94 ),
    inference(superposition,[],[f3483,f3598]) ).

thf(f6352,plain,
    spl303_344,
    inference(avatar_split_clause,[],[f3066,f6350]) ).

thf(f6350,plain,
    ( spl303_344
  <=> ! [X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
        | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 )
        | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_344])]) ).

thf(f3066,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
      | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(forward_demodulation,[],[f1754,f1527]) ).

thf(f1754,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f6348,plain,
    spl303_343,
    inference(avatar_split_clause,[],[f3065,f6346]) ).

thf(f6346,plain,
    ( spl303_343
  <=> ! [X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
        | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
        | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_343])]) ).

thf(f3065,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(forward_demodulation,[],[f1755,f1527]) ).

thf(f1755,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f6344,plain,
    spl303_342,
    inference(avatar_split_clause,[],[f1707,f6342]) ).

thf(f6342,plain,
    ( spl303_342
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0)))) = X0 )
        | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_342])]) ).

thf(f1707,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0)))) = X0 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ),
    inference(cnf_transformation,[],[f1248]) ).

thf(f1248,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0)))) = X0 )
          | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) ) )
        & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X0 )
          | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) != vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61,sK62])],[f1246,f1247]) ).

thf(f1247,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))) = X0 )
            | ( X2 = X3 ) )
          & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) = X0 )
            | ( X2 != X3 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 ) )
     => ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0)))) = X0 )
          | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) ) )
        & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X0 )
          | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) != vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1246,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))) = X0 )
            | ( X2 = X3 ) )
          & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) = X0 )
            | ( X2 != X3 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ),
    inference(rectify,[],[f1245]) ).

thf(f1245,plain,
    ! [X1: list_S529945141ession,X0: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X0 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) ) ),
    inference(nnf_transformation,[],[f1165]) ).

thf(f1165,plain,
    ! [X1: list_S529945141ession,X0: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X0 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6340,plain,
    spl303_341,
    inference(avatar_split_clause,[],[f1700,f6338]) ).

thf(f6338,plain,
    ( spl303_341
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0)))) = X0 )
        | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_341])]) ).

thf(f1700,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0)))) = X0 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ),
    inference(cnf_transformation,[],[f1242]) ).

thf(f1242,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0)))) = X0 )
          | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) ) )
        & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X0 )
          | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) != vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58])],[f1240,f1241]) ).

thf(f1241,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4))) = X0 )
            | ( X2 = X3 ) )
          & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X4)) = X0 )
            | ( X2 != X3 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) = X1 ) )
     => ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0)))) = X0 )
          | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) ) )
        & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X0 )
          | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) != vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1240,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4))) = X0 )
            | ( X2 = X3 ) )
          & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X4)) = X0 )
            | ( X2 != X3 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ),
    inference(rectify,[],[f1239]) ).

thf(f1239,plain,
    ! [X1: list_Secrecy_KS,X0: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X0 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) ) ),
    inference(nnf_transformation,[],[f1163]) ).

thf(f1163,plain,
    ! [X1: list_Secrecy_KS,X0: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X0 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f6323,plain,
    spl303_340,
    inference(avatar_split_clause,[],[f2065,f6321]) ).

thf(f2065,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0))) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(equality_resolution,[],[f1818]) ).

thf(f1818,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0))) = X2 )
      | ( nil_Secrecy_KS = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f6319,plain,
    spl303_339,
    inference(avatar_split_clause,[],[f2867,f6317]) ).

thf(f6317,plain,
    ( spl303_339
  <=> ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
        | ( X0 != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_339])]) ).

thf(f2867,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
      | ( X0 != X1 ) ),
    inference(equality_proxy_clausification,[],[f2866]) ).

thf(f2866,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
      | ( $false = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2862]) ).

thf(f2862,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $false = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1616]) ).

thf(f1616,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ),
    inference(cnf_transformation,[],[f443]) ).

thf(f443,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ),
    inference(fool_elimination,[],[f2]) ).

thf(f2,axiom,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
      = ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_KS_Oinject_I2_J) ).

thf(f6305,plain,
    spl303_338,
    inference(avatar_split_clause,[],[f3074,f6303]) ).

thf(f6303,plain,
    ( spl303_338
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
        | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)) )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_338])]) ).

thf(f3074,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(forward_demodulation,[],[f1768,f1527]) ).

thf(f1768,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK99,X1),X0)),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),secrecy_Expression),sK100,X1),X0)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK102,X1)),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),X1) ) ),
    inference(cnf_transformation,[],[f1291]) ).

thf(f6301,plain,
    spl303_337,
    inference(avatar_split_clause,[],[f3071,f6299]) ).

thf(f6299,plain,
    ( spl303_337
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)) )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_337])]) ).

thf(f3071,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(forward_demodulation,[],[f1762,f1526]) ).

thf(f1762,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK95,X1),X0)),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),secrecy_KS),sK96,X1),X0)) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK98,X1)),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),X1) ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f6289,plain,
    spl303_336,
    inference(avatar_split_clause,[],[f3067,f6287]) ).

thf(f6287,plain,
    ( spl303_336
  <=> ! [X0: secrecy_specID,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
        | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 )
        | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_336])]) ).

thf(f3067,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
      | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 )
      | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(forward_demodulation,[],[f1753,f1527]) ).

thf(f1753,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Secrets),sK93,X1),X0)) = X1 )
      | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_Expression,sTfun(secrecy_specID,secrecy_Keys),sK94,X1),X0)) = X1 )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),X1) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),knowle1268625169orrect,X0),X1) ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f6285,plain,
    spl303_335,
    inference(avatar_split_clause,[],[f2019,f6283]) ).

thf(f6283,plain,
    ( spl303_335
  <=> ! [X4: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession,X2: secrecy_Expression,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X3),X4) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_335])]) ).

thf(f2019,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X3),X4) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(cnf_transformation,[],[f1161]) ).

thf(f1161,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X3),X4) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(flattening,[],[f1160]) ).

thf(f1160,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X3),X4) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(ennf_transformation,[],[f762]) ).

thf(f762,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) )
     => ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X3),X4) )
       => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ) ) ),
    inference(fool_elimination,[],[f761]) ).

thf(f761,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2)
     => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X3),X4)
       => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ) ),
    inference(rectify,[],[f111]) ).

thf(f111,axiom,
    ! [X60: secrecy_Expression > secrecy_Expression > $o,X39: secrecy_Expression,X15: secrecy_Expression,X28: list_S529945141ession,X31: list_S529945141ession] :
      ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X60,X39),X15)
     => ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),X28),X31)
       => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_listrelp_OCons) ).

thf(f6257,plain,
    spl303_334,
    inference(avatar_split_clause,[],[f2865,f6255]) ).

thf(f6255,plain,
    ( spl303_334
  <=> ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
        ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_334])]) ).

thf(f2865,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
      | ( X0 = X1 ) ),
    inference(equality_proxy_clausification,[],[f2864]) ).

thf(f2864,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
      | ( $true = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2863]) ).

thf(f2863,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $true = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1616]) ).

thf(f6177,plain,
    spl303_333,
    inference(avatar_split_clause,[],[f2861,f6175]) ).

thf(f6175,plain,
    ( spl303_333
  <=> ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
        ( ( X0 = X1 )
        | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) != vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_333])]) ).

thf(f2861,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( X0 = X1 )
      | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) != vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) ) ),
    inference(equality_proxy_clausification,[],[f2860]) ).

thf(f2860,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( X0 = X1 )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0)),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2856]) ).

thf(f2856,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0)),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1617]) ).

thf(f1617,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0)),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) ),
    inference(cnf_transformation,[],[f444]) ).

thf(f444,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0)),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) ),
    inference(fool_elimination,[],[f13]) ).

thf(f13,axiom,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) )
      = ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Expression_Oinject_I2_J) ).

thf(f6173,plain,
    spl303_332,
    inference(avatar_split_clause,[],[f3059,f6171]) ).

thf(f6171,plain,
    ( spl303_332
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK85,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)))) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_332])]) ).

thf(f3059,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK85,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1744,f1527]) ).

thf(f1744,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK85,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1276]) ).

thf(f1276,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK85,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86,sK87,sK88])],[f1273,f1275,f1274]) ).

thf(f1274,plain,
    ! [X0: list_S529945141ession > $o] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X4) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK85,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1275,plain,
    ! [X0: list_S529945141ession > $o] :
      ( ? [X5: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
     => ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1273,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X4) ) )
      | ? [X5: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(rectify,[],[f1021]) ).

thf(f1021,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X5) ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(flattening,[],[f1020]) ).

thf(f1020,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X5) ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f544]) ).

thf(f544,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
     => ( ! [X2: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
       => ( ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,X0,X5) )
             => ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
               => ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,X0,X1) ) ) ) ),
    inference(fool_elimination,[],[f543]) ).

thf(f543,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession)
     => ( ! [X2: secrecy_Expression] : vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))
       => ( ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,X0,X5)
             => ( vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))
               => vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) ) )
         => vAPP(list_S529945141ession,$o,X0,X1) ) ) ),
    inference(rectify,[],[f38]) ).

thf(f38,axiom,
    ! [X18: list_S529945141ession > $o,X28: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X18,nil_Se901661471ession)
     => ( ! [X20: secrecy_Expression] : vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))
       => ( ! [X20: secrecy_Expression,X33: secrecy_Expression,X38: list_S529945141ession] :
              ( vAPP(list_S529945141ession,$o,X18,X38)
             => ( vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X38))
               => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X38))) ) )
         => vAPP(list_S529945141ession,$o,X18,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_induct__list012) ).

thf(f6169,plain,
    spl303_331,
    inference(avatar_split_clause,[],[f3056,f6167]) ).

thf(f6167,plain,
    ( spl303_331
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0)))) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_331])]) ).

thf(f3056,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0)))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1741,f1527]) ).

thf(f1741,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0)))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1272]) ).

thf(f1272,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0)))) )
        & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
          | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) = vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) ) )
        & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
          | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) != vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) ) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82,sK83,sK84])],[f1269,f1271,f1270]) ).

thf(f1270,plain,
    ! [X0: list_S529945141ession > $o] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
            | ( X2 = X3 ) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
            | ( X2 != X3 ) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0)))) )
        & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
          | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) = vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) ) )
        & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
          | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) != vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1271,plain,
    ! [X0: list_S529945141ession > $o] :
      ( ? [X5: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
     => ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1269,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4))) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
            | ( X2 = X3 ) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
            | ( X2 != X3 ) ) )
      | ? [X5: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(rectify,[],[f1019]) ).

thf(f1019,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
            | ( X3 = X4 ) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) )
            | ( X3 != X4 ) ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(flattening,[],[f1018]) ).

thf(f1018,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
            | ( X3 = X4 ) )
          & ( ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) )
            | ( X3 != X4 ) ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f542]) ).

thf(f542,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
     => ( ! [X2: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
       => ( ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( ( X3 = X4 )
               => ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) ) )
             => ( ( ( X3 != X4 )
                 => ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) ) )
               => ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,X0,X1) ) ) ) ),
    inference(fool_elimination,[],[f541]) ).

thf(f541,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession)
     => ( ! [X2: secrecy_Expression] : vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))
       => ( ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( ( X3 = X4 )
               => vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) )
             => ( ( ( X3 != X4 )
                 => vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) )
               => vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) ) )
         => vAPP(list_S529945141ession,$o,X0,X1) ) ) ),
    inference(rectify,[],[f47]) ).

thf(f47,axiom,
    ! [X18: list_S529945141ession > $o,X35: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X18,nil_Se901661471ession)
     => ( ! [X20: secrecy_Expression] : vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))
       => ( ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
              ( ( ( X20 = X33 )
               => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)) )
             => ( ( ( X20 != X33 )
                 => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32)) )
               => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))) ) )
         => vAPP(list_S529945141ession,$o,X18,X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_remdups__adj_Oinduct) ).

thf(f6165,plain,
    spl303_330,
    inference(avatar_split_clause,[],[f3051,f6163]) ).

thf(f6163,plain,
    ( spl303_330
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK73,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_330])]) ).

thf(f3051,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK73,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1734,f1526]) ).

thf(f1734,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK73,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1264]) ).

thf(f1264,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK73,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74,sK75,sK76])],[f1261,f1263,f1262]) ).

thf(f1262,plain,
    ! [X0: list_Secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X4) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK73,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1263,plain,
    ! [X0: list_Secrecy_KS > $o] :
      ( ? [X5: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1261,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X4) ) )
      | ? [X5: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(rectify,[],[f1013]) ).

thf(f1013,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X5) ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1012]) ).

thf(f1012,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X5) ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f536]) ).

thf(f536,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
     => ( ! [X2: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
       => ( ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X5) )
             => ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
               => ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) ) ) ) ),
    inference(fool_elimination,[],[f535]) ).

thf(f535,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS)
     => ( ! [X2: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))
       => ( ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,X0,X5)
             => ( vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))
               => vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) ) )
         => vAPP(list_Secrecy_KS,$o,X0,X1) ) ) ),
    inference(rectify,[],[f37]) ).

thf(f37,axiom,
    ! [X18: list_Secrecy_KS > $o,X28: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X18,nil_Secrecy_KS)
     => ( ! [X20: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))
       => ( ! [X20: secrecy_KS,X33: secrecy_KS,X38: list_Secrecy_KS] :
              ( vAPP(list_Secrecy_KS,$o,X18,X38)
             => ( vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X38))
               => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X38))) ) )
         => vAPP(list_Secrecy_KS,$o,X18,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_induct__list012) ).

thf(f6161,plain,
    spl303_329,
    inference(avatar_split_clause,[],[f3048,f6159]) ).

thf(f6159,plain,
    ( spl303_329
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0)))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_329])]) ).

thf(f3048,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0)))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1731,f1526]) ).

thf(f1731,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0)))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1260]) ).

thf(f1260,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0)))) )
        & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
          | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) = vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) ) )
        & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
          | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) != vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) ) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70,sK71,sK72])],[f1257,f1259,f1258]) ).

thf(f1258,plain,
    ! [X0: list_Secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4))) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
            | ( X2 = X3 ) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X4)) )
            | ( X2 != X3 ) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0)))) )
        & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
          | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) = vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) ) )
        & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
          | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) != vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1259,plain,
    ! [X0: list_Secrecy_KS > $o] :
      ( ? [X5: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1257,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4))) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
            | ( X2 = X3 ) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X4)) )
            | ( X2 != X3 ) ) )
      | ? [X5: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(rectify,[],[f1011]) ).

thf(f1011,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
            | ( X3 = X4 ) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) )
            | ( X3 != X4 ) ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1010]) ).

thf(f1010,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
            | ( X3 = X4 ) )
          & ( ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) )
            | ( X3 != X4 ) ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f534]) ).

thf(f534,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
     => ( ! [X2: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
       => ( ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( ( X3 = X4 )
               => ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) ) )
             => ( ( ( X3 != X4 )
                 => ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) ) )
               => ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) ) ) ) ),
    inference(fool_elimination,[],[f533]) ).

thf(f533,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS)
     => ( ! [X2: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))
       => ( ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( ( X3 = X4 )
               => vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) )
             => ( ( ( X3 != X4 )
                 => vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) )
               => vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) ) )
         => vAPP(list_Secrecy_KS,$o,X0,X1) ) ) ),
    inference(rectify,[],[f46]) ).

thf(f46,axiom,
    ! [X18: list_Secrecy_KS > $o,X35: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X18,nil_Secrecy_KS)
     => ( ! [X20: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))
       => ( ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
              ( ( ( X20 = X33 )
               => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)) )
             => ( ( ( X20 != X33 )
                 => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32)) )
               => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32))) ) )
         => vAPP(list_Secrecy_KS,$o,X18,X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_remdups__adj_Oinduct) ).

thf(f6157,plain,
    spl303_328,
    inference(avatar_split_clause,[],[f2071,f6155]) ).

thf(f2071,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)) = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X1 ) ),
    inference(equality_resolution,[],[f1822]) ).

thf(f1822,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,X2),X1),X0)) = X0 )
      | ( X1 = X2 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1303]) ).

thf(f1303,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,X2),X1),X0))) = X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,X2),X1),X0)) = X0 ) )
      | ( ( X1 = X2 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK117,sK118])],[f1056,f1302]) ).

thf(f1302,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),X4)) = X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X0 ) )
     => ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,X2),X1),X0))) = X2 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,X2),X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1056,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),X4)) = X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X0 ) )
      | ( ( X1 = X2 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) != X2 ) ),
    inference(flattening,[],[f1055]) ).

thf(f1055,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),X4)) = X2 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X0 ) )
      | ( ( X1 = X2 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) != X2 ) ),
    inference(ennf_transformation,[],[f904]) ).

thf(f904,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) = X2 )
     => ( ( ( nil_Se901661471ession = X0 )
         => ( X1 != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X0 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X1),X4)) != X2 ) ) ) ),
    inference(rectify,[],[f132]) ).

thf(f132,axiom,
    ! [X39: list_S529945141ession,X56: list_S529945141ession,X15: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X39),X56) = X15 )
     => ( ( ( nil_Se901661471ession = X39 )
         => ( X15 != X56 ) )
       => ~ ! [X20: secrecy_Expression,X32: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32) = X39 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X56),X32)) != X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_splice_Oelims) ).

thf(f6153,plain,
    spl303_327,
    inference(avatar_split_clause,[],[f2066,f6151]) ).

thf(f2066,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)) = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) = X1 ) ),
    inference(equality_resolution,[],[f1817]) ).

thf(f1817,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0)) = X0 )
      | ( X1 = X2 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f6149,plain,
    spl303_326,
    inference(avatar_split_clause,[],[f2009,f6147]) ).

thf(f6147,plain,
    ( spl303_326
  <=> ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
        | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_326])]) ).

thf(f2009,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK296,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession),sK297,X1),X0)) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(cnf_transformation,[],[f1473]) ).

thf(f6145,plain,
    spl303_325,
    inference(avatar_split_clause,[],[f2007,f6143]) ).

thf(f6143,plain,
    ( spl303_325
  <=> ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)) )
        | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_325])]) ).

thf(f2007,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(cnf_transformation,[],[f1473]) ).

thf(f6141,plain,
    spl303_324,
    inference(avatar_split_clause,[],[f2006,f6139]) ).

thf(f6139,plain,
    ( spl303_324
  <=> ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)) )
        | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_324])]) ).

thf(f2006,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: secrecy_Expression > secrecy_Expression > $o] :
      ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK294,X1),X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression),sK295,X1),X0)) )
      | ( $true != vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),$o),sP17,X1),X0) ) ),
    inference(cnf_transformation,[],[f1473]) ).

thf(f6137,plain,
    spl303_323,
    inference(avatar_split_clause,[],[f1990,f6135]) ).

thf(f6135,plain,
    ( spl303_323
  <=> ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
        | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_323])]) ).

thf(f1990,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK275,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS),sK276,X1),X0)) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(cnf_transformation,[],[f1459]) ).

thf(f6133,plain,
    spl303_322,
    inference(avatar_split_clause,[],[f2859,f6131]) ).

thf(f6131,plain,
    ( spl303_322
  <=> ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
        ( ( X0 != X1 )
        | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_322])]) ).

thf(f2859,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( X0 != X1 )
      | ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) ) ),
    inference(equality_proxy_clausification,[],[f2858]) ).

thf(f2858,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( X0 != X1 )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0)),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2857]) ).

thf(f2857,plain,
    ! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( $false = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0)),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1617]) ).

thf(f6129,plain,
    spl303_321,
    inference(avatar_split_clause,[],[f1988,f6127]) ).

thf(f6127,plain,
    ( spl303_321
  <=> ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)) )
        | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_321])]) ).

thf(f1988,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(cnf_transformation,[],[f1459]) ).

thf(f6125,plain,
    spl303_320,
    inference(avatar_split_clause,[],[f1987,f6123]) ).

thf(f6123,plain,
    ( spl303_320
  <=> ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)) )
        | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_320])]) ).

thf(f1987,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: secrecy_KS > secrecy_KS > $o] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK273,X1),X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS),sK274,X1),X0)) )
      | ( $true != vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),$o),sP16,X1),X0) ) ),
    inference(cnf_transformation,[],[f1459]) ).

thf(f6029,plain,
    spl303_319,
    inference(avatar_split_clause,[],[f3058,f6027]) ).

thf(f6027,plain,
    ( spl303_319
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
        | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) != vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_319])]) ).

thf(f3058,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
      | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) != vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1739,f1527]) ).

thf(f1739,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
      | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) != vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1272]) ).

thf(f6025,plain,
    spl303_318,
    inference(avatar_split_clause,[],[f3057,f6023]) ).

thf(f6023,plain,
    ( spl303_318
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
        | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) = vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_318])]) ).

thf(f3057,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
      | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) = vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1740,f1527]) ).

thf(f1740,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK83,X0))) )
      | ( vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK81,X0) = vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK82,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK84,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1272]) ).

thf(f6021,plain,
    spl303_317,
    inference(avatar_split_clause,[],[f2855,f6019]) ).

thf(f6019,plain,
    ( spl303_317
  <=> ! [X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
        | ( X0 != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_317])]) ).

thf(f2855,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
      | ( X0 != X1 ) ),
    inference(equality_proxy_clausification,[],[f2854]) ).

thf(f2854,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
      | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2850]) ).

thf(f2850,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1618]) ).

thf(f1618,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) ),
    inference(cnf_transformation,[],[f446]) ).

thf(f446,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) ),
    inference(fool_elimination,[],[f445]) ).

thf(f445,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
      = ( X0 = X1 ) ),
    inference(rectify,[],[f12]) ).

thf(f12,axiom,
    ! [X12: secrecy_Keys,X13: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X12) = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X13) )
      = ( X12 = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_KS_Oinject_I1_J) ).

thf(f6017,plain,
    spl303_316,
    inference(avatar_split_clause,[],[f3050,f6015]) ).

thf(f6015,plain,
    ( spl303_316
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) != vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_316])]) ).

thf(f3050,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
      | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) != vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1729,f1526]) ).

thf(f1729,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
      | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) != vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1260]) ).

thf(f6013,plain,
    spl303_315,
    inference(avatar_split_clause,[],[f3049,f6011]) ).

thf(f6011,plain,
    ( spl303_315
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
        | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) = vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_315])]) ).

thf(f3049,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
      | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) = vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1730,f1526]) ).

thf(f1730,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK71,X0))) )
      | ( vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK69,X0) = vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK70,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK72,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1260]) ).

thf(f6009,plain,
    spl303_314,
    inference(avatar_split_clause,[],[f1856,f6007]) ).

thf(f6007,plain,
    ( spl303_314
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK147,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_314])]) ).

thf(f1856,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK147,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) ) ),
    inference(cnf_transformation,[],[f1335]) ).

thf(f1335,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK147,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK147,sK148,sK149,sK150])],[f1332,f1334,f1333]) ).

thf(f1333,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),X5) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X5),X4) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),secrecy_Expression,sK147,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0))),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1334,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o] :
      ( ? [X6: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X6) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1332,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession,X5: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)),X5) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X5),X4) ) )
      | ? [X6: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X6) ) ),
    inference(rectify,[],[f1080]) ).

thf(f1080,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X4: secrecy_Expression,X5: list_S529945141ession,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)),X6) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),X5) ) )
      | ? [X3: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3) ) ),
    inference(flattening,[],[f1079]) ).

thf(f1079,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ? [X4: secrecy_Expression,X5: list_S529945141ession,X6: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)),X6) )
          & ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),X5) ) )
      | ? [X3: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3) ) ),
    inference(ennf_transformation,[],[f642]) ).

thf(f642,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ! [X3: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3) )
     => ( ! [X4: secrecy_Expression,X5: list_S529945141ession,X6: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),X5) )
           => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)),X6) ) )
       => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f641]) ).

thf(f641,plain,
    ! [X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ! [X3: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),X3)
     => ( ! [X4: secrecy_Expression,X5: list_S529945141ession,X6: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X6),X5)
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)),X6) )
       => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f36]) ).

thf(f36,axiom,
    ! [X18: list_S529945141ession > list_S529945141ession > $o,X35: list_S529945141ession,X36: list_S529945141ession] :
      ( ! [X37: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,nil_Se901661471ession),X37)
     => ( ! [X20: secrecy_Expression,X32: list_S529945141ession,X34: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X34),X32)
           => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),X34) )
       => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X18,X35),X36) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_splice_Oinduct) ).

thf(f6005,plain,
    spl303_313,
    inference(avatar_split_clause,[],[f1851,f6003]) ).

thf(f6003,plain,
    ( spl303_313
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK137,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_313])]) ).

thf(f1851,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK137,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) ) ),
    inference(cnf_transformation,[],[f1326]) ).

thf(f1326,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK137,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK137,sK138,sK139,sK140])],[f1323,f1325,f1324]) ).

thf(f1324,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),X5) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X5),X4) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),secrecy_KS,sK137,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0))),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)) )
        & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1325,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o] :
      ( ? [X6: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X6) )
     => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1323,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS,X5: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)),X5) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X5),X4) ) )
      | ? [X6: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X6) ) ),
    inference(rectify,[],[f1076]) ).

thf(f1076,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X4: secrecy_KS,X5: list_Secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)),X6) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),X5) ) )
      | ? [X3: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3) ) ),
    inference(flattening,[],[f1075]) ).

thf(f1075,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ? [X4: secrecy_KS,X5: list_Secrecy_KS,X6: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)),X6) )
          & ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),X5) ) )
      | ? [X3: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3) ) ),
    inference(ennf_transformation,[],[f638]) ).

thf(f638,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ! [X3: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3) )
     => ( ! [X4: secrecy_KS,X5: list_Secrecy_KS,X6: list_Secrecy_KS] :
            ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),X5) )
           => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)),X6) ) )
       => ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f637]) ).

thf(f637,plain,
    ! [X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ! [X3: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),X3)
     => ( ! [X4: secrecy_KS,X5: list_Secrecy_KS,X6: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X6),X5)
           => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)),X6) )
       => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f35]) ).

thf(f35,axiom,
    ! [X18: list_Secrecy_KS > list_Secrecy_KS > $o,X35: list_Secrecy_KS,X36: list_Secrecy_KS] :
      ( ! [X37: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,nil_Secrecy_KS),X37)
     => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS,X34: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X34),X32)
           => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),X34) )
       => vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X18,X35),X36) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_splice_Oinduct) ).

thf(f5993,plain,
    spl303_312,
    inference(avatar_split_clause,[],[f1899,f5991]) ).

thf(f5991,plain,
    ( spl303_312
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)),X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_312])]) ).

thf(f1899,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)),X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1393]) ).

thf(f1393,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)),X0)) )
        & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK217,sK218,sK219,sK220])],[f1390,f1392,f1391]) ).

thf(f1391,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X0)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X2 ) )
     => ( ? [X6: list_S529945141ession,X5: secrecy_Expression] :
            ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)),X0)) )
            & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0) = X5 )
            & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1392,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X6: list_S529945141ession,X5: secrecy_Expression] :
          ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)),X0)) )
          & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0) = X5 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
     => ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)),X0)) )
        & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1390,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X0)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ),
    inference(rectify,[],[f1389]) ).

thf(f1389,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) ) ),
    inference(nnf_transformation,[],[f1174]) ).

thf(f1174,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f5989,plain,
    spl303_311,
    inference(avatar_split_clause,[],[f1895,f5987]) ).

thf(f5987,plain,
    ( spl303_311
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_311])]) ).

thf(f1895,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1388]) ).

thf(f1388,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0))) )
        & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK213,sK214,sK215,sK216])],[f1385,f1387,f1386]) ).

thf(f1386,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X4)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X2 ) )
     => ( ? [X6: list_S529945141ession,X5: secrecy_Expression] :
            ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0))) )
            & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0) = X5 )
            & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1387,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X6: list_S529945141ession,X5: secrecy_Expression] :
          ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0))) )
          & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0) = X5 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
     => ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0))) )
        & ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1385,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X4)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X1 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ),
    inference(rectify,[],[f1384]) ).

thf(f1384,plain,
    ! [X1: list_S529945141ession,X0: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: list_S529945141ession] :
          ( ? [X9: secrecy_Expression,X10: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) ) ),
    inference(nnf_transformation,[],[f1175]) ).

thf(f1175,plain,
    ! [X1: list_S529945141ession,X0: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: list_S529945141ession] :
          ( ? [X9: secrecy_Expression,X10: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f5985,plain,
    spl303_310,
    inference(avatar_split_clause,[],[f2853,f5983]) ).

thf(f5983,plain,
    ( spl303_310
  <=> ! [X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_310])]) ).

thf(f2853,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
      | ( X0 = X1 ) ),
    inference(equality_proxy_clausification,[],[f2852]) ).

thf(f2852,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) )
      | ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2851]) ).

thf(f2851,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1618]) ).

thf(f5981,plain,
    spl303_309,
    inference(avatar_split_clause,[],[f1886,f5979]) ).

thf(f5979,plain,
    ( spl303_309
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)),X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_309])]) ).

thf(f1886,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)),X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1383]) ).

thf(f1383,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)),X0)) )
        & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK209,sK210,sK211,sK212])],[f1380,f1382,f1381]) ).

thf(f1381,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X0)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X2 ) )
     => ( ? [X6: list_Secrecy_KS,X5: secrecy_KS] :
            ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)),X0)) )
            & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0) = X5 )
            & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1382,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X6: list_Secrecy_KS,X5: secrecy_KS] :
          ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)),X0)) )
          & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0) = X5 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
     => ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)),X0)) )
        & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1380,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X0)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ),
    inference(rectify,[],[f1379]) ).

thf(f1379,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) ) ),
    inference(nnf_transformation,[],[f1171]) ).

thf(f1171,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f5977,plain,
    spl303_308,
    inference(avatar_split_clause,[],[f1882,f5975]) ).

thf(f5975,plain,
    ( spl303_308
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_308])]) ).

thf(f1882,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1378]) ).

thf(f1378,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0))) )
        & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0)) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK205,sK206,sK207,sK208])],[f1375,f1377,f1376]) ).

thf(f1376,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X4)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X2 ) )
     => ( ? [X6: list_Secrecy_KS,X5: secrecy_KS] :
            ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0))) )
            & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0) = X5 )
            & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1377,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X6: list_Secrecy_KS,X5: secrecy_KS] :
          ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0))) )
          & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0) = X5 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
     => ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0))) )
        & ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1375,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X4)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X1 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ),
    inference(rectify,[],[f1374]) ).

thf(f1374,plain,
    ! [X1: list_Secrecy_KS,X0: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: list_Secrecy_KS] :
          ( ? [X9: secrecy_KS,X10: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) ) ),
    inference(nnf_transformation,[],[f1172]) ).

thf(f1172,plain,
    ! [X1: list_Secrecy_KS,X0: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: list_Secrecy_KS] :
          ( ? [X9: secrecy_KS,X10: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f5853,plain,
    spl303_307,
    inference(avatar_split_clause,[],[f3082,f5851]) ).

thf(f5851,plain,
    ( spl303_307
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)))),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_307])]) ).

thf(f3082,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)))),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)))) ),
    inference(forward_demodulation,[],[f3081,f3005]) ).

thf(f3005,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f1609,f1527]) ).

thf(f1609,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) ),
    inference(cnf_transformation,[],[f849]) ).

thf(f849,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) ),
    inference(rectify,[],[f194]) ).

thf(f194,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_rotate1_Osimps_I2_J) ).

thf(f3081,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)))),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)))) ),
    inference(forward_demodulation,[],[f1797,f1527]) ).

thf(f1797,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)))),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)))) ),
    inference(cnf_transformation,[],[f899]) ).

thf(f899,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)))),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)))) ),
    inference(rectify,[],[f344]) ).

thf(f344,axiom,
    ! [X101: list_S529945141ession,X39: secrecy_Expression,X102: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X101),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X102))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X101),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)))),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X102)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_remdups__adj__append) ).

thf(f5849,plain,
    spl303_306,
    inference(avatar_split_clause,[],[f3080,f5847]) ).

thf(f5847,plain,
    ( spl303_306
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)))),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_306])]) ).

thf(f3080,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)))),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)))) ),
    inference(forward_demodulation,[],[f3079,f3004]) ).

thf(f3004,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f1608,f1526]) ).

thf(f1608,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) ),
    inference(cnf_transformation,[],[f848]) ).

thf(f848,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) ),
    inference(rectify,[],[f193]) ).

thf(f193,axiom,
    ! [X39: secrecy_KS,X28: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_rotate1_Osimps_I2_J) ).

thf(f3079,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)))),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)))) ),
    inference(forward_demodulation,[],[f1796,f1526]) ).

thf(f1796,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)))),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)))) ),
    inference(cnf_transformation,[],[f898]) ).

thf(f898,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)))),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)))) ),
    inference(rectify,[],[f343]) ).

thf(f343,axiom,
    ! [X101: list_Secrecy_KS,X39: secrecy_KS,X102: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X101),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X102))) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X101),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)))),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X102)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_remdups__adj__append) ).

thf(f5845,plain,
    spl303_305,
    inference(avatar_split_clause,[],[f2849,f5843]) ).

thf(f5843,plain,
    ( spl303_305
  <=> ! [X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( X0 = X1 )
        | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) != vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_305])]) ).

thf(f2849,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( X0 = X1 )
      | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) != vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1) ) ),
    inference(equality_proxy_clausification,[],[f2848]) ).

thf(f2848,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( X0 = X1 )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0)),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2844]) ).

thf(f2844,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) )
      | ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0)),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1619]) ).

thf(f1619,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] : ( vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0)),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) ),
    inference(cnf_transformation,[],[f448]) ).

thf(f448,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] : ( vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0)),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) ),
    inference(fool_elimination,[],[f447]) ).

thf(f447,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) = vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1) )
      = ( X0 = X1 ) ),
    inference(rectify,[],[f72]) ).

thf(f72,axiom,
    ! [X12: secrecy_Keys,X13: secrecy_Keys] :
      ( ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X12) = vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X13) )
      = ( X12 = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Expression_Oinject_I1_J) ).

thf(f5841,plain,
    spl303_304,
    inference(avatar_split_clause,[],[f3041,f5839]) ).

thf(f5839,plain,
    ( spl303_304
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X0 )
        | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) != vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_304])]) ).

thf(f3041,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X0 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) != vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ),
    inference(inner_rewriting,[],[f1706]) ).

thf(f1706,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X0 )
      | ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0) != vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ),
    inference(cnf_transformation,[],[f1248]) ).

thf(f5837,plain,
    spl303_303,
    inference(avatar_split_clause,[],[f3040,f5835]) ).

thf(f5835,plain,
    ( spl303_303
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X0 )
        | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) != vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_303])]) ).

thf(f3040,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X0 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) != vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ),
    inference(inner_rewriting,[],[f1699]) ).

thf(f1699,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X0 )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0) != vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ),
    inference(cnf_transformation,[],[f1242]) ).

thf(f5833,plain,
    spl303_302,
    inference(avatar_split_clause,[],[f1827,f5831]) ).

thf(f5831,plain,
    ( spl303_302
  <=> ! [X2: list_S529945141ession,X0: list_l425507653ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X2 )
        | ( nil_li311616943ession = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_302])]) ).

thf(f1827,plain,
    ! [X2: list_S529945141ession,X0: list_l425507653ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK121,X2),X1),X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK122,X2),X1),X0))) = X2 )
      | ( nil_li311616943ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ),
    inference(cnf_transformation,[],[f1305]) ).

thf(f5829,plain,
    spl303_301,
    inference(avatar_split_clause,[],[f1826,f5827]) ).

thf(f5827,plain,
    ( spl303_301
  <=> ! [X2: list_S529945141ession,X0: list_l425507653ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0))),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)) = X1 )
        | ( nil_li311616943ession = X0 )
        | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_301])]) ).

thf(f1826,plain,
    ! [X2: list_S529945141ession,X0: list_l425507653ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession)),sK119,X2),X1),X0))),vAPP(list_l425507653ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),sK120,X2),X1),X0)) = X1 )
      | ( nil_li311616943ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2) != vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0) ) ),
    inference(cnf_transformation,[],[f1305]) ).

thf(f5789,plain,
    spl303_300,
    inference(avatar_split_clause,[],[f2847,f5787]) ).

thf(f5787,plain,
    ( spl303_300
  <=> ! [X0: secrecy_Keys,X1: secrecy_Keys] :
        ( ( X0 != X1 )
        | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) = vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_300])]) ).

thf(f2847,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( X0 != X1 )
      | ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) = vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1) ) ),
    inference(equality_proxy_clausification,[],[f2846]) ).

thf(f2846,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( X0 != X1 )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0)),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) ) ),
    inference(equality_proxy_clausification,[],[f2845]) ).

thf(f2845,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( $false = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),vEQ(secrecy_Keys),X0),X1) )
      | ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),vEQ(secrecy_Expression),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0)),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) ) ),
    inference(binary_proxy_clausification,[],[f1619]) ).

thf(f5785,plain,
    spl303_299,
    inference(avatar_split_clause,[],[f2072,f5783]) ).

thf(f2072,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1)),X1),X0)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(equality_resolution,[],[f1821]) ).

thf(f1821,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK117,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK118,X2),X1),X0)) = X0 )
      | ( nil_Se901661471ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1303]) ).

thf(f5781,plain,
    spl303_298,
    inference(avatar_split_clause,[],[f2067,f5779]) ).

thf(f2067,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1)),X1),X0)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(equality_resolution,[],[f1816]) ).

thf(f1816,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK115,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK116,X2),X1),X0)) = X0 )
      | ( nil_Secrecy_KS = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f1301]) ).

thf(f5777,plain,
    spl303_297,
    inference(avatar_split_clause,[],[f1946,f5775]) ).

thf(f5775,plain,
    ( spl303_297
  <=> ! [X4: list_S529945141ession,X0: list_S529945141ession,X3: secrecy_Expression,X2: secrecy_Expression,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_297])]) ).

thf(f1946,plain,
    ! [X2: secrecy_Expression,X3: secrecy_Expression,X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X4: list_S529945141ession] :
      ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X3),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1438]) ).

thf(f5773,plain,
    spl303_296,
    inference(avatar_split_clause,[],[f1945,f5771]) ).

thf(f5771,plain,
    ( spl303_296
  <=> ! [X4: list_S529945141ession,X0: list_S529945141ession,X3: secrecy_Expression,X2: secrecy_Expression,X1: secrecy_Expression > secrecy_Expression > $o] :
        ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_296])]) ).

thf(f1945,plain,
    ! [X2: secrecy_Expression,X3: secrecy_Expression,X0: list_S529945141ession,X1: secrecy_Expression > secrecy_Expression > $o,X4: list_S529945141ession] :
      ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X1,X2),X3) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),vAPP(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)),vAPP(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o))),vAPP(list_S529945141ession,sTfun(secrecy_Expression,sTfun(secrecy_Expression,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o)))),sP14,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1438]) ).

thf(f5769,plain,
    spl303_295,
    inference(avatar_split_clause,[],[f1919,f5767]) ).

thf(f5767,plain,
    ( spl303_295
  <=> ! [X4: list_Secrecy_KS,X0: list_Secrecy_KS,X3: secrecy_KS,X2: secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_295])]) ).

thf(f1919,plain,
    ! [X2: secrecy_KS,X3: secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X4: list_Secrecy_KS] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X3),X2) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1409]) ).

thf(f5765,plain,
    spl303_294,
    inference(avatar_split_clause,[],[f1918,f5763]) ).

thf(f5763,plain,
    ( spl303_294
  <=> ! [X4: list_Secrecy_KS,X0: list_Secrecy_KS,X3: secrecy_KS,X2: secrecy_KS,X1: secrecy_KS > secrecy_KS > $o] :
        ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_294])]) ).

thf(f1918,plain,
    ! [X2: secrecy_KS,X3: secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS > secrecy_KS > $o,X4: list_Secrecy_KS] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X1,X2),X3) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),vAPP(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)),vAPP(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o))),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,sTfun(secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o)))),sP9,X4),X3),X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1409]) ).

thf(f5737,plain,
    spl303_293,
    inference(avatar_split_clause,[],[f1903,f5735]) ).

thf(f5735,plain,
    ( spl303_293
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
        | ( nil_Se901661471ession = X1 )
        | ( nil_Se901661471ession = X2 )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_293])]) ).

thf(f1903,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
      | ( nil_Se901661471ession = X1 )
      | ( nil_Se901661471ession = X2 )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1176]) ).

thf(f1176,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
      | ( ( nil_Se901661471ession = X1 )
        & ( X0 = X2 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( X0 = X1 ) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(definition_folding,[],[f1107,f1175,f1174]) ).

thf(f1107,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: list_S529945141ession] :
          ( ? [X9: secrecy_Expression,X10: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 ) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( ( nil_Se901661471ession = X1 )
        & ( X0 = X2 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( X0 = X1 ) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(flattening,[],[f1106]) ).

thf(f1106,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X7: secrecy_Expression,X8: list_S529945141ession] :
          ( ? [X9: secrecy_Expression,X10: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 ) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ? [X5: secrecy_Expression,X6: list_S529945141ession] :
              ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 ) )
      | ( ( nil_Se901661471ession = X1 )
        & ( X0 = X2 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( X0 = X1 ) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f909]) ).

thf(f909,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) )
     => ( ( ( X0 = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ( ( ( X0 = X2 )
           => ( nil_Se901661471ession != X1 ) )
         => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 )
               => ! [X5: secrecy_Expression,X6: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 )
                   => ( ( X3 = X5 )
                     => ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) ) ) ) )
           => ~ ! [X7: secrecy_Expression,X8: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 )
                 => ! [X9: secrecy_Expression,X10: list_S529945141ession] :
                      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 )
                     => ( ( X7 = X9 )
                       => ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) ) ) ) ) ) ) ) ),
    inference(flattening,[],[f676]) ).

thf(f676,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) )
     => ( ( ( X0 = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ( ( ( X0 = X2 )
           => ( nil_Se901661471ession != X1 ) )
         => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 )
               => ! [X5: secrecy_Expression,X6: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 )
                   => ( ( X3 = X5 )
                     => ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) ) ) ) )
           => ~ ! [X7: secrecy_Expression,X8: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 )
                 => ! [X9: secrecy_Expression,X10: list_S529945141ession] :
                      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 )
                     => ( ( X7 = X9 )
                       => ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f675]) ).

thf(f675,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2))
     => ( ( ( X0 = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ( ( ( X0 = X2 )
           => ( nil_Se901661471ession != X1 ) )
         => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4) = X1 )
               => ! [X5: secrecy_Expression,X6: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X5),X6) = X0 )
                   => ( ( X3 = X5 )
                     => ~ vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X6),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X4),X2)) ) ) )
           => ~ ! [X7: secrecy_Expression,X8: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X7),X8) = X2 )
                 => ! [X9: secrecy_Expression,X10: list_S529945141ession] :
                      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X9),X10) = X0 )
                     => ( ( X7 = X9 )
                       => ~ vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X10),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X8)) ) ) ) ) ) ) ),
    inference(rectify,[],[f324]) ).

thf(f324,axiom,
    ! [X71: list_S529945141ession,X28: list_S529945141ession,X31: list_S529945141ession] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X71),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),X31))
     => ( ( ( X28 = X71 )
         => ( nil_Se901661471ession != X31 ) )
       => ( ( ( X31 = X71 )
           => ( nil_Se901661471ession != X28 ) )
         => ( ! [X20: secrecy_Expression,X88: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X88) = X28 )
               => ! [X99: secrecy_Expression,X100: list_S529945141ession] :
                    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X99),X100) = X71 )
                   => ( ( X20 = X99 )
                     => ~ vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X100),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X88),X31)) ) ) )
           => ~ ! [X33: secrecy_Expression,X92: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X92) = X31 )
                 => ! [X99: secrecy_Expression,X100: list_S529945141ession] :
                      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X99),X100) = X71 )
                     => ( ( X33 = X99 )
                       => ~ vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X100),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),X92)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_shufflesE) ).

thf(f5733,plain,
    spl303_292,
    inference(avatar_split_clause,[],[f1902,f5731]) ).

thf(f5731,plain,
    ( spl303_292
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
        | ( nil_Se901661471ession = X1 )
        | ( X0 = X1 )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_292])]) ).

thf(f1902,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
      | ( nil_Se901661471ession = X1 )
      | ( X0 = X1 )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1176]) ).

thf(f5729,plain,
    spl303_291,
    inference(avatar_split_clause,[],[f1901,f5727]) ).

thf(f5727,plain,
    ( spl303_291
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
        | ( X0 = X2 )
        | ( nil_Se901661471ession = X2 )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_291])]) ).

thf(f1901,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
      | ( X0 = X2 )
      | ( nil_Se901661471ession = X2 )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1176]) ).

thf(f5725,plain,
    spl303_290,
    inference(avatar_split_clause,[],[f1900,f5723]) ).

thf(f5723,plain,
    ( spl303_290
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
        | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
        | ( X0 = X2 )
        | ( X0 = X1 )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_290])]) ).

thf(f1900,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X0),X1) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X1),X0),X2) )
      | ( X0 = X2 )
      | ( X0 = X1 )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1176]) ).

thf(f5721,plain,
    spl303_289,
    inference(avatar_split_clause,[],[f1890,f5719]) ).

thf(f5719,plain,
    ( spl303_289
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
        | ( nil_Secrecy_KS = X1 )
        | ( nil_Secrecy_KS = X2 )
        | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_289])]) ).

thf(f1890,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
      | ( nil_Secrecy_KS = X1 )
      | ( nil_Secrecy_KS = X2 )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1173]) ).

thf(f1173,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( X0 = X2 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( X0 = X1 ) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(definition_folding,[],[f1104,f1172,f1171]) ).

thf(f1104,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: list_Secrecy_KS] :
          ( ? [X9: secrecy_KS,X10: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 ) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( X0 = X2 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( X0 = X1 ) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(flattening,[],[f1103]) ).

thf(f1103,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X7: secrecy_KS,X8: list_Secrecy_KS] :
          ( ? [X9: secrecy_KS,X10: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) )
              & ( X7 = X9 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 ) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ? [X5: secrecy_KS,X6: list_Secrecy_KS] :
              ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) )
              & ( X3 = X5 )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 ) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( X0 = X2 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( X0 = X1 ) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(ennf_transformation,[],[f908]) ).

thf(f908,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) )
     => ( ( ( X0 = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ( ( ( X0 = X2 )
           => ( nil_Secrecy_KS != X1 ) )
         => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 )
               => ! [X5: secrecy_KS,X6: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 )
                   => ( ( X3 = X5 )
                     => ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) ) ) ) )
           => ~ ! [X7: secrecy_KS,X8: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 )
                 => ! [X9: secrecy_KS,X10: list_Secrecy_KS] :
                      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 )
                     => ( ( X7 = X9 )
                       => ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) ) ) ) ) ) ) ) ),
    inference(flattening,[],[f672]) ).

thf(f672,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) )
     => ( ( ( X0 = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ( ( ( X0 = X2 )
           => ( nil_Secrecy_KS != X1 ) )
         => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 )
               => ! [X5: secrecy_KS,X6: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 )
                   => ( ( X3 = X5 )
                     => ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) ) ) ) )
           => ~ ! [X7: secrecy_KS,X8: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 )
                 => ! [X9: secrecy_KS,X10: list_Secrecy_KS] :
                      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 )
                     => ( ( X7 = X9 )
                       => ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f671]) ).

thf(f671,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2))
     => ( ( ( X0 = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ( ( ( X0 = X2 )
           => ( nil_Secrecy_KS != X1 ) )
         => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4) = X1 )
               => ! [X5: secrecy_KS,X6: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X5),X6) = X0 )
                   => ( ( X3 = X5 )
                     => ~ vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X6),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X4),X2)) ) ) )
           => ~ ! [X7: secrecy_KS,X8: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X7),X8) = X2 )
                 => ! [X9: secrecy_KS,X10: list_Secrecy_KS] :
                      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X9),X10) = X0 )
                     => ( ( X7 = X9 )
                       => ~ vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X10),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X8)) ) ) ) ) ) ) ),
    inference(rectify,[],[f323]) ).

thf(f323,axiom,
    ! [X71: list_Secrecy_KS,X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X71),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X28),X31))
     => ( ( ( X28 = X71 )
         => ( nil_Secrecy_KS != X31 ) )
       => ( ( ( X31 = X71 )
           => ( nil_Secrecy_KS != X28 ) )
         => ( ! [X20: secrecy_KS,X88: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X88) = X28 )
               => ! [X99: secrecy_KS,X100: list_Secrecy_KS] :
                    ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X99),X100) = X71 )
                   => ( ( X20 = X99 )
                     => ~ vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X100),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X88),X31)) ) ) )
           => ~ ! [X33: secrecy_KS,X92: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X92) = X31 )
                 => ! [X99: secrecy_KS,X100: list_Secrecy_KS] :
                      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X99),X100) = X71 )
                     => ( ( X33 = X99 )
                       => ~ vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X100),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X28),X92)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_shufflesE) ).

thf(f5717,plain,
    spl303_288,
    inference(avatar_split_clause,[],[f1889,f5715]) ).

thf(f5715,plain,
    ( spl303_288
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
        | ( nil_Secrecy_KS = X1 )
        | ( X0 = X1 )
        | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_288])]) ).

thf(f1889,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
      | ( nil_Secrecy_KS = X1 )
      | ( X0 = X1 )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1173]) ).

thf(f5713,plain,
    spl303_287,
    inference(avatar_split_clause,[],[f1888,f5711]) ).

thf(f5711,plain,
    ( spl303_287
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
        | ( X0 = X2 )
        | ( nil_Secrecy_KS = X2 )
        | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_287])]) ).

thf(f1888,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
      | ( X0 = X2 )
      | ( nil_Secrecy_KS = X2 )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1173]) ).

thf(f5709,plain,
    spl303_286,
    inference(avatar_split_clause,[],[f1887,f5707]) ).

thf(f5707,plain,
    ( spl303_286
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
        | ( X0 = X2 )
        | ( X0 = X1 )
        | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_286])]) ).

thf(f1887,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X0),X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X1),X0),X2) )
      | ( X0 = X2 )
      | ( X0 = X1 )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,X0),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1173]) ).

thf(f5684,plain,
    spl303_285,
    inference(avatar_split_clause,[],[f1897,f5682]) ).

thf(f5682,plain,
    ( spl303_285
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)) = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_285])]) ).

thf(f1897,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK220,X2),X1),X0)) = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1393]) ).

thf(f5680,plain,
    spl303_284,
    inference(avatar_split_clause,[],[f1896,f5678]) ).

thf(f5678,plain,
    ( spl303_284
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)) = X2 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_284])]) ).

thf(f1896,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK218,X2),X1),X0)) = X2 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1393]) ).

thf(f5676,plain,
    spl303_283,
    inference(avatar_split_clause,[],[f1893,f5674]) ).

thf(f5674,plain,
    ( spl303_283
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)) = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_283])]) ).

thf(f1893,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK216,X2),X1),X0)) = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1388]) ).

thf(f5672,plain,
    spl303_282,
    inference(avatar_split_clause,[],[f1892,f5670]) ).

thf(f5670,plain,
    ( spl303_282
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0)) = X2 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_282])]) ).

thf(f1892,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sK214,X2),X1),X0)) = X2 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1388]) ).

thf(f5668,plain,
    spl303_281,
    inference(avatar_split_clause,[],[f1884,f5666]) ).

thf(f5666,plain,
    ( spl303_281
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)) = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_281])]) ).

thf(f1884,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK212,X2),X1),X0)) = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1383]) ).

thf(f5664,plain,
    spl303_280,
    inference(avatar_split_clause,[],[f1883,f5662]) ).

thf(f5662,plain,
    ( spl303_280
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)) = X2 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_280])]) ).

thf(f1883,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK210,X2),X1),X0)) = X2 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1383]) ).

thf(f5660,plain,
    spl303_279,
    inference(avatar_split_clause,[],[f1880,f5658]) ).

thf(f5658,plain,
    ( spl303_279
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)) = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_279])]) ).

thf(f1880,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK208,X2),X1),X0)) = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1378]) ).

thf(f5656,plain,
    spl303_278,
    inference(avatar_split_clause,[],[f1879,f5654]) ).

thf(f5654,plain,
    ( spl303_278
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0)) = X2 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_278])]) ).

thf(f1879,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sK206,X2),X1),X0)) = X2 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1378]) ).

thf(f5642,plain,
    spl303_277,
    inference(avatar_split_clause,[],[f1758,f5640]) ).

thf(f5640,plain,
    ( spl303_277
  <=> ! [X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
        | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_277])]) ).

thf(f1758,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(cnf_transformation,[],[f1039]) ).

thf(f1039,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(flattening,[],[f1038]) ).

thf(f1038,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(ennf_transformation,[],[f562]) ).

thf(f562,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
     => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)) )
       => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
          | ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) ) ) ) ),
    inference(fool_elimination,[],[f561]) ).

thf(f561,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1))
     => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1))
       => ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1))
          | vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X0)) ) ) ),
    inference(rectify,[],[f75]) ).

thf(f75,axiom,
    ! [X4: secrecy_specID,X3: secrecy_Keys] :
      ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X4),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3))
     => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X4),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3))
       => ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X4),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3))
          | vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X3),vAPP(secrecy_specID,set_Secrecy_Keys,specKeys,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_eoutKnowCorrect__L1k) ).

thf(f5638,plain,
    spl303_276,
    inference(avatar_split_clause,[],[f1757,f5636]) ).

thf(f5636,plain,
    ( spl303_276
  <=> ! [X0: secrecy_specID,X1: secrecy_Secrets] :
        ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
        | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_276])]) ).

thf(f1757,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(cnf_transformation,[],[f1037]) ).

thf(f1037,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(flattening,[],[f1036]) ).

thf(f1036,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
      | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(ennf_transformation,[],[f560]) ).

thf(f560,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
     => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)) )
       => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
          | ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) ) ) ) ),
    inference(fool_elimination,[],[f559]) ).

thf(f559,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))
     => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1))
       => ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))
          | vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X0)) ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X4: secrecy_specID,X3: secrecy_Secrets] :
      ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle233900195orrect,X4),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3))
     => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),eout,X4),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X3))
       => ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X4),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3))
          | vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X3),vAPP(secrecy_specID,set_Secrecy_Secrets,specSecrets,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_eoutKnowCorrect__L1s) ).

thf(f5630,plain,
    spl303_275,
    inference(avatar_split_clause,[],[f1957,f5628]) ).

thf(f5628,plain,
    ( spl303_275
  <=> ! [X0: secrecy_Expression > secrecy_Expression,X3: list_S529945141ession,X2: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),X3) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X1)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_275])]) ).

thf(f1957,plain,
    ! [X2: list_S529945141ession,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),X3) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X1)),X3)) ),
    inference(cnf_transformation,[],[f918]) ).

thf(f918,plain,
    ! [X0: secrecy_Expression > secrecy_Expression,X1: secrecy_Expression,X2: list_S529945141ession,X3: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),X3) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X0),X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X0,X1)),X3)) ),
    inference(rectify,[],[f116]) ).

thf(f116,axiom,
    ! [X59: secrecy_Expression > secrecy_Expression,X46: secrecy_Expression,X65: list_S529945141ession,X66: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X59),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X46),X65)),X66) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(secrecy_Expression,secrecy_Expression),sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),map_ta1624757057ession,X59),X65),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Expression,secrecy_Expression,X59,X46)),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_map__tailrec__rev_Osimps_I2_J) ).

thf(f5543,plain,
    spl303_274,
    inference(avatar_split_clause,[],[f3060,f5541]) ).

thf(f5541,plain,
    ( spl303_274
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0))) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_274])]) ).

thf(f3060,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1743,f1527]) ).

thf(f1743,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK86,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1276]) ).

thf(f5539,plain,
    spl303_273,
    inference(avatar_split_clause,[],[f3052,f5537]) ).

thf(f5537,plain,
    ( spl303_273
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0))) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_273])]) ).

thf(f3052,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1733,f1526]) ).

thf(f1733,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK74,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1264]) ).

thf(f5535,plain,
    spl303_272,
    inference(avatar_split_clause,[],[f3035,f5533]) ).

thf(f5533,plain,
    ( spl303_272
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
        | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)))) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_272])]) ).

thf(f3035,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)))) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f3034,f1527]) ).

thf(f3034,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)))) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f3033,f3005]) ).

thf(f3033,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),nil_Se901661471ession))) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1689,f1527]) ).

thf(f1689,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),nil_Se901661471ession))) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1238]) ).

thf(f1238,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),nil_Se901661471ession))) )
        & ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)) )
        & ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55])],[f1235,f1237,f1236]) ).

thf(f1236,plain,
    ! [X1: list_S529945141ession > $o] :
      ( ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X3) )
          & ( nil_Se901661471ession != X3 ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK53,X1)),nil_Se901661471ession))) )
        & ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)) )
        & ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1237,plain,
    ! [X1: list_S529945141ession > $o] :
      ( ? [X4: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),nil_Se901661471ession)) )
     => ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1235,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X3) )
          & ( nil_Se901661471ession != X3 ) )
      | ? [X4: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f984]) ).

thf(f984,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X4) )
          & ( nil_Se901661471ession != X4 ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(flattening,[],[f983]) ).

thf(f983,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X4) )
          & ( nil_Se901661471ession != X4 ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f516]) ).

thf(f516,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( nil_Se901661471ession != X0 )
     => ( ! [X2: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
       => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
              ( ( nil_Se901661471ession != X4 )
             => ( ( $true = vAPP(list_S529945141ession,$o,X1,X4) )
               => ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession))) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,X1,X0) ) ) ) ),
    inference(fool_elimination,[],[f515]) ).

thf(f515,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( nil_Se901661471ession != X0 )
     => ( ! [X2: secrecy_Expression] : vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))
       => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
              ( ( nil_Se901661471ession != X4 )
             => ( vAPP(list_S529945141ession,$o,X1,X4)
               => vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),nil_Se901661471ession))) ) )
         => vAPP(list_S529945141ession,$o,X1,X0) ) ) ),
    inference(rectify,[],[f179]) ).

thf(f179,axiom,
    ! [X28: list_S529945141ession,X18: list_S529945141ession > $o] :
      ( ( nil_Se901661471ession != X28 )
     => ( ! [X20: secrecy_Expression] : vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))
       => ( ! [X20: secrecy_Expression,X32: list_S529945141ession] :
              ( ( nil_Se901661471ession != X32 )
             => ( vAPP(list_S529945141ession,$o,X18,X32)
               => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X32),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))) ) )
         => vAPP(list_S529945141ession,$o,X18,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_rev__nonempty__induct) ).

thf(f5531,plain,
    spl303_271,
    inference(avatar_split_clause,[],[f3027,f5529]) ).

thf(f5529,plain,
    ( spl303_271
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_271])]) ).

thf(f3027,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)))) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f3026,f1526]) ).

thf(f3026,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)))) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f3025,f3004]) ).

thf(f3025,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),nil_Secrecy_KS))) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1679,f1526]) ).

thf(f1679,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),nil_Secrecy_KS))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1230]) ).

thf(f1230,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),nil_Secrecy_KS))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)) )
        & ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49])],[f1227,f1229,f1228]) ).

thf(f1228,plain,
    ! [X1: list_Secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X3) )
          & ( nil_Secrecy_KS != X3 ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK47,X1)),nil_Secrecy_KS))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)) )
        & ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1229,plain,
    ! [X1: list_Secrecy_KS > $o] :
      ( ? [X4: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),nil_Secrecy_KS)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1227,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X3) )
          & ( nil_Secrecy_KS != X3 ) )
      | ? [X4: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f976]) ).

thf(f976,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X4) )
          & ( nil_Secrecy_KS != X4 ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(flattening,[],[f975]) ).

thf(f975,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X4) )
          & ( nil_Secrecy_KS != X4 ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f512]) ).

thf(f512,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( nil_Secrecy_KS != X0 )
     => ( ! [X2: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
       => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
              ( ( nil_Secrecy_KS != X4 )
             => ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X4) )
               => ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS))) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) ) ) ) ),
    inference(fool_elimination,[],[f511]) ).

thf(f511,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( nil_Secrecy_KS != X0 )
     => ( ! [X2: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))
       => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
              ( ( nil_Secrecy_KS != X4 )
             => ( vAPP(list_Secrecy_KS,$o,X1,X4)
               => vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X4),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),nil_Secrecy_KS))) ) )
         => vAPP(list_Secrecy_KS,$o,X1,X0) ) ) ),
    inference(rectify,[],[f178]) ).

thf(f178,axiom,
    ! [X28: list_Secrecy_KS,X18: list_Secrecy_KS > $o] :
      ( ( nil_Secrecy_KS != X28 )
     => ( ! [X20: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))
       => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS] :
              ( ( nil_Secrecy_KS != X32 )
             => ( vAPP(list_Secrecy_KS,$o,X18,X32)
               => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X32),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))) ) )
         => vAPP(list_Secrecy_KS,$o,X18,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_rev__nonempty__induct) ).

thf(f5527,plain,
    spl303_270,
    inference(avatar_split_clause,[],[f2017,f5525]) ).

thf(f5525,plain,
    ( spl303_270
  <=> ! [X4: list_S529945141ession,X0: secrecy_Keys > secrecy_Keys > $o,X3: secrecy_specID,X2: secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X4)) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) )
        | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_270])]) ).

thf(f2017,plain,
    ! [X2: secrecy_Keys,X3: secrecy_specID,X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X4)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ),
    inference(cnf_transformation,[],[f1157]) ).

thf(f1157,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X4)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ),
    inference(flattening,[],[f1156]) ).

thf(f1156,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X4)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ),
    inference(ennf_transformation,[],[f758]) ).

thf(f758,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X4)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) )
        & ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) ) ),
    inference(fool_elimination,[],[f757]) ).

thf(f757,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X4))
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2))
        & vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) ),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    ! [X6: secrecy_Keys > secrecy_Keys > $o,X7: secrecy_Keys,X8: secrecy_Keys,X2: secrecy_specID,X9: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X7),X9))
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X8))
        & vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X6,X7),X8) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_knows4) ).

thf(f5523,plain,
    spl303_269,
    inference(avatar_split_clause,[],[f2016,f5521]) ).

thf(f5521,plain,
    ( spl303_269
  <=> ! [X4: list_S529945141ession,X0: secrecy_Keys > secrecy_Keys > $o,X3: secrecy_specID,X2: secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X2),X4)) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
        | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_269])]) ).

thf(f2016,plain,
    ! [X2: secrecy_Keys,X3: secrecy_specID,X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X2),X4)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ),
    inference(cnf_transformation,[],[f1155]) ).

thf(f1155,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X2),X4)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ),
    inference(flattening,[],[f1154]) ).

thf(f1154,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X2),X4)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) ),
    inference(ennf_transformation,[],[f756]) ).

thf(f756,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X2),X4)) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
        & ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) ) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) ) ),
    inference(fool_elimination,[],[f755]) ).

thf(f755,plain,
    ! [X0: secrecy_Keys > secrecy_Keys > $o,X1: secrecy_Keys,X2: secrecy_Keys,X3: secrecy_specID,X4: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X2),X4))
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X3),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1))
        & vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X0,X1),X2) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X3),X4) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X6: secrecy_Keys > secrecy_Keys > $o,X7: secrecy_Keys,X8: secrecy_Keys,X2: secrecy_specID,X9: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X8),X9))
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X7))
        & vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),X6,X7),X8) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_knows5) ).

thf(f5515,plain,
    spl303_268,
    inference(avatar_split_clause,[],[f1982,f5513]) ).

thf(f1982,plain,
    ! [X2: list_S529945141ession,X3: secrecy_Expression,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X1)),X2)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1137]) ).

thf(f1137,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession,X3: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X1)),X2)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f740]) ).

thf(f740,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession,X3: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) )
     => ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X1)),X2)) ) ),
    inference(fool_elimination,[],[f739]) ).

thf(f739,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession,X3: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X1)),X2)) ),
    inference(rectify,[],[f338]) ).

thf(f338,axiom,
    ! [X71: list_S529945141ession,X28: list_S529945141ession,X31: list_S529945141ession,X98: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X71),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),X31))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X98),X71)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X98),X28)),X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_Cons__in__shuffles__leftI) ).

thf(f5511,plain,
    spl303_267,
    inference(avatar_split_clause,[],[f1981,f5509]) ).

thf(f1981,plain,
    ! [X2: list_S529945141ession,X3: secrecy_Expression,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X2))) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1136]) ).

thf(f1136,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession,X3: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X2))) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f738]) ).

thf(f738,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession,X3: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2)) )
     => ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X2))) ) ),
    inference(fool_elimination,[],[f737]) ).

thf(f737,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession,X3: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),X2))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X0)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X2))) ),
    inference(rectify,[],[f337]) ).

thf(f337,axiom,
    ! [X71: list_S529945141ession,X28: list_S529945141ession,X31: list_S529945141ession,X98: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X71),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),X31))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X98),X71)),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X98),X31))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Cons__in__shuffles__rightI) ).

thf(f5507,plain,
    spl303_266,
    inference(avatar_split_clause,[],[f1705,f5505]) ).

thf(f5505,plain,
    ( spl303_266
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_266])]) ).

thf(f1705,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK60,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK61,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK62,X1),X0))) = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X1),X0) ) ),
    inference(cnf_transformation,[],[f1248]) ).

thf(f5503,plain,
    spl303_265,
    inference(avatar_split_clause,[],[f1698,f5501]) ).

thf(f5501,plain,
    ( spl303_265
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_265])]) ).

thf(f1698,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK56,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK57,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK58,X1),X0))) = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X1),X0) ) ),
    inference(cnf_transformation,[],[f1242]) ).

thf(f5483,plain,
    spl303_264,
    inference(avatar_split_clause,[],[f1855,f5481]) ).

thf(f1855,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession > list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,X1),X2) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK149,X0)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK148,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),X0,nil_Se901661471ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),list_S529945141ession,sK150,X0)) ) ),
    inference(cnf_transformation,[],[f1335]) ).

thf(f5479,plain,
    spl303_263,
    inference(avatar_split_clause,[],[f1850,f5477]) ).

thf(f1850,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS > list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,X1),X2) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK139,X0)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK138,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),X0,nil_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),list_Secrecy_KS,sK140,X0)) ) ),
    inference(cnf_transformation,[],[f1326]) ).

thf(f5453,plain,
    ( spl303_262
    | ~ spl303_37
    | ~ spl303_88 ),
    inference(avatar_split_clause,[],[f3581,f3565,f3326,f5451]) ).

thf(f3581,plain,
    ( ! [X0: secrecy_Expression] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) )
    | ~ spl303_37
    | ~ spl303_88 ),
    inference(superposition,[],[f3327,f3566]) ).

thf(f5449,plain,
    spl303_261,
    inference(avatar_split_clause,[],[f3030,f5447]) ).

thf(f5447,plain,
    ( spl303_261
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK50,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1))) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_261])]) ).

thf(f3030,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK50,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1))) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1686,f1527]) ).

thf(f1686,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK50,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1))) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1234]) ).

thf(f1234,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK50,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1))) )
        & ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1)) )
        & ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52])],[f1231,f1233,f1232]) ).

thf(f1232,plain,
    ! [X1: list_S529945141ession > $o] :
      ( ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X3) )
          & ( nil_Se901661471ession != X3 ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK50,X1)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1))) )
        & ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1)) )
        & ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1233,plain,
    ! [X1: list_S529945141ession > $o] :
      ( ? [X4: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),nil_Se901661471ession)) )
     => ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1231,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X3) )
          & ( nil_Se901661471ession != X3 ) )
      | ? [X4: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f982]) ).

thf(f982,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X4) )
          & ( nil_Se901661471ession != X4 ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(flattening,[],[f981]) ).

thf(f981,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ? [X3: secrecy_Expression,X4: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) )
          & ( $true = vAPP(list_S529945141ession,$o,X1,X4) )
          & ( nil_Se901661471ession != X4 ) )
      | ? [X2: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f514]) ).

thf(f514,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( nil_Se901661471ession != X0 )
     => ( ! [X2: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) )
       => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
              ( ( nil_Se901661471ession != X4 )
             => ( ( $true = vAPP(list_S529945141ession,$o,X1,X4) )
               => ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) ) ) )
         => ( $true = vAPP(list_S529945141ession,$o,X1,X0) ) ) ) ),
    inference(fool_elimination,[],[f513]) ).

thf(f513,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( nil_Se901661471ession != X0 )
     => ( ! [X2: secrecy_Expression] : vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))
       => ( ! [X3: secrecy_Expression,X4: list_S529945141ession] :
              ( ( nil_Se901661471ession != X4 )
             => ( vAPP(list_S529945141ession,$o,X1,X4)
               => vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) ) )
         => vAPP(list_S529945141ession,$o,X1,X0) ) ) ),
    inference(rectify,[],[f43]) ).

thf(f43,axiom,
    ! [X28: list_S529945141ession,X18: list_S529945141ession > $o] :
      ( ( nil_Se901661471ession != X28 )
     => ( ! [X20: secrecy_Expression] : vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))
       => ( ! [X20: secrecy_Expression,X32: list_S529945141ession] :
              ( ( nil_Se901661471ession != X32 )
             => ( vAPP(list_S529945141ession,$o,X18,X32)
               => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)) ) )
         => vAPP(list_S529945141ession,$o,X18,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_list__nonempty__induct) ).

thf(f5445,plain,
    spl303_260,
    inference(avatar_split_clause,[],[f3022,f5443]) ).

thf(f5443,plain,
    ( spl303_260
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK44,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1))) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_260])]) ).

thf(f3022,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK44,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1))) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1676,f1526]) ).

thf(f1676,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK44,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1226]) ).

thf(f1226,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK44,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1)) )
        & ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46])],[f1223,f1225,f1224]) ).

thf(f1224,plain,
    ! [X1: list_Secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X3) )
          & ( nil_Secrecy_KS != X3 ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK44,X1)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1)) )
        & ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1225,plain,
    ! [X1: list_Secrecy_KS > $o] :
      ( ? [X4: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),nil_Secrecy_KS)) )
     => ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1223,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X3) )
          & ( nil_Secrecy_KS != X3 ) )
      | ? [X4: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f974]) ).

thf(f974,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X4) )
          & ( nil_Secrecy_KS != X4 ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(flattening,[],[f973]) ).

thf(f973,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ? [X3: secrecy_KS,X4: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X1,X4) )
          & ( nil_Secrecy_KS != X4 ) )
      | ? [X2: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f510]) ).

thf(f510,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( nil_Secrecy_KS != X0 )
     => ( ! [X2: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) )
       => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
              ( ( nil_Secrecy_KS != X4 )
             => ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X4) )
               => ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) ) ) )
         => ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) ) ) ) ),
    inference(fool_elimination,[],[f509]) ).

thf(f509,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( nil_Secrecy_KS != X0 )
     => ( ! [X2: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))
       => ( ! [X3: secrecy_KS,X4: list_Secrecy_KS] :
              ( ( nil_Secrecy_KS != X4 )
             => ( vAPP(list_Secrecy_KS,$o,X1,X4)
               => vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) ) )
         => vAPP(list_Secrecy_KS,$o,X1,X0) ) ) ),
    inference(rectify,[],[f42]) ).

thf(f42,axiom,
    ! [X28: list_Secrecy_KS,X18: list_Secrecy_KS > $o] :
      ( ( nil_Secrecy_KS != X28 )
     => ( ! [X20: secrecy_KS] : vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))
       => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS] :
              ( ( nil_Secrecy_KS != X32 )
             => ( vAPP(list_Secrecy_KS,$o,X18,X32)
               => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)) ) )
         => vAPP(list_Secrecy_KS,$o,X18,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_list__nonempty__induct) ).

thf(f5417,plain,
    ( spl303_259
    | ~ spl303_35
    | ~ spl303_87 ),
    inference(avatar_split_clause,[],[f3578,f3561,f3318,f5415]) ).

thf(f3578,plain,
    ( ! [X0: secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_35
    | ~ spl303_87 ),
    inference(superposition,[],[f3319,f3562]) ).

thf(f5413,plain,
    spl303_258,
    inference(avatar_split_clause,[],[f1940,f5411]) ).

thf(f5411,plain,
    ( spl303_258
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) )
        | ( nil_Se901661471ession = X2 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_258])]) ).

thf(f1940,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) )
      | ( nil_Se901661471ession = X2 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1187]) ).

thf(f1187,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) )
      | ( ( nil_Se901661471ession = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1121,f1186]) ).

thf(f1121,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(flattening,[],[f1120]) ).

thf(f1120,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f914]) ).

thf(f914,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 )
             => ! [X6: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) ) ) ) ) ) ),
    inference(flattening,[],[f694]) ).

thf(f694,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 )
             => ! [X6: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) ) ) ) ) ) ),
    inference(fool_elimination,[],[f693]) ).

thf(f693,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2)
     => ( ( ( nil_Se901661471ession = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 )
             => ! [X6: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
                 => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X3),X4)
                   => ~ vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X5),X6) ) ) ) ) ),
    inference(rectify,[],[f126]) ).

thf(f126,axiom,
    ! [X60: secrecy_Expression > secrecy_Expression > $o,X36: list_S529945141ession,X40: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),X36),X40)
     => ( ( ( nil_Se901661471ession = X36 )
         => ( nil_Se901661471ession != X40 ) )
       => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32) = X36 )
             => ! [X34: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34) = X40 )
                 => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X60,X20),X33)
                   => ~ vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),X32),X34) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_listrelp_Ocases) ).

thf(f5409,plain,
    spl303_257,
    inference(avatar_split_clause,[],[f1939,f5407]) ).

thf(f5407,plain,
    ( spl303_257
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_257])]) ).

thf(f1939,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),$o)),sP13,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1187]) ).

thf(f5405,plain,
    spl303_256,
    inference(avatar_split_clause,[],[f1934,f5403]) ).

thf(f5403,plain,
    ( spl303_256
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) )
        | ( nil_Se901661471ession = X2 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_256])]) ).

thf(f1934,plain,
    ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) )
      | ( nil_Se901661471ession = X2 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1185]) ).

thf(f1185,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) )
      | ( ( nil_Se901661471ession = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1119,f1184]) ).

thf(f1119,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(flattening,[],[f1118]) ).

thf(f1118,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ? [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
          ( ? [X6: list_S529945141ession] :
              ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) )
              & ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
              & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( ( nil_Se901661471ession = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f913]) ).

thf(f913,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 )
             => ! [X6: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) ) ) ) ) ) ),
    inference(flattening,[],[f692]) ).

thf(f692,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 )
             => ! [X6: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) ) ) ) ) ) ),
    inference(fool_elimination,[],[f691]) ).

thf(f691,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2)
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( nil_Se901661471ession != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: secrecy_Expression,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 )
             => ! [X6: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X6) = X2 )
                 => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X0,X3),X4)
                   => ~ vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X5),X6) ) ) ) ) ),
    inference(rectify,[],[f124]) ).

thf(f124,axiom,
    ! [X60: secrecy_KS > secrecy_Expression > $o,X36: list_Secrecy_KS,X40: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X60),X36),X40)
     => ( ( ( nil_Secrecy_KS = X36 )
         => ( nil_Se901661471ession != X40 ) )
       => ~ ! [X20: secrecy_KS,X33: secrecy_Expression,X32: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32) = X36 )
             => ! [X34: list_S529945141ession] :
                  ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X34) = X40 )
                 => ( vAPP(secrecy_Expression,$o,vAPP(secrecy_KS,sTfun(secrecy_Expression,$o),X60,X20),X33)
                   => ~ vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X60),X32),X34) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_listrelp_Ocases) ).

thf(f5401,plain,
    spl303_255,
    inference(avatar_split_clause,[],[f1933,f5399]) ).

thf(f5399,plain,
    ( spl303_255
  <=> ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_255])]) ).

thf(f1933,plain,
    ! [X2: list_S529945141ession,X0: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,sTfun(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),$o)),sP12,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1185]) ).

thf(f5397,plain,
    spl303_254,
    inference(avatar_split_clause,[],[f1928,f5395]) ).

thf(f5395,plain,
    ( spl303_254
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) )
        | ( nil_Secrecy_KS = X2 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_254])]) ).

thf(f1928,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) )
      | ( nil_Secrecy_KS = X2 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1183]) ).

thf(f1183,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1117,f1182]) ).

thf(f1117,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(flattening,[],[f1116]) ).

thf(f1116,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f912]) ).

thf(f912,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 )
             => ! [X6: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) ) ) ) ) ) ),
    inference(flattening,[],[f690]) ).

thf(f690,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) )
     => ( ( ( nil_Se901661471ession = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 )
             => ! [X6: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) ) ) ) ) ) ),
    inference(fool_elimination,[],[f689]) ).

thf(f689,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2)
     => ( ( ( nil_Se901661471ession = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ~ ! [X3: secrecy_Expression,X4: secrecy_KS,X5: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5) = X1 )
             => ! [X6: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
                 => ( vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X0,X3),X4)
                   => ~ vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X5),X6) ) ) ) ) ),
    inference(rectify,[],[f125]) ).

thf(f125,axiom,
    ! [X60: secrecy_Expression > secrecy_KS > $o,X36: list_S529945141ession,X40: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X60),X36),X40)
     => ( ( ( nil_Se901661471ession = X36 )
         => ( nil_Secrecy_KS != X40 ) )
       => ~ ! [X20: secrecy_Expression,X33: secrecy_KS,X32: list_S529945141ession] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32) = X36 )
             => ! [X34: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34) = X40 )
                 => ( vAPP(secrecy_KS,$o,vAPP(secrecy_Expression,sTfun(secrecy_KS,$o),X60,X20),X33)
                   => ~ vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X60),X32),X34) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_listrelp_Ocases) ).

thf(f5393,plain,
    spl303_253,
    inference(avatar_split_clause,[],[f1927,f5391]) ).

thf(f5391,plain,
    ( spl303_253
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
        ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) )
        | ( nil_Se901661471ession = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_253])]) ).

thf(f1927,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o),vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),$o)),sP11,X1),X2),X0) )
      | ( nil_Se901661471ession = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1183]) ).

thf(f5389,plain,
    spl303_252,
    inference(avatar_split_clause,[],[f1913,f5387]) ).

thf(f5387,plain,
    ( spl303_252
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) )
        | ( nil_Secrecy_KS = X2 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_252])]) ).

thf(f1913,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) )
      | ( nil_Secrecy_KS = X2 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1178]) ).

thf(f1178,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(definition_folding,[],[f1113,f1177]) ).

thf(f1113,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(flattening,[],[f1112]) ).

thf(f1112,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ? [X6: list_Secrecy_KS] :
              ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) )
              & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
              & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 ) )
      | ( ( nil_Secrecy_KS = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(ennf_transformation,[],[f910]) ).

thf(f910,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 )
             => ! [X6: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) ) ) ) ) ) ),
    inference(flattening,[],[f686]) ).

thf(f686,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) )
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 )
             => ! [X6: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
                 => ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4) )
                   => ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) ) ) ) ) ) ),
    inference(fool_elimination,[],[f685]) ).

thf(f685,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2)
     => ( ( ( nil_Secrecy_KS = X1 )
         => ( nil_Secrecy_KS != X2 ) )
       => ~ ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5) = X1 )
             => ! [X6: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X6) = X2 )
                 => ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X0,X3),X4)
                   => ~ vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X5),X6) ) ) ) ) ),
    inference(rectify,[],[f123]) ).

thf(f123,axiom,
    ! [X60: secrecy_KS > secrecy_KS > $o,X36: list_Secrecy_KS,X40: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X60),X36),X40)
     => ( ( ( nil_Secrecy_KS = X36 )
         => ( nil_Secrecy_KS != X40 ) )
       => ~ ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32) = X36 )
             => ! [X34: list_Secrecy_KS] :
                  ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X34) = X40 )
                 => ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),X60,X20),X33)
                   => ~ vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X60),X32),X34) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_listrelp_Ocases) ).

thf(f5385,plain,
    spl303_251,
    inference(avatar_split_clause,[],[f1912,f5383]) ).

thf(f5383,plain,
    ( spl303_251
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_251])]) ).

thf(f1912,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),$o)),sP8,X1),X2),X0) )
      | ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1178]) ).

thf(f5377,plain,
    ( spl303_250
    | ~ spl303_3
    | ~ spl303_33 ),
    inference(avatar_split_clause,[],[f3344,f3310,f3143,f5375]) ).

thf(f5375,plain,
    ( spl303_250
  <=> ! [X0: secrecy_Expression] : ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_250])]) ).

thf(f3310,plain,
    ( spl303_33
  <=> ! [X0: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_33])]) ).

thf(f3344,plain,
    ( ! [X0: secrecy_Expression] : ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) )
    | ~ spl303_3
    | ~ spl303_33 ),
    inference(trivial_inequality_removal,[],[f3343]) ).

thf(f3343,plain,
    ( ! [X0: secrecy_Expression] :
        ( ( $true != $true )
        | ( $false = vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) ) )
    | ~ spl303_3
    | ~ spl303_33 ),
    inference(superposition,[],[f3311,f3144]) ).

thf(f3311,plain,
    ( ! [X0: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) )
    | ~ spl303_33 ),
    inference(avatar_component_clause,[],[f3310]) ).

thf(f5369,plain,
    spl303_249,
    inference(avatar_split_clause,[],[f1898,f5367]) ).

thf(f5367,plain,
    ( spl303_249
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_249])]) ).

thf(f1898,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK217,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK219,X2),X1),X0) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP6,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1393]) ).

thf(f5365,plain,
    spl303_248,
    inference(avatar_split_clause,[],[f1894,f5363]) ).

thf(f5363,plain,
    ( spl303_248
  <=> ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_248])]) ).

thf(f1894,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK213,X2),X1),X0) = vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression)),sK215,X2),X1),X0) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(list_S529945141ession,sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sP7,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1388]) ).

thf(f5361,plain,
    spl303_247,
    inference(avatar_split_clause,[],[f1885,f5359]) ).

thf(f5359,plain,
    ( spl303_247
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_247])]) ).

thf(f1885,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK209,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK211,X2),X1),X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP4,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1383]) ).

thf(f5357,plain,
    spl303_246,
    inference(avatar_split_clause,[],[f1881,f5355]) ).

thf(f5355,plain,
    ( spl303_246
  <=> ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0) )
        | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_246])]) ).

thf(f1881,plain,
    ! [X2: list_Secrecy_KS,X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK205,X2),X1),X0) = vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS)),sK207,X2),X1),X0) )
      | ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1378]) ).

thf(f5343,plain,
    ( spl303_245
    | ~ spl303_3
    | ~ spl303_32 ),
    inference(avatar_split_clause,[],[f3342,f3306,f3143,f5341]) ).

thf(f5341,plain,
    ( spl303_245
  <=> ! [X0: secrecy_KS] : ( $false = vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_245])]) ).

thf(f3306,plain,
    ( spl303_32
  <=> ! [X0: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_32])]) ).

thf(f3342,plain,
    ( ! [X0: secrecy_KS] : ( $false = vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_3
    | ~ spl303_32 ),
    inference(trivial_inequality_removal,[],[f3341]) ).

thf(f3341,plain,
    ( ! [X0: secrecy_KS] :
        ( ( $true != $true )
        | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) ) )
    | ~ spl303_3
    | ~ spl303_32 ),
    inference(superposition,[],[f3307,f3144]) ).

thf(f3307,plain,
    ( ! [X0: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) )
    | ~ spl303_32 ),
    inference(avatar_component_clause,[],[f3306]) ).

thf(f5339,plain,
    spl303_244,
    inference(avatar_split_clause,[],[f1752,f5337]) ).

thf(f5337,plain,
    ( spl303_244
  <=> ! [X0: set_li185139947ession,X1: secrecy_Expression] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)) )
        | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),nil_Se901661471ession)) )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_244])]) ).

thf(f1752,plain,
    ! [X0: set_li185139947ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),nil_Se901661471ession)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X0) ) ),
    inference(cnf_transformation,[],[f1033]) ).

thf(f1033,plain,
    ! [X0: set_li185139947ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),nil_Se901661471ession)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X0) ) ),
    inference(flattening,[],[f1032]) ).

thf(f1032,plain,
    ! [X0: set_li185139947ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),nil_Se901661471ession)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X0) ) ),
    inference(ennf_transformation,[],[f556]) ).

thf(f556,plain,
    ! [X0: set_li185139947ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X0) )
     => ( ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),nil_Se901661471ession)) )
       => ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)) ) ) ),
    inference(fool_elimination,[],[f555]) ).

thf(f555,plain,
    ! [X0: set_li185139947ession,X1: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X0)
     => ( vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),nil_Se901661471ession))
       => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)) ) ),
    inference(rectify,[],[f267]) ).

thf(f267,axiom,
    ! [X95: set_li185139947ession,X10: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),X95)
     => ( vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X10),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X95),nil_Se901661471ession))
       => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X95),X10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_empty__Shift) ).

thf(f5335,plain,
    spl303_243,
    inference(avatar_split_clause,[],[f1751,f5333]) ).

thf(f5333,plain,
    ( spl303_243
  <=> ! [X0: set_list_Secrecy_KS,X1: secrecy_KS] :
        ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X0),X1)) )
        | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X0),nil_Secrecy_KS)) )
        | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_243])]) ).

thf(f1751,plain,
    ! [X0: set_list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X0),nil_Secrecy_KS)) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X0) ) ),
    inference(cnf_transformation,[],[f1031]) ).

thf(f1031,plain,
    ! [X0: set_list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X0),nil_Secrecy_KS)) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X0) ) ),
    inference(flattening,[],[f1030]) ).

thf(f1030,plain,
    ! [X0: set_list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X0),nil_Secrecy_KS)) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X0) ) ),
    inference(ennf_transformation,[],[f554]) ).

thf(f554,plain,
    ! [X0: set_list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X0) )
     => ( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X0),nil_Secrecy_KS)) )
       => ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X0),X1)) ) ) ),
    inference(fool_elimination,[],[f553]) ).

thf(f553,plain,
    ! [X0: set_list_Secrecy_KS,X1: secrecy_KS] :
      ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X0)
     => ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X0),nil_Secrecy_KS))
       => vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X0),X1)) ) ),
    inference(rectify,[],[f268]) ).

thf(f268,axiom,
    ! [X95: set_list_Secrecy_KS,X10: secrecy_KS] :
      ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),X95)
     => ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X10),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X95),nil_Secrecy_KS))
       => vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(secrecy_KS,set_list_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(secrecy_KS,set_list_Secrecy_KS),bNF_Gr660123862ecy_KS,X95),X10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_empty__Shift) ).

thf(f5331,plain,
    spl303_242,
    inference(avatar_split_clause,[],[f1750,f5329]) ).

thf(f5329,plain,
    ( spl303_242
  <=> ! [X0: set_li849033543y_Keys,X1: secrecy_Keys] :
        ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X0),X1)) )
        | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X0),nil_Secrecy_Keys)) )
        | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_242])]) ).

thf(f1750,plain,
    ! [X0: set_li849033543y_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X0),nil_Secrecy_Keys)) )
      | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X0) ) ),
    inference(cnf_transformation,[],[f1029]) ).

thf(f1029,plain,
    ! [X0: set_li849033543y_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X0),nil_Secrecy_Keys)) )
      | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X0) ) ),
    inference(flattening,[],[f1028]) ).

thf(f1028,plain,
    ! [X0: set_li849033543y_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X0),nil_Secrecy_Keys)) )
      | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X0) ) ),
    inference(ennf_transformation,[],[f552]) ).

thf(f552,plain,
    ! [X0: set_li849033543y_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X0) )
     => ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X0),nil_Secrecy_Keys)) )
       => ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X0),X1)) ) ) ),
    inference(fool_elimination,[],[f551]) ).

thf(f551,plain,
    ! [X0: set_li849033543y_Keys,X1: secrecy_Keys] :
      ( vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X0)
     => ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X0),nil_Secrecy_Keys))
       => vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X0),X1)) ) ),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    ! [X95: set_li849033543y_Keys,X10: secrecy_Keys] :
      ( vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),X95)
     => ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X10),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X95),nil_Secrecy_Keys))
       => vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,nil_Secrecy_Keys),vAPP(secrecy_Keys,set_li849033543y_Keys,vAPP(set_li849033543y_Keys,sTfun(secrecy_Keys,set_li849033543y_Keys),bNF_Gr414702370y_Keys,X95),X10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_empty__Shift) ).

thf(f5327,plain,
    spl303_241,
    inference(avatar_split_clause,[],[f1749,f5325]) ).

thf(f5325,plain,
    ( spl303_241
  <=> ! [X0: set_li2007071804ecrets,X1: secrecy_Secrets] :
        ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X0),X1)) )
        | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X0),nil_Secrecy_Secrets)) )
        | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_241])]) ).

thf(f1749,plain,
    ! [X0: set_li2007071804ecrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X0),nil_Secrecy_Secrets)) )
      | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X0) ) ),
    inference(cnf_transformation,[],[f1027]) ).

thf(f1027,plain,
    ! [X0: set_li2007071804ecrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X0),nil_Secrecy_Secrets)) )
      | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X0) ) ),
    inference(flattening,[],[f1026]) ).

thf(f1026,plain,
    ! [X0: set_li2007071804ecrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X0),X1)) )
      | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X0),nil_Secrecy_Secrets)) )
      | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X0) ) ),
    inference(ennf_transformation,[],[f550]) ).

thf(f550,plain,
    ! [X0: set_li2007071804ecrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X0) )
     => ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X0),nil_Secrecy_Secrets)) )
       => ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X0),X1)) ) ) ),
    inference(fool_elimination,[],[f549]) ).

thf(f549,plain,
    ! [X0: set_li2007071804ecrets,X1: secrecy_Secrets] :
      ( vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X0)
     => ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X0),nil_Secrecy_Secrets))
       => vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X0),X1)) ) ),
    inference(rectify,[],[f265]) ).

thf(f265,axiom,
    ! [X95: set_li2007071804ecrets,X10: secrecy_Secrets] :
      ( vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),X95)
     => ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X10),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X95),nil_Secrecy_Secrets))
       => vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,nil_Secrecy_Secrets),vAPP(secrecy_Secrets,set_li2007071804ecrets,vAPP(set_li2007071804ecrets,sTfun(secrecy_Secrets,set_li2007071804ecrets),bNF_Gr28627573ecrets,X95),X10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_empty__Shift) ).

thf(f5319,plain,
    spl303_240,
    inference(avatar_split_clause,[],[f2020,f5317]) ).

thf(f5317,plain,
    ( spl303_240
  <=> ! [X4: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X3: list_S529945141ession,X2: secrecy_Expression,X1: secrecy_Expression] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
        | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_240])]) ).

thf(f2020,plain,
    ! [X2: secrecy_Expression,X3: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(cnf_transformation,[],[f1162]) ).

thf(f1162,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) )
      | ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) ) ),
    inference(ennf_transformation,[],[f764]) ).

thf(f764,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ) ),
    inference(fool_elimination,[],[f763]) ).

thf(f763,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X0,X1),X2)
     => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X3)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X4)) ),
    inference(rectify,[],[f107]) ).

thf(f107,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X39: secrecy_Expression,X15: secrecy_Expression,X28: list_S529945141ession,X31: list_S529945141ession] :
      ( vAPP(secrecy_Expression,$o,vAPP(secrecy_Expression,sTfun(secrecy_Expression,$o),X58,X39),X15)
     => vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_ord_Olexordp__eq_OCons) ).

thf(f5315,plain,
    ( spl303_239
    | ~ spl303_3
    | ~ spl303_31 ),
    inference(avatar_split_clause,[],[f3336,f3302,f3143,f5313]) ).

thf(f5313,plain,
    ( spl303_239
  <=> ! [X0: secrecy_Expression] : ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_239])]) ).

thf(f3302,plain,
    ( spl303_31
  <=> ! [X0: secrecy_Expression] : ( $true != vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_31])]) ).

thf(f3336,plain,
    ( ! [X0: secrecy_Expression] : ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) )
    | ~ spl303_3
    | ~ spl303_31 ),
    inference(trivial_inequality_removal,[],[f3335]) ).

thf(f3335,plain,
    ( ! [X0: secrecy_Expression] :
        ( ( $true != $true )
        | ( $false = vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) ) )
    | ~ spl303_3
    | ~ spl303_31 ),
    inference(superposition,[],[f3303,f3144]) ).

thf(f3303,plain,
    ( ! [X0: secrecy_Expression] : ( $true != vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) )
    | ~ spl303_31 ),
    inference(avatar_component_clause,[],[f3302]) ).

thf(f5311,plain,
    spl303_238,
    inference(avatar_split_clause,[],[f1782,f5309]) ).

thf(f5309,plain,
    ( spl303_238
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_238])]) ).

thf(f1782,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)) )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0) )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0) ) ),
    inference(cnf_transformation,[],[f1299]) ).

thf(f1299,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0) ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X1 )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113,sK114])],[f890,f1298]) ).

thf(f1298,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X2: list_S529945141ession,X3: list_S529945141ession,X4: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X3) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X4) )
            | ( nil_Se901661471ession = X4 )
            | ( nil_Se901661471ession = X3 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),X2) = X1 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),X2) = X0 ) )
     => ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)) )
          | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0) )
          | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0) ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f890,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
    ? [X2: list_S529945141ession,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X3) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X4) )
        | ( nil_Se901661471ession = X4 )
        | ( nil_Se901661471ession = X3 ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X4),X2) = X1 )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),X2) = X0 ) ),
    inference(rectify,[],[f229]) ).

thf(f229,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
    ? [X91: list_S529945141ession,X88: list_S529945141ession,X92: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X88) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X92) )
        | ( nil_Se901661471ession = X92 )
        | ( nil_Se901661471ession = X88 ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X92),X91) = X31 )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X88),X91) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_longest__common__suffix) ).

thf(f5307,plain,
    spl303_237,
    inference(avatar_split_clause,[],[f1779,f5305]) ).

thf(f5305,plain,
    ( spl303_237
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_237])]) ).

thf(f1779,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0) )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0) ) ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f1297,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0) ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) = X1 )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK109,sK110,sK111])],[f889,f1296]) ).

thf(f1296,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X2: list_S529945141ession,X3: list_S529945141ession,X4: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X3) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X4) )
            | ( nil_Se901661471ession = X4 )
            | ( nil_Se901661471ession = X3 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X4) = X1 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X3) = X0 ) )
     => ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) )
          | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0) )
          | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0) ) )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f889,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
    ? [X2: list_S529945141ession,X3: list_S529945141ession,X4: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X3) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X4) )
        | ( nil_Se901661471ession = X4 )
        | ( nil_Se901661471ession = X3 ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X4) = X1 )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),X3) = X0 ) ),
    inference(rectify,[],[f279]) ).

thf(f279,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
    ? [X96: list_S529945141ession,X88: list_S529945141ession,X92: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X88) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X92) )
        | ( nil_Se901661471ession = X92 )
        | ( nil_Se901661471ession = X88 ) )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X96),X92) = X31 )
      & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X96),X88) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_longest__common__prefix) ).

thf(f5303,plain,
    spl303_236,
    inference(avatar_split_clause,[],[f1776,f5301]) ).

thf(f5301,plain,
    ( spl303_236
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_236])]) ).

thf(f1776,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)) )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0) )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0) ) ),
    inference(cnf_transformation,[],[f1295]) ).

thf(f1295,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0) ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X1 )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107,sK108])],[f888,f1294]) ).

thf(f1294,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X2: list_Secrecy_KS,X3: list_Secrecy_KS,X4: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X3) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X4) )
            | ( nil_Secrecy_KS = X4 )
            | ( nil_Secrecy_KS = X3 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X4),X2) = X1 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),X2) = X0 ) )
     => ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)) )
          | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0) )
          | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0) ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f888,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
    ? [X2: list_Secrecy_KS,X3: list_Secrecy_KS,X4: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X3) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X4) )
        | ( nil_Secrecy_KS = X4 )
        | ( nil_Secrecy_KS = X3 ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X4),X2) = X1 )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),X2) = X0 ) ),
    inference(rectify,[],[f230]) ).

thf(f230,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
    ? [X91: list_Secrecy_KS,X88: list_Secrecy_KS,X92: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X88) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X92) )
        | ( nil_Secrecy_KS = X92 )
        | ( nil_Secrecy_KS = X88 ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X92),X91) = X31 )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X88),X91) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_longest__common__suffix) ).

thf(f5299,plain,
    spl303_235,
    inference(avatar_split_clause,[],[f1773,f5297]) ).

thf(f5297,plain,
    ( spl303_235
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_235])]) ).

thf(f1773,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0) )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0) ) ),
    inference(cnf_transformation,[],[f1293]) ).

thf(f1293,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0) ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) = X1 )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK103,sK104,sK105])],[f887,f1292]) ).

thf(f1292,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X2: list_Secrecy_KS,X3: list_Secrecy_KS,X4: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X3) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X4) )
            | ( nil_Secrecy_KS = X4 )
            | ( nil_Secrecy_KS = X3 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),X4) = X1 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),X3) = X0 ) )
     => ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) )
          | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0) )
          | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0) ) )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f887,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
    ? [X2: list_Secrecy_KS,X3: list_Secrecy_KS,X4: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X3) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X4) )
        | ( nil_Secrecy_KS = X4 )
        | ( nil_Secrecy_KS = X3 ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),X4) = X1 )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),X3) = X0 ) ),
    inference(rectify,[],[f280]) ).

thf(f280,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
    ? [X96: list_Secrecy_KS,X88: list_Secrecy_KS,X92: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X88) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X92) )
        | ( nil_Secrecy_KS = X92 )
        | ( nil_Secrecy_KS = X88 ) )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X96),X92) = X31 )
      & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X96),X88) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_longest__common__prefix) ).

thf(f5287,plain,
    spl303_234,
    inference(avatar_split_clause,[],[f1951,f5285]) ).

thf(f5285,plain,
    ( spl303_234
  <=> ! [X2: set_li849033543y_Keys,X0: list_Secrecy_Keys,X1: secrecy_Keys] :
        ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X2),X0)) )
        | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X1),nil_Secrecy_Keys))),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_234])]) ).

thf(f1951,plain,
    ! [X2: set_li849033543y_Keys,X0: list_Secrecy_Keys,X1: secrecy_Keys] :
      ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X2),X0)) )
      | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X1),nil_Secrecy_Keys))),X2) ) ),
    inference(cnf_transformation,[],[f1125]) ).

thf(f1125,plain,
    ! [X0: list_Secrecy_Keys,X1: secrecy_Keys,X2: set_li849033543y_Keys] :
      ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X2),X0)) )
      | ( $true != vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X1),nil_Secrecy_Keys))),X2) ) ),
    inference(ennf_transformation,[],[f700]) ).

thf(f700,plain,
    ! [X0: list_Secrecy_Keys,X1: secrecy_Keys,X2: set_li849033543y_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X1),nil_Secrecy_Keys))),X2) )
     => ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X2),X0)) ) ),
    inference(fool_elimination,[],[f699]) ).

thf(f699,plain,
    ! [X0: list_Secrecy_Keys,X1: secrecy_Keys,X2: set_li849033543y_Keys] :
      ( vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X1),nil_Secrecy_Keys))),X2)
     => vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X2),X0)) ),
    inference(rectify,[],[f243]) ).

thf(f243,axiom,
    ! [X94: list_Secrecy_Keys,X10: secrecy_Keys,X95: set_li849033543y_Keys] :
      ( vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X94),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X10),nil_Secrecy_Keys))),X95)
     => vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X10),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X95),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_SuccI) ).

thf(f5283,plain,
    spl303_233,
    inference(avatar_split_clause,[],[f1950,f5281]) ).

thf(f5281,plain,
    ( spl303_233
  <=> ! [X2: set_li2007071804ecrets,X0: list_Secrecy_Secrets,X1: secrecy_Secrets] :
        ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X2),X0)) )
        | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X0),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X1),nil_Secrecy_Secrets))),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_233])]) ).

thf(f1950,plain,
    ! [X2: set_li2007071804ecrets,X0: list_Secrecy_Secrets,X1: secrecy_Secrets] :
      ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X2),X0)) )
      | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X0),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X1),nil_Secrecy_Secrets))),X2) ) ),
    inference(cnf_transformation,[],[f1124]) ).

thf(f1124,plain,
    ! [X0: list_Secrecy_Secrets,X1: secrecy_Secrets,X2: set_li2007071804ecrets] :
      ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X2),X0)) )
      | ( $true != vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X0),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X1),nil_Secrecy_Secrets))),X2) ) ),
    inference(ennf_transformation,[],[f698]) ).

thf(f698,plain,
    ! [X0: list_Secrecy_Secrets,X1: secrecy_Secrets,X2: set_li2007071804ecrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X0),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X1),nil_Secrecy_Secrets))),X2) )
     => ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X2),X0)) ) ),
    inference(fool_elimination,[],[f697]) ).

thf(f697,plain,
    ! [X0: list_Secrecy_Secrets,X1: secrecy_Secrets,X2: set_li2007071804ecrets] :
      ( vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X0),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X1),nil_Secrecy_Secrets))),X2)
     => vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X2),X0)) ),
    inference(rectify,[],[f242]) ).

thf(f242,axiom,
    ! [X94: list_Secrecy_Secrets,X10: secrecy_Secrets,X95: set_li2007071804ecrets] :
      ( vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X94),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X10),nil_Secrecy_Secrets))),X95)
     => vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X10),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X95),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_SuccI) ).

thf(f5279,plain,
    ( spl303_232
    | ~ spl303_3
    | ~ spl303_30 ),
    inference(avatar_split_clause,[],[f3334,f3298,f3143,f5277]) ).

thf(f5277,plain,
    ( spl303_232
  <=> ! [X0: secrecy_KS] : ( $false = vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_232])]) ).

thf(f3298,plain,
    ( spl303_30
  <=> ! [X0: secrecy_KS] : ( $true != vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_30])]) ).

thf(f3334,plain,
    ( ! [X0: secrecy_KS] : ( $false = vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) )
    | ~ spl303_3
    | ~ spl303_30 ),
    inference(trivial_inequality_removal,[],[f3333]) ).

thf(f3333,plain,
    ( ! [X0: secrecy_KS] :
        ( ( $true != $true )
        | ( $false = vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) ) )
    | ~ spl303_3
    | ~ spl303_30 ),
    inference(superposition,[],[f3299,f3144]) ).

thf(f3299,plain,
    ( ! [X0: secrecy_KS] : ( $true != vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) )
    | ~ spl303_30 ),
    inference(avatar_component_clause,[],[f3298]) ).

thf(f5275,plain,
    spl303_231,
    inference(avatar_split_clause,[],[f1877,f5273]) ).

thf(f5273,plain,
    ( spl303_231
  <=> ! [X2: list_Secrecy_Keys,X0: secrecy_Keys,X1: set_li849033543y_Keys] :
        ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X2),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X0),nil_Secrecy_Keys))),X1) )
        | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_231])]) ).

thf(f1877,plain,
    ! [X2: list_Secrecy_Keys,X0: secrecy_Keys,X1: set_li849033543y_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X2),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X0),nil_Secrecy_Keys))),X1) )
      | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1101]) ).

thf(f1101,plain,
    ! [X0: secrecy_Keys,X1: set_li849033543y_Keys,X2: list_Secrecy_Keys] :
      ( ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X2),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X0),nil_Secrecy_Keys))),X1) )
      | ( $true != vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X1),X2)) ) ),
    inference(ennf_transformation,[],[f668]) ).

thf(f668,plain,
    ! [X0: secrecy_Keys,X1: set_li849033543y_Keys,X2: list_Secrecy_Keys] :
      ( ( $true = vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X1),X2)) )
     => ( $true = vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X2),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X0),nil_Secrecy_Keys))),X1) ) ),
    inference(fool_elimination,[],[f667]) ).

thf(f667,plain,
    ! [X0: secrecy_Keys,X1: set_li849033543y_Keys,X2: list_Secrecy_Keys] :
      ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X0),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X1),X2))
     => vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X2),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X0),nil_Secrecy_Keys))),X1) ),
    inference(rectify,[],[f247]) ).

thf(f247,axiom,
    ! [X10: secrecy_Keys,X95: set_li849033543y_Keys,X94: list_Secrecy_Keys] :
      ( vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X10),vAPP(list_Secrecy_Keys,set_Secrecy_Keys,vAPP(set_li849033543y_Keys,sTfun(list_Secrecy_Keys,set_Secrecy_Keys),bNF_Gr344893606y_Keys,X95),X94))
     => vAPP(set_li849033543y_Keys,$o,vAPP(list_Secrecy_Keys,sTfun(set_li849033543y_Keys,$o),member341114536y_Keys,vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(list_Secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),append_Secrecy_Keys,X94),vAPP(list_Secrecy_Keys,list_Secrecy_Keys,vAPP(secrecy_Keys,sTfun(list_Secrecy_Keys,list_Secrecy_Keys),cons_Secrecy_Keys,X10),nil_Secrecy_Keys))),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_SuccD) ).

thf(f5271,plain,
    spl303_230,
    inference(avatar_split_clause,[],[f1876,f5269]) ).

thf(f5269,plain,
    ( spl303_230
  <=> ! [X2: list_Secrecy_Secrets,X0: secrecy_Secrets,X1: set_li2007071804ecrets] :
        ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X2),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X0),nil_Secrecy_Secrets))),X1) )
        | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_230])]) ).

thf(f1876,plain,
    ! [X2: list_Secrecy_Secrets,X0: secrecy_Secrets,X1: set_li2007071804ecrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X2),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X0),nil_Secrecy_Secrets))),X1) )
      | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1100]) ).

thf(f1100,plain,
    ! [X0: secrecy_Secrets,X1: set_li2007071804ecrets,X2: list_Secrecy_Secrets] :
      ( ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X2),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X0),nil_Secrecy_Secrets))),X1) )
      | ( $true != vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X1),X2)) ) ),
    inference(ennf_transformation,[],[f666]) ).

thf(f666,plain,
    ! [X0: secrecy_Secrets,X1: set_li2007071804ecrets,X2: list_Secrecy_Secrets] :
      ( ( $true = vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X1),X2)) )
     => ( $true = vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X2),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X0),nil_Secrecy_Secrets))),X1) ) ),
    inference(fool_elimination,[],[f665]) ).

thf(f665,plain,
    ! [X0: secrecy_Secrets,X1: set_li2007071804ecrets,X2: list_Secrecy_Secrets] :
      ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X0),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X1),X2))
     => vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X2),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X0),nil_Secrecy_Secrets))),X1) ),
    inference(rectify,[],[f246]) ).

thf(f246,axiom,
    ! [X10: secrecy_Secrets,X95: set_li2007071804ecrets,X94: list_Secrecy_Secrets] :
      ( vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X10),vAPP(list_Secrecy_Secrets,set_Secrecy_Secrets,vAPP(set_li2007071804ecrets,sTfun(list_Secrecy_Secrets,set_Secrecy_Secrets),bNF_Gr957048817ecrets,X95),X94))
     => vAPP(set_li2007071804ecrets,$o,vAPP(list_Secrecy_Secrets,sTfun(set_li2007071804ecrets,$o),member1138497285ecrets,vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(list_Secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),append186372209ecrets,X94),vAPP(list_Secrecy_Secrets,list_Secrecy_Secrets,vAPP(secrecy_Secrets,sTfun(list_Secrecy_Secrets,list_Secrecy_Secrets),cons_Secrecy_Secrets,X10),nil_Secrecy_Secrets))),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_SuccD) ).

thf(f5181,plain,
    spl303_229,
    inference(avatar_split_clause,[],[f2996,f5179]) ).

thf(f2996,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK34,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0))) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1568,f1527]) ).

thf(f1568,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK34,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0))) = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1214]) ).

thf(f1214,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK34,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0))) = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37])],[f1211,f1213,f1212]) ).

thf(f1212,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) = X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK34,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK35,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK36,X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1213,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X4: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),nil_Se901661471ession) = X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK37,X0)),nil_Se901661471ession) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1211,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X1: secrecy_Expression,X2: secrecy_Expression,X3: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) = X0 )
      | ? [X4: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f953]) ).

thf(f953,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X0 )
      | ? [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(flattening,[],[f952]) ).

thf(f952,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) = X0 )
      | ? [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f819]) ).

thf(f819,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( ! [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) != X0 )
       => ~ ! [X2: secrecy_Expression,X3: secrecy_Expression,X4: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X4)) != X0 ) ) ),
    inference(rectify,[],[f51]) ).

thf(f51,axiom,
    ! [X39: list_S529945141ession] :
      ( ( nil_Se901661471ession != X39 )
     => ( ! [X20: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession) != X39 )
       => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32)) != X39 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_remdups__adj_Ocases) ).

thf(f5172,plain,
    spl303_228,
    inference(avatar_split_clause,[],[f2992,f5170]) ).

thf(f2992,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK27,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK28,X0))) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1558,f1526]) ).

thf(f1558,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK27,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK28,X0))) = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1206]) ).

thf(f1206,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK27,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK28,X0))) = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29])],[f1203,f1205,f1204]) ).

thf(f1204,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X1: secrecy_KS,X2: secrecy_KS,X3: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) = X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK26,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK27,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK28,X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1205,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X4: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),nil_Secrecy_KS) = X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK29,X0)),nil_Secrecy_KS) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1203,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X1: secrecy_KS,X2: secrecy_KS,X3: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) = X0 )
      | ? [X4: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f942]) ).

thf(f942,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) = X0 )
      | ? [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(flattening,[],[f941]) ).

thf(f941,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) = X0 )
      | ? [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f809]) ).

thf(f809,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( ! [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) != X0 )
       => ~ ! [X2: secrecy_KS,X3: secrecy_KS,X4: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X4)) != X0 ) ) ),
    inference(rectify,[],[f50]) ).

thf(f50,axiom,
    ! [X39: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X39 )
     => ( ! [X20: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS) != X39 )
       => ~ ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32)) != X39 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_remdups__adj_Ocases) ).

thf(f5168,plain,
    spl303_227,
    inference(avatar_split_clause,[],[f2050,f5166]) ).

thf(f2050,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ),
    inference(equality_resolution,[],[f1711]) ).

thf(f1711,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1250]) ).

thf(f1250,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) )
      | ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X0 ) )
      | ( ( nil_Se901661471ession = X1 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f1166,f1249]) ).

thf(f1249,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X2: secrecy_Expression] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X1 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X0 ) )
     => ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X1 )
        & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1166,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) )
      | ? [X2: secrecy_Expression] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X1 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X0 ) )
      | ( ( nil_Se901661471ession = X1 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(definition_folding,[],[f998,f1165]) ).

thf(f998,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X0 ) )
      | ? [X2: secrecy_Expression] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X1 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X0 ) )
      | ( ( nil_Se901661471ession = X1 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(flattening,[],[f997]) ).

thf(f997,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ? [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
          ( ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X0 ) )
      | ? [X2: secrecy_Expression] :
          ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X1 )
          & ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X0 ) )
      | ( ( nil_Se901661471ession = X1 )
        & ( nil_Se901661471ession = X0 ) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(ennf_transformation,[],[f881]) ).

thf(f881,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = X1 )
     => ( ( ( nil_Se901661471ession = X0 )
         => ( nil_Se901661471ession != X1 ) )
       => ( ! [X2: secrecy_Expression] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) = X0 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession) != X1 ) )
         => ~ ! [X3: secrecy_Expression,X4: secrecy_Expression,X5: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5)) = X0 )
               => ~ ( ( ( X3 != X4 )
                     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X4),X5))) = X1 ) )
                    & ( ( X3 = X4 )
                     => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X3),X5)) = X1 ) ) ) ) ) ) ),
    inference(rectify,[],[f351]) ).

thf(f351,axiom,
    ! [X39: list_S529945141ession,X15: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X39) = X15 )
     => ( ( ( nil_Se901661471ession = X39 )
         => ( nil_Se901661471ession != X15 ) )
       => ( ! [X20: secrecy_Expression] :
              ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession) = X39 )
             => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession) != X15 ) )
         => ~ ! [X20: secrecy_Expression,X33: secrecy_Expression,X32: list_S529945141ession] :
                ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32)) = X39 )
               => ~ ( ( ( X20 != X33 )
                     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),X32))) = X15 ) )
                    & ( ( X20 = X33 )
                     => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)) = X15 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_remdups__adj_Oelims) ).

thf(f5164,plain,
    spl303_226,
    inference(avatar_split_clause,[],[f2046,f5162]) ).

thf(f2046,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ),
    inference(equality_resolution,[],[f1704]) ).

thf(f1704,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1244]) ).

thf(f1244,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) )
      | ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X0 ) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f1164,f1243]) ).

thf(f1243,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X2: secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X1 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X0 ) )
     => ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X1 )
        & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1164,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) )
      | ? [X2: secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X1 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X0 ) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(definition_folding,[],[f996,f1163]) ).

thf(f996,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X0 ) )
      | ? [X2: secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X1 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X0 ) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(flattening,[],[f995]) ).

thf(f995,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ? [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
          ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) = X1 )
            | ( X3 = X4 ) )
          & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) = X1 )
            | ( X3 != X4 ) )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X0 ) )
      | ? [X2: secrecy_KS] :
          ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X1 )
          & ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X0 ) )
      | ( ( nil_Secrecy_KS = X1 )
        & ( nil_Secrecy_KS = X0 ) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(ennf_transformation,[],[f880]) ).

thf(f880,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = X1 )
     => ( ( ( nil_Secrecy_KS = X0 )
         => ( nil_Secrecy_KS != X1 ) )
       => ( ! [X2: secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) = X0 )
             => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS) != X1 ) )
         => ~ ! [X3: secrecy_KS,X4: secrecy_KS,X5: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5)) = X0 )
               => ~ ( ( ( X3 != X4 )
                     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X4),X5))) = X1 ) )
                    & ( ( X3 = X4 )
                     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X3),X5)) = X1 ) ) ) ) ) ) ),
    inference(rectify,[],[f350]) ).

thf(f350,axiom,
    ! [X39: list_Secrecy_KS,X15: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X39) = X15 )
     => ( ( ( nil_Secrecy_KS = X39 )
         => ( nil_Secrecy_KS != X15 ) )
       => ( ! [X20: secrecy_KS] :
              ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS) = X39 )
             => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS) != X15 ) )
         => ~ ! [X20: secrecy_KS,X33: secrecy_KS,X32: list_Secrecy_KS] :
                ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32)) = X39 )
               => ~ ( ( ( X20 != X33 )
                     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),X32))) = X15 ) )
                    & ( ( X20 = X33 )
                     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)) = X15 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_remdups__adj_Oelims) ).

thf(f5160,plain,
    spl303_225,
    inference(avatar_split_clause,[],[f1795,f5158]) ).

thf(f1795,plain,
    ! [X2: secrecy_Expression > list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X2,X0)),vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,X1),X2)) ),
    inference(cnf_transformation,[],[f897]) ).

thf(f897,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: secrecy_Expression > list_S529945141ession] : ( vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X2,X0)),vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,X1),X2)) ),
    inference(rectify,[],[f133]) ).

thf(f133,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession,X59: secrecy_Expression > list_S529945141ession] : ( vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),X59) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X59,X39)),vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,X28),X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_bind__simps_I2_J) ).

thf(f5156,plain,
    spl303_224,
    inference(avatar_split_clause,[],[f1550,f5154]) ).

thf(f5154,plain,
    ( spl303_224
  <=> ! [X0: list_l425507653ession] :
        ( ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_l425507653ession,secrecy_Expression,sK22,X0)),vAPP(list_l425507653ession,list_S529945141ession,sK23,X0))),vAPP(list_l425507653ession,list_l425507653ession,sK24,X0)) = X0 )
        | ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),vAPP(list_l425507653ession,list_l425507653ession,sK25,X0)) = X0 )
        | ( nil_li311616943ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_224])]) ).

thf(f1550,plain,
    ! [X0: list_l425507653ession] :
      ( ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_l425507653ession,secrecy_Expression,sK22,X0)),vAPP(list_l425507653ession,list_S529945141ession,sK23,X0))),vAPP(list_l425507653ession,list_l425507653ession,sK24,X0)) = X0 )
      | ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),vAPP(list_l425507653ession,list_l425507653ession,sK25,X0)) = X0 )
      | ( nil_li311616943ession = X0 ) ),
    inference(cnf_transformation,[],[f1202]) ).

thf(f1202,plain,
    ! [X0: list_l425507653ession] :
      ( ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_l425507653ession,secrecy_Expression,sK22,X0)),vAPP(list_l425507653ession,list_S529945141ession,sK23,X0))),vAPP(list_l425507653ession,list_l425507653ession,sK24,X0)) = X0 )
      | ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),vAPP(list_l425507653ession,list_l425507653ession,sK25,X0)) = X0 )
      | ( nil_li311616943ession = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25])],[f1199,f1201,f1200]) ).

thf(f1200,plain,
    ! [X0: list_l425507653ession] :
      ( ? [X1: secrecy_Expression,X2: list_S529945141ession,X3: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),X3) = X0 )
     => ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_l425507653ession,secrecy_Expression,sK22,X0)),vAPP(list_l425507653ession,list_S529945141ession,sK23,X0))),vAPP(list_l425507653ession,list_l425507653ession,sK24,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1201,plain,
    ! [X0: list_l425507653ession] :
      ( ? [X4: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),X4) = X0 )
     => ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),vAPP(list_l425507653ession,list_l425507653ession,sK25,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1199,plain,
    ! [X0: list_l425507653ession] :
      ( ? [X1: secrecy_Expression,X2: list_S529945141ession,X3: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),X3) = X0 )
      | ? [X4: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),X4) = X0 )
      | ( nil_li311616943ession = X0 ) ),
    inference(rectify,[],[f933]) ).

thf(f933,plain,
    ! [X0: list_l425507653ession] :
      ( ? [X2: secrecy_Expression,X3: list_S529945141ession,X4: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)),X4) = X0 )
      | ? [X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),X1) = X0 )
      | ( nil_li311616943ession = X0 ) ),
    inference(flattening,[],[f932]) ).

thf(f932,plain,
    ! [X0: list_l425507653ession] :
      ( ? [X2: secrecy_Expression,X3: list_S529945141ession,X4: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)),X4) = X0 )
      | ? [X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),X1) = X0 )
      | ( nil_li311616943ession = X0 ) ),
    inference(ennf_transformation,[],[f801]) ).

thf(f801,plain,
    ! [X0: list_l425507653ession] :
      ( ( nil_li311616943ession != X0 )
     => ( ! [X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),X1) != X0 )
       => ~ ! [X2: secrecy_Expression,X3: list_S529945141ession,X4: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)),X4) != X0 ) ) ),
    inference(rectify,[],[f59]) ).

thf(f59,axiom,
    ! [X39: list_l425507653ession] :
      ( ( nil_li311616943ession != X39 )
     => ( ! [X48: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),X48) != X39 )
       => ~ ! [X20: secrecy_Expression,X32: list_S529945141ession,X48: list_l425507653ession] : ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),X32)),X48) != X39 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_transpose_Ocases) ).

thf(f5152,plain,
    spl303_223,
    inference(avatar_split_clause,[],[f1548,f5150]) ).

thf(f5150,plain,
    ( spl303_223
  <=> ! [X0: list_list_Secrecy_KS] :
        ( ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_list_Secrecy_KS,secrecy_KS,sK18,X0)),vAPP(list_list_Secrecy_KS,list_Secrecy_KS,sK19,X0))),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK20,X0)) = X0 )
        | ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK21,X0)) = X0 )
        | ( nil_list_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_223])]) ).

thf(f1548,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_list_Secrecy_KS,secrecy_KS,sK18,X0)),vAPP(list_list_Secrecy_KS,list_Secrecy_KS,sK19,X0))),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK20,X0)) = X0 )
      | ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK21,X0)) = X0 )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1198]) ).

thf(f1198,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_list_Secrecy_KS,secrecy_KS,sK18,X0)),vAPP(list_list_Secrecy_KS,list_Secrecy_KS,sK19,X0))),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK20,X0)) = X0 )
      | ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK21,X0)) = X0 )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f1195,f1197,f1196]) ).

thf(f1196,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ? [X1: secrecy_KS,X2: list_Secrecy_KS,X3: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),X3) = X0 )
     => ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_list_Secrecy_KS,secrecy_KS,sK18,X0)),vAPP(list_list_Secrecy_KS,list_Secrecy_KS,sK19,X0))),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK20,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1197,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ? [X4: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),X4) = X0 )
     => ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,sK21,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1195,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ? [X1: secrecy_KS,X2: list_Secrecy_KS,X3: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),X3) = X0 )
      | ? [X4: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),X4) = X0 )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f929]) ).

thf(f929,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: list_Secrecy_KS,X4: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)),X4) = X0 )
      | ? [X1: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),X1) = X0 )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(flattening,[],[f928]) ).

thf(f928,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ? [X2: secrecy_KS,X3: list_Secrecy_KS,X4: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)),X4) = X0 )
      | ? [X1: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),X1) = X0 )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f799]) ).

thf(f799,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( nil_list_Secrecy_KS != X0 )
     => ( ! [X1: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),X1) != X0 )
       => ~ ! [X2: secrecy_KS,X3: list_Secrecy_KS,X4: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)),X4) != X0 ) ) ),
    inference(rectify,[],[f58]) ).

thf(f58,axiom,
    ! [X39: list_list_Secrecy_KS] :
      ( ( nil_list_Secrecy_KS != X39 )
     => ( ! [X48: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),X48) != X39 )
       => ~ ! [X20: secrecy_KS,X32: list_Secrecy_KS,X48: list_list_Secrecy_KS] : ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),X32)),X48) != X39 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_transpose_Ocases) ).

thf(f5121,plain,
    spl303_222,
    inference(avatar_split_clause,[],[f1814,f5119]) ).

thf(f1814,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1050]) ).

thf(f1050,plain,
    ! [X0: secrecy_Expression,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) )
        | ( X0 = X1 ) )
      & ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X2)) )
        | ( X0 != X1 ) ) ),
    inference(ennf_transformation,[],[f900]) ).

thf(f900,plain,
    ! [X0: secrecy_Expression,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( ( X0 != X1 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) ) )
      & ( ( X0 = X1 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X2)) ) ) ),
    inference(rectify,[],[f352]) ).

thf(f352,axiom,
    ! [X39: secrecy_Expression,X15: secrecy_Expression,X28: list_S529945141ession] :
      ( ( ( X15 != X39 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X28))) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X28))) ) )
      & ( ( X15 = X39 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X15),X28))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_remdups__adj_Osimps_I3_J) ).

thf(f5113,plain,
    ( spl303_221
    | ~ spl303_11
    | ~ spl303_26
    | ~ spl303_60
    | ~ spl303_137 ),
    inference(avatar_split_clause,[],[f3936,f3930,f3445,f3282,f3212,f5110]) ).

thf(f5110,plain,
    ( spl303_221
  <=> ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_221])]) ).

thf(f3445,plain,
    ( spl303_60
  <=> ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession) = vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_60])]) ).

thf(f3930,plain,
    ( spl303_137
  <=> ! [X0: list_S529945141ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_137])]) ).

thf(f3936,plain,
    ( ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession)) )
    | ~ spl303_11
    | ~ spl303_26
    | ~ spl303_60
    | ~ spl303_137 ),
    inference(forward_demodulation,[],[f3935,f3214]) ).

thf(f3935,plain,
    ( ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,nil_li311616943ession) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession)) )
    | ~ spl303_26
    | ~ spl303_60
    | ~ spl303_137 ),
    inference(forward_demodulation,[],[f3933,f3283]) ).

thf(f3933,plain,
    ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,nil_li311616943ession)) = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession)) )
    | ~ spl303_60
    | ~ spl303_137 ),
    inference(superposition,[],[f3931,f3447]) ).

thf(f3447,plain,
    ( ( vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession) = vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession) )
    | ~ spl303_60 ),
    inference(avatar_component_clause,[],[f3445]) ).

thf(f3931,plain,
    ( ! [X0: list_S529945141ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) )
    | ~ spl303_137 ),
    inference(avatar_component_clause,[],[f3930]) ).

thf(f5108,plain,
    spl303_220,
    inference(avatar_split_clause,[],[f1842,f5106]) ).

thf(f5106,plain,
    ( spl303_220
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X2)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_220])]) ).

thf(f1842,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(cnf_transformation,[],[f1068]) ).

thf(f1068,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(flattening,[],[f1067]) ).

thf(f1067,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(ennf_transformation,[],[f630]) ).

thf(f630,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X2)) ) ),
    inference(fool_elimination,[],[f629]) ).

thf(f629,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2)
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X1),X2)) ),
    inference(rectify,[],[f11]) ).

thf(f11,axiom,
    ! [X2: secrecy_specID,X10: secrecy_Keys,X11: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X11)
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X10)) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X10),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_knows6) ).

thf(f5104,plain,
    spl303_219,
    inference(avatar_split_clause,[],[f1841,f5102]) ).

thf(f5102,plain,
    ( spl303_219
  <=> ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) )
        | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_219])]) ).

thf(f1841,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(cnf_transformation,[],[f1066]) ).

thf(f1066,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(flattening,[],[f1065]) ).

thf(f1065,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(ennf_transformation,[],[f628]) ).

thf(f628,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        & ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) ) ),
    inference(fool_elimination,[],[f627]) ).

thf(f627,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2)
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) ),
    inference(rectify,[],[f19]) ).

thf(f19,axiom,
    ! [X2: secrecy_specID,X10: secrecy_Keys,X11: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X11)
        & vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X10)) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X10),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_knows7) ).

thf(f5007,plain,
    spl303_218,
    inference(avatar_split_clause,[],[f2052,f5005]) ).

thf(f2052,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ),
    inference(equality_resolution,[],[f1709]) ).

thf(f1709,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X1 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1250]) ).

thf(f5003,plain,
    spl303_217,
    inference(avatar_split_clause,[],[f2051,f5001]) ).

thf(f2051,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(equality_resolution,[],[f1710]) ).

thf(f1710,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X1 )
      | ( nil_Se901661471ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1250]) ).

thf(f4999,plain,
    spl303_216,
    inference(avatar_split_clause,[],[f2048,f4997]) ).

thf(f2048,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ),
    inference(equality_resolution,[],[f1702]) ).

thf(f1702,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X1 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1244]) ).

thf(f4994,plain,
    spl303_215,
    inference(avatar_split_clause,[],[f2047,f4992]) ).

thf(f2047,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(equality_resolution,[],[f1703]) ).

thf(f1703,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X1 )
      | ( nil_Secrecy_KS = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1244]) ).

thf(f4990,plain,
    spl303_214,
    inference(avatar_split_clause,[],[f1794,f4988]) ).

thf(f1794,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),X2)) ),
    inference(cnf_transformation,[],[f896]) ).

thf(f896,plain,
    ! [X0: secrecy_Expression > list_S529945141ession,X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X0,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),X2)) ),
    inference(rectify,[],[f188]) ).

thf(f188,axiom,
    ! [X59: secrecy_Expression > list_S529945141ession,X39: secrecy_Expression,X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X59),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(secrecy_Expression,list_S529945141ession,X59,X39)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X59),X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_maps__simps_I1_J) ).

thf(f4924,plain,
    spl303_213,
    inference(avatar_split_clause,[],[f3118,f4922]) ).

thf(f4922,plain,
    ( spl303_213
  <=> ! [X2: set_li185139947ession,X0: list_S529945141ession,X1: secrecy_Expression] :
        ( ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))),X2) )
        | ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_213])]) ).

thf(f3118,plain,
    ! [X2: set_li185139947ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))),X2) )
      | ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) ) ),
    inference(forward_demodulation,[],[f3117,f3005]) ).

thf(f3117,plain,
    ! [X2: set_li185139947ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))),X2) )
      | ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) ) ),
    inference(forward_demodulation,[],[f1953,f1527]) ).

thf(f1953,plain,
    ! [X2: set_li185139947ession,X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2) ) ),
    inference(cnf_transformation,[],[f1127]) ).

thf(f1127,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: set_li185139947ession] :
      ( ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2) ) ),
    inference(ennf_transformation,[],[f704]) ).

thf(f704,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: set_li185139947ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2) )
     => ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) ) ),
    inference(fool_elimination,[],[f703]) ).

thf(f703,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression,X2: set_li185139947ession] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))),X2)
     => vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X1),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X2),X0)) ),
    inference(rectify,[],[f245]) ).

thf(f245,axiom,
    ! [X94: list_S529945141ession,X10: secrecy_Expression,X95: set_li185139947ession] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X94),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),nil_Se901661471ession))),X95)
     => vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X10),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X95),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_SuccI) ).

thf(f4920,plain,
    spl303_212,
    inference(avatar_split_clause,[],[f3116,f4918]) ).

thf(f4918,plain,
    ( spl303_212
  <=> ! [X2: set_list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
        ( ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))),X2) )
        | ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_212])]) ).

thf(f3116,plain,
    ! [X2: set_list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))),X2) )
      | ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) ) ),
    inference(forward_demodulation,[],[f3115,f3004]) ).

thf(f3115,plain,
    ! [X2: set_list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))),X2) )
      | ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) ) ),
    inference(forward_demodulation,[],[f1952,f1526]) ).

thf(f1952,plain,
    ! [X2: set_list_Secrecy_KS,X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2) ) ),
    inference(cnf_transformation,[],[f1126]) ).

thf(f1126,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: set_list_Secrecy_KS] :
      ( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) )
      | ( $true != vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2) ) ),
    inference(ennf_transformation,[],[f702]) ).

thf(f702,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: set_list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2) )
     => ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) ) ),
    inference(fool_elimination,[],[f701]) ).

thf(f701,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS,X2: set_list_Secrecy_KS] :
      ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))),X2)
     => vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X2),X0)) ),
    inference(rectify,[],[f244]) ).

thf(f244,axiom,
    ! [X94: list_Secrecy_KS,X10: secrecy_KS,X95: set_list_Secrecy_KS] :
      ( vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X94),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),nil_Secrecy_KS))),X95)
     => vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X10),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X95),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_SuccI) ).

thf(f4915,plain,
    spl303_211,
    inference(avatar_split_clause,[],[f3113,f4913]) ).

thf(f4913,plain,
    ( spl303_211
  <=> ! [X2: list_Secrecy_KS,X0: secrecy_KS,X1: set_list_Secrecy_KS] :
        ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X2))),X1) )
        | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_211])]) ).

thf(f3113,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS,X1: set_list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X2))),X1) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2)) ) ),
    inference(forward_demodulation,[],[f3112,f3004]) ).

thf(f3112,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS,X1: set_list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS))),X1) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2)) ) ),
    inference(forward_demodulation,[],[f1878,f1526]) ).

thf(f1878,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS,X1: set_list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS))),X1) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1102]) ).

thf(f1102,plain,
    ! [X0: secrecy_KS,X1: set_list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS))),X1) )
      | ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2)) ) ),
    inference(ennf_transformation,[],[f670]) ).

thf(f670,plain,
    ! [X0: secrecy_KS,X1: set_list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2)) )
     => ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS))),X1) ) ),
    inference(fool_elimination,[],[f669]) ).

thf(f669,plain,
    ! [X0: secrecy_KS,X1: set_list_Secrecy_KS,X2: list_Secrecy_KS] :
      ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X0),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X1),X2))
     => vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X2),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS))),X1) ),
    inference(rectify,[],[f248]) ).

thf(f248,axiom,
    ! [X10: secrecy_KS,X95: set_list_Secrecy_KS,X94: list_Secrecy_KS] :
      ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X10),vAPP(list_Secrecy_KS,set_Secrecy_KS,vAPP(set_list_Secrecy_KS,sTfun(list_Secrecy_KS,set_Secrecy_KS),bNF_Gr577175642ecy_KS,X95),X94))
     => vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X94),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X10),nil_Secrecy_KS))),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_SuccD) ).

thf(f4911,plain,
    spl303_210,
    inference(avatar_split_clause,[],[f3111,f4909]) ).

thf(f4909,plain,
    ( spl303_210
  <=> ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: set_li185139947ession] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X2))),X1) )
        | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_210])]) ).

thf(f3111,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: set_li185139947ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X2))),X1) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2)) ) ),
    inference(forward_demodulation,[],[f3110,f3005]) ).

thf(f3110,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: set_li185139947ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession))),X1) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2)) ) ),
    inference(forward_demodulation,[],[f1875,f1527]) ).

thf(f1875,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: set_li185139947ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession))),X1) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1099]) ).

thf(f1099,plain,
    ! [X0: secrecy_Expression,X1: set_li185139947ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession))),X1) )
      | ( $true != vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f664]) ).

thf(f664,plain,
    ! [X0: secrecy_Expression,X1: set_li185139947ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2)) )
     => ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession))),X1) ) ),
    inference(fool_elimination,[],[f663]) ).

thf(f663,plain,
    ! [X0: secrecy_Expression,X1: set_li185139947ession,X2: list_S529945141ession] :
      ( vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X0),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X1),X2))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession))),X1) ),
    inference(rectify,[],[f249]) ).

thf(f249,axiom,
    ! [X10: secrecy_Expression,X95: set_li185139947ession,X94: list_S529945141ession] :
      ( vAPP(set_Se1942955227ession,$o,vAPP(secrecy_Expression,sTfun(set_Se1942955227ession,$o),member279582780ession,X10),vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X95),X94))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X94),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),nil_Se901661471ession))),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_SuccD) ).

thf(f4907,plain,
    spl303_209,
    inference(avatar_split_clause,[],[f3061,f4905]) ).

thf(f4905,plain,
    ( spl303_209
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_209])]) ).

thf(f3061,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1742,f1527]) ).

thf(f1742,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK87,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK88,X0)),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1276]) ).

thf(f4903,plain,
    spl303_208,
    inference(avatar_split_clause,[],[f3053,f4901]) ).

thf(f4901,plain,
    ( spl303_208
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_208])]) ).

thf(f3053,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1732,f1526]) ).

thf(f1732,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK75,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK76,X0)),nil_Secrecy_KS)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1264]) ).

thf(f4891,plain,
    spl303_207,
    inference(avatar_split_clause,[],[f1840,f4889]) ).

thf(f1840,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ),
    inference(cnf_transformation,[],[f1064]) ).

thf(f1064,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ),
    inference(flattening,[],[f1063]) ).

thf(f1063,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ),
    inference(ennf_transformation,[],[f626]) ).

thf(f626,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
        & ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    inference(fool_elimination,[],[f625]) ).

thf(f625,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2)
        & vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(rectify,[],[f172]) ).

thf(f172,axiom,
    ! [X2: secrecy_specID,X11: list_S529945141ession,X76: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X76)
        & vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X11) )
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X11),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_knows3) ).

thf(f4834,plain,
    spl303_206,
    inference(avatar_split_clause,[],[f2946,f4832]) ).

thf(f4832,plain,
    ( spl303_206
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_206])]) ).

thf(f2946,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(equality_proxy_clausification,[],[f2945]) ).

thf(f2945,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) ) ),
    inference(binary_proxy_clausification,[],[f2943]) ).

thf(f2943,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(sTfun(secrecy_KS,$o),$o,vSIGMA(secrecy_KS),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS)),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS),nil_Secrecy_KS))),X0))) ) ),
    inference(equality_proxy_clausification,[],[f2937]) ).

thf(f2937,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(sTfun(secrecy_KS,$o),$o,vSIGMA(secrecy_KS),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS)),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS),nil_Secrecy_KS))),X0))) ) ),
    inference(binary_proxy_clausification,[],[f1536]) ).

thf(f1536,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(sTfun(secrecy_KS,$o),$o,vSIGMA(secrecy_KS),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS)),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS),nil_Secrecy_KS))),X0))) ),
    inference(cnf_transformation,[],[f392]) ).

thf(f392,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0)),vAPP(sTfun(secrecy_KS,$o),$o,vSIGMA(secrecy_KS),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o)),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),sTfun(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(secrecy_KS,sTfun(list_Secrecy_KS,$o))),bCOMB,vEQ(list_Secrecy_KS)),vAPP(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS),vAPP(sTfun(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(secrecy_KS,list_Secrecy_KS)),cCOMB,cons_Secrecy_KS),nil_Secrecy_KS))),X0))) ),
    inference(fool_elimination,[],[f391]) ).

thf(f391,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        = ( ? [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS) = X0 ) ) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f305]) ).

thf(f305,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X28) )
        = ( ? [X47: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X47),nil_Secrecy_KS) = X28 ) ) )
      | ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_tl__Nil) ).

thf(f4830,plain,
    spl303_205,
    inference(avatar_split_clause,[],[f3063,f4828]) ).

thf(f4828,plain,
    ( spl303_205
  <=> ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
        ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK91,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)))) )
        | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_205])]) ).

thf(f3063,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK91,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)))) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f3062,f3005]) ).

thf(f3062,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK91,X0)),nil_Se901661471ession))) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(forward_demodulation,[],[f1748,f1527]) ).

thf(f1748,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK91,X0)),nil_Se901661471ession))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1280]) ).

thf(f1280,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK91,X0)),nil_Se901661471ession))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92])],[f1025,f1279]) ).

thf(f1279,plain,
    ! [X0: list_S529945141ession > $o] :
      ( ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X3) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK91,X0)),nil_Se901661471ession))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1025,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X3) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(flattening,[],[f1024]) ).

thf(f1024,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X3) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f548]) ).

thf(f548,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
     => ( ! [X2: secrecy_Expression,X3: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,X0,X3) )
           => ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) ) )
       => ( $true = vAPP(list_S529945141ession,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f547]) ).

thf(f547,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession)
     => ( ! [X2: secrecy_Expression,X3: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,X0,X3)
           => vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X3),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession))) )
       => vAPP(list_S529945141ession,$o,X0,X1) ) ),
    inference(rectify,[],[f187]) ).

thf(f187,axiom,
    ! [X18: list_S529945141ession > $o,X28: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X18,nil_Se901661471ession)
     => ( ! [X20: secrecy_Expression,X32: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,X18,X32)
           => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X32),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X20),nil_Se901661471ession))) )
       => vAPP(list_S529945141ession,$o,X18,X28) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_rev__induct) ).

thf(f4826,plain,
    spl303_204,
    inference(avatar_split_clause,[],[f3055,f4824]) ).

thf(f4824,plain,
    ( spl303_204
  <=> ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK79,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)))) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
        | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_204])]) ).

thf(f3055,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK79,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)))) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f3054,f3004]) ).

thf(f3054,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK79,X0)),nil_Secrecy_KS))) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(forward_demodulation,[],[f1738,f1526]) ).

thf(f1738,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK79,X0)),nil_Secrecy_KS))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1268]) ).

thf(f1268,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK79,X0)),nil_Secrecy_KS))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f1017,f1267]) ).

thf(f1267,plain,
    ! [X0: list_Secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK79,X0)),nil_Secrecy_KS))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1017,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1016]) ).

thf(f1016,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f540]) ).

thf(f540,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
     => ( ! [X2: secrecy_KS,X3: list_Secrecy_KS] :
            ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) )
           => ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) ) )
       => ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f539]) ).

thf(f539,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS)
     => ( ! [X2: secrecy_KS,X3: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,X0,X3)
           => vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X3),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS))) )
       => vAPP(list_Secrecy_KS,$o,X0,X1) ) ),
    inference(rectify,[],[f186]) ).

thf(f186,axiom,
    ! [X18: list_Secrecy_KS > $o,X28: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X18,nil_Secrecy_KS)
     => ( ! [X20: secrecy_KS,X32: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,X18,X32)
           => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X32),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X20),nil_Secrecy_KS))) )
       => vAPP(list_Secrecy_KS,$o,X18,X28) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_rev__induct) ).

thf(f4822,plain,
    spl303_203,
    inference(avatar_split_clause,[],[f2053,f4820]) ).

thf(f2053,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),X0)),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(equality_resolution,[],[f1708]) ).

thf(f1708,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),sP1,X0),X1) )
      | ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,vAPP(list_S529945141ession,sTfun(list_S529945141ession,secrecy_Expression),sK63,X1),X0)),nil_Se901661471ession) = X0 )
      | ( nil_Se901661471ession = X0 )
      | ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1250]) ).

thf(f4818,plain,
    spl303_202,
    inference(avatar_split_clause,[],[f2049,f4816]) ).

thf(f2049,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),X0)),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(equality_resolution,[],[f1701]) ).

thf(f1701,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),sP0,X0),X1) )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,secrecy_KS),sK59,X1),X0)),nil_Secrecy_KS) = X0 )
      | ( nil_Secrecy_KS = X0 )
      | ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) != X1 ) ),
    inference(cnf_transformation,[],[f1244]) ).

thf(f4745,plain,
    spl303_201,
    inference(avatar_split_clause,[],[f2900,f4743]) ).

thf(f4743,plain,
    ( spl303_201
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( nil_Se901661471ession != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_201])]) ).

thf(f2900,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
      | ( nil_Se901661471ession != X0 ) ),
    inference(equality_proxy_clausification,[],[f2899]) ).

thf(f2899,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) ) ),
    inference(binary_proxy_clausification,[],[f2897]) ).

thf(f2897,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(sTfun(secrecy_Expression,$o),$o,vSIGMA(secrecy_Expression),vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),cCOMB,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession))),X0))) ) ),
    inference(equality_proxy_clausification,[],[f2891]) ).

thf(f2891,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(sTfun(secrecy_Expression,$o),$o,vSIGMA(secrecy_Expression),vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),cCOMB,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession))),X0))) ) ),
    inference(binary_proxy_clausification,[],[f1542]) ).

thf(f1542,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(sTfun(secrecy_Expression,$o),$o,vSIGMA(secrecy_Expression),vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),cCOMB,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession))),X0))) ),
    inference(cnf_transformation,[],[f404]) ).

thf(f404,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0)),vAPP(sTfun(secrecy_Expression,$o),$o,vSIGMA(secrecy_Expression),vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,$o)),cCOMB,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o)),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),sTfun(sTfun(secrecy_Expression,list_S529945141ession),sTfun(secrecy_Expression,sTfun(list_S529945141ession,$o))),bCOMB,vEQ(list_S529945141ession)),vAPP(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession),vAPP(sTfun(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(secrecy_Expression,list_S529945141ession)),cCOMB,cons_S112077679ession),nil_Se901661471ession))),X0))) ),
    inference(fool_elimination,[],[f403]) ).

thf(f403,plain,
    ! [X0: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        = ( ? [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession) = X0 ) ) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f308]) ).

thf(f308,axiom,
    ! [X28: list_S529945141ession] :
      ( ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X28) )
        = ( ? [X47: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X47),nil_Se901661471ession) = X28 ) ) )
      | ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_Nil__tl) ).

thf(f4700,plain,
    spl303_200,
    inference(avatar_split_clause,[],[f3114,f4698]) ).

thf(f3114,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ),
    inference(forward_demodulation,[],[f1905,f1527]) ).

thf(f1905,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1109]) ).

thf(f1109,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f680]) ).

thf(f680,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) ) ),
    inference(fool_elimination,[],[f679]) ).

thf(f679,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) ),
    inference(rectify,[],[f127]) ).

thf(f127,axiom,
    ! [X18: secrecy_specID,X46: secrecy_Expression,X68: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X18),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X46),X68))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X18),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X46),nil_Se901661471ession)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_notSpecKeysSecretsExpr__L1) ).

thf(f4696,plain,
    spl303_199,
    inference(avatar_split_clause,[],[f3036,f4694]) ).

thf(f4694,plain,
    ( spl303_199
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_199])]) ).

thf(f3036,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1688,f1527]) ).

thf(f1688,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1)) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1238]) ).

thf(f4692,plain,
    spl303_198,
    inference(avatar_split_clause,[],[f3031,f4690]) ).

thf(f4690,plain,
    ( spl303_198
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
        ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
        | ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_198])]) ).

thf(f3031,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1685,f1527]) ).

thf(f1685,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1)) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1234]) ).

thf(f4688,plain,
    spl303_197,
    inference(avatar_split_clause,[],[f3028,f4686]) ).

thf(f4686,plain,
    ( spl303_197
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_197])]) ).

thf(f3028,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1678,f1526]) ).

thf(f1678,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1230]) ).

thf(f4684,plain,
    spl303_196,
    inference(avatar_split_clause,[],[f3023,f4682]) ).

thf(f4682,plain,
    ( spl303_196
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
        ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
        | ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_196])]) ).

thf(f3023,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1675,f1526]) ).

thf(f1675,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1226]) ).

thf(f4680,plain,
    spl303_195,
    inference(avatar_split_clause,[],[f1891,f4678]) ).

thf(f4678,plain,
    ( spl303_195
  <=> ! [X2: secrecy_Expression,X0: list_S529945141ession,X1: set_li185139947ession] :
        ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X0)),X1) )
        | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_195])]) ).

thf(f1891,plain,
    ! [X2: secrecy_Expression,X0: list_S529945141ession,X1: set_li185139947ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X0)),X1) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1105]) ).

thf(f1105,plain,
    ! [X0: list_S529945141ession,X1: set_li185139947ession,X2: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X0)),X1) )
      | ( $true != vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f674]) ).

thf(f674,plain,
    ! [X0: list_S529945141ession,X1: set_li185139947ession,X2: secrecy_Expression] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X1),X2)) )
     => ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X0)),X1) ) ),
    inference(fool_elimination,[],[f673]) ).

thf(f673,plain,
    ! [X0: list_S529945141ession,X1: set_li185139947ession,X2: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X0),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X1),X2))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X0)),X1) ),
    inference(rectify,[],[f269]) ).

thf(f269,axiom,
    ! [X94: list_S529945141ession,X95: set_li185139947ession,X10: secrecy_Expression] :
      ( vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,X94),vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X95),X10))
     => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X94)),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_ShiftD) ).

thf(f4676,plain,
    spl303_194,
    inference(avatar_split_clause,[],[f1723,f4674]) ).

thf(f1723,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
      | ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) ) ),
    inference(cnf_transformation,[],[f1004]) ).

thf(f1004,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
      | ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) )
        & ( nil_Se901661471ession != X1 )
        & ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f883]) ).

thf(f883,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) != vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) )
        | ( nil_Se901661471ession = X1 )
        | ( nil_Se901661471ession = X0 ) )
     => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) ) ),
    inference(rectify,[],[f341]) ).

thf(f341,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X28) != vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X31) )
        | ( nil_Se901661471ession = X31 )
        | ( nil_Se901661471ession = X28 ) )
     => ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X28)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_remdups__adj__append_H) ).

thf(f4672,plain,
    spl303_193,
    inference(avatar_split_clause,[],[f1720,f4670]) ).

thf(f4670,plain,
    ( spl303_193
  <=> ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) )
        | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_193])]) ).

thf(f1720,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) )
      | ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) ) ),
    inference(cnf_transformation,[],[f1003]) ).

thf(f1003,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) )
      | ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) )
        & ( nil_Secrecy_KS != X1 )
        & ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f882]) ).

thf(f882,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) != vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X1 )
        | ( nil_Secrecy_KS = X0 ) )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) ) ),
    inference(rectify,[],[f342]) ).

thf(f342,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X28) != vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X31) )
        | ( nil_Secrecy_KS = X31 )
        | ( nil_Secrecy_KS = X28 ) )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X28)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_remdups__adj__append_H) ).

thf(f4648,plain,
    spl303_192,
    inference(avatar_split_clause,[],[f1613,f4646]) ).

thf(f1613,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) ),
    inference(cnf_transformation,[],[f853]) ).

thf(f853,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)))) ),
    inference(rectify,[],[f347]) ).

thf(f347,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_remdups__adj__Cons__alt) ).

thf(f4636,plain,
    spl303_191,
    inference(avatar_split_clause,[],[f3068,f4634]) ).

thf(f4634,plain,
    ( spl303_191
  <=> ! [X0: secrecy_specID,X1: secrecy_Secrets] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_191])]) ).

thf(f3068,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(forward_demodulation,[],[f1759,f1527]) ).

thf(f1759,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(cnf_transformation,[],[f1040]) ).

thf(f1040,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) ) ),
    inference(ennf_transformation,[],[f564]) ).

thf(f564,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) ) ),
    inference(fool_elimination,[],[f563]) ).

thf(f563,plain,
    ! [X0: secrecy_specID,X1: secrecy_Secrets] :
      ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1)),nil_Se901661471ession)) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X2: secrecy_specID,X3: secrecy_Secrets] :
      ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X3)),nil_Se901661471ession)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_know2knows__s) ).

thf(f4632,plain,
    spl303_190,
    inference(avatar_split_clause,[],[f3047,f4630]) ).

thf(f4630,plain,
    ( spl303_190
  <=> ! [X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
        | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_190])]) ).

thf(f3047,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
      | ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(forward_demodulation,[],[f1727,f1527]) ).

thf(f1727,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ) ),
    inference(cnf_transformation,[],[f1007]) ).

thf(f1007,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ) ),
    inference(ennf_transformation,[],[f886]) ).

thf(f886,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
     => ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(flattening,[],[f530]) ).

thf(f530,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
     => ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(fool_elimination,[],[f529]) ).

thf(f529,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ~ vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession))
     => ~ vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ),
    inference(rectify,[],[f68]) ).

thf(f68,axiom,
    ! [X2: secrecy_specID,X3: secrecy_Keys] :
      ( ~ vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3)),nil_Se901661471ession))
     => ~ vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_knows2know__neg__k) ).

thf(f4628,plain,
    spl303_189,
    inference(avatar_split_clause,[],[f3046,f4626]) ).

thf(f4626,plain,
    ( spl303_189
  <=> ! [X0: secrecy_specID,X1: secrecy_Keys] :
        ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
        | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_189])]) ).

thf(f3046,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(forward_demodulation,[],[f1724,f1527]) ).

thf(f1724,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(cnf_transformation,[],[f1005]) ).

thf(f1005,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) ) ),
    inference(ennf_transformation,[],[f884]) ).

thf(f884,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ) ),
    inference(flattening,[],[f526]) ).

thf(f526,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ( $true != vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1)) )
     => ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ) ),
    inference(fool_elimination,[],[f525]) ).

thf(f525,plain,
    ! [X0: secrecy_specID,X1: secrecy_Keys] :
      ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X0),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1))
     => ~ vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X1)),nil_Se901661471ession)) ),
    inference(rectify,[],[f67]) ).

thf(f67,axiom,
    ! [X2: secrecy_specID,X3: secrecy_Keys] :
      ( ~ vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,X2),vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3))
     => ~ vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3)),nil_Se901661471ession)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_know2knows__neg__k) ).

thf(f4527,plain,
    spl303_188,
    inference(avatar_split_clause,[],[f1792,f4525]) ).

thf(f1792,plain,
    ! [X2: list_S529945141ession,X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(cnf_transformation,[],[f894]) ).

thf(f894,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(rectify,[],[f134]) ).

thf(f134,axiom,
    ! [X46: list_S529945141ession,X69: list_S529945141ession,X70: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X46),X69)),X70) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X46),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X69),X70)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_append_Oassoc) ).

thf(f4523,plain,
    spl303_187,
    inference(avatar_split_clause,[],[f1791,f4521]) ).

thf(f1791,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(cnf_transformation,[],[f893]) ).

thf(f893,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(rectify,[],[f162]) ).

thf(f162,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession,X31: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),X31) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_append__Cons) ).

thf(f4519,plain,
    spl303_186,
    inference(avatar_split_clause,[],[f1790,f4517]) ).

thf(f1790,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X2),X1)) ),
    inference(cnf_transformation,[],[f892]) ).

thf(f892,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)),X2) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X2),X1)) ),
    inference(rectify,[],[f175]) ).

thf(f175,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession,X31: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),X31) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X31),X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_splice_Osimps_I2_J) ).

thf(f4515,plain,
    spl303_185,
    inference(avatar_split_clause,[],[f1789,f4513]) ).

thf(f4513,plain,
    ( spl303_185
  <=> ! [X2: list_S529945141ession,X0: set_li185139947ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)),X2) = vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_185])]) ).

thf(f1789,plain,
    ! [X2: list_S529945141ession,X0: set_li185139947ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)),X2) = vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ),
    inference(cnf_transformation,[],[f891]) ).

thf(f891,plain,
    ! [X0: set_li185139947ession,X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X0),X1)),X2) = vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ),
    inference(rectify,[],[f270]) ).

thf(f270,axiom,
    ! [X95: set_li185139947ession,X10: secrecy_Expression,X94: list_S529945141ession] : ( vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,vAPP(secrecy_Expression,set_li185139947ession,vAPP(set_li185139947ession,sTfun(secrecy_Expression,set_li185139947ession),bNF_Gr275623750ession,X95),X10)),X94) = vAPP(list_S529945141ession,set_Se1942955227ession,vAPP(set_li185139947ession,sTfun(list_S529945141ession,set_Se1942955227ession),bNF_Gr979629770ession,X95),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X10),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_Succ__Shift) ).

thf(f4511,plain,
    spl303_184,
    inference(avatar_split_clause,[],[f1746,f4509]) ).

thf(f1746,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1278]) ).

thf(f1278,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90])],[f1023,f1277]) ).

thf(f1277,plain,
    ! [X0: list_S529945141ession > $o] :
      ( ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X3) ) )
     => ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK89,X0)),vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0))) )
        & ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1023,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X3) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(flattening,[],[f1022]) ).

thf(f1022,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ? [X2: secrecy_Expression,X3: list_S529945141ession] :
          ( ( $true != vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
          & ( $true = vAPP(list_S529945141ession,$o,X0,X3) ) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(ennf_transformation,[],[f546]) ).

thf(f546,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) )
     => ( ! [X2: secrecy_Expression,X3: list_S529945141ession] :
            ( ( $true = vAPP(list_S529945141ession,$o,X0,X3) )
           => ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) ) )
       => ( $true = vAPP(list_S529945141ession,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f545]) ).

thf(f545,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession)
     => ( ! [X2: secrecy_Expression,X3: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,X0,X3)
           => vAPP(list_S529945141ession,$o,X0,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),X3)) )
       => vAPP(list_S529945141ession,$o,X0,X1) ) ),
    inference(rectify,[],[f28]) ).

thf(f28,axiom,
    ! [X18: list_S529945141ession > $o,X25: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,X18,nil_Se901661471ession)
     => ( ! [X16: secrecy_Expression,X17: list_S529945141ession] :
            ( vAPP(list_S529945141ession,$o,X18,X17)
           => vAPP(list_S529945141ession,$o,X18,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X16),X17)) )
       => vAPP(list_S529945141ession,$o,X18,X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_list_Oinducts) ).

thf(f4507,plain,
    spl303_183,
    inference(avatar_split_clause,[],[f1736,f4505]) ).

thf(f1736,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1266]) ).

thf(f1266,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f1015,f1265]) ).

thf(f1265,plain,
    ! [X0: list_Secrecy_KS > $o] :
      ( ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) ) )
     => ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK77,X0)),vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0))) )
        & ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1015,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(flattening,[],[f1014]) ).

thf(f1014,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_KS,X3: list_Secrecy_KS] :
          ( ( $true != vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) )
          & ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) ) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(ennf_transformation,[],[f538]) ).

thf(f538,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) )
     => ( ! [X2: secrecy_KS,X3: list_Secrecy_KS] :
            ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X3) )
           => ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) ) )
       => ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f537]) ).

thf(f537,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS)
     => ( ! [X2: secrecy_KS,X3: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,X0,X3)
           => vAPP(list_Secrecy_KS,$o,X0,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),X3)) )
       => vAPP(list_Secrecy_KS,$o,X0,X1) ) ),
    inference(rectify,[],[f27]) ).

thf(f27,axiom,
    ! [X18: list_Secrecy_KS > $o,X25: list_Secrecy_KS] :
      ( vAPP(list_Secrecy_KS,$o,X18,nil_Secrecy_KS)
     => ( ! [X16: secrecy_KS,X17: list_Secrecy_KS] :
            ( vAPP(list_Secrecy_KS,$o,X18,X17)
           => vAPP(list_Secrecy_KS,$o,X18,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X16),X17)) )
       => vAPP(list_Secrecy_KS,$o,X18,X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list_Oinducts) ).

thf(f4503,plain,
    ( spl303_182
    | ~ spl303_37
    | ~ spl303_94 ),
    inference(avatar_split_clause,[],[f3653,f3597,f3326,f4501]) ).

thf(f4501,plain,
    ( spl303_182
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) != X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_182])]) ).

thf(f3653,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,sK39,X0) != X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_37
    | ~ spl303_94 ),
    inference(superposition,[],[f3327,f3598]) ).

thf(f4443,plain,
    spl303_181,
    inference(avatar_split_clause,[],[f3037,f4441]) ).

thf(f3037,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1687,f1527]) ).

thf(f1687,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK54,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK55,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1238]) ).

thf(f4439,plain,
    spl303_180,
    inference(avatar_split_clause,[],[f3032,f4437]) ).

thf(f3032,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1684,f1527]) ).

thf(f1684,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession > $o] :
      ( ( $true = vAPP(list_S529945141ession,$o,X1,X0) )
      | ( nil_Se901661471ession != vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK51,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,X1,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(sTfun(list_S529945141ession,$o),secrecy_Expression,sK52,X1)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1234]) ).

thf(f4435,plain,
    spl303_179,
    inference(avatar_split_clause,[],[f3029,f4433]) ).

thf(f3029,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1677,f1526]) ).

thf(f1677,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK48,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK49,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1230]) ).

thf(f4431,plain,
    spl303_178,
    inference(avatar_split_clause,[],[f3024,f4429]) ).

thf(f3024,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1674,f1526]) ).

thf(f1674,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS > $o] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X1,X0) )
      | ( nil_Secrecy_KS != vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK45,X1) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X1,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(sTfun(list_Secrecy_KS,$o),secrecy_KS,sK46,X1)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1226]) ).

thf(f4402,plain,
    ( spl303_177
    | ~ spl303_37
    | ~ spl303_93 ),
    inference(avatar_split_clause,[],[f3649,f3593,f3326,f4400]) ).

thf(f4400,plain,
    ( spl303_177
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != X0 )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_177])]) ).

thf(f3649,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) != X0 )
        | ( nil_Se901661471ession = X0 ) )
    | ~ spl303_37
    | ~ spl303_93 ),
    inference(superposition,[],[f3327,f3594]) ).

thf(f4383,plain,
    spl303_176,
    inference(avatar_split_clause,[],[f3009,f4381]) ).

thf(f3009,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f1612,f1527]) ).

thf(f1612,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) ),
    inference(cnf_transformation,[],[f852]) ).

thf(f852,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) ),
    inference(rectify,[],[f264]) ).

thf(f264,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_rev_Osimps_I2_J) ).

thf(f4379,plain,
    spl303_175,
    inference(avatar_split_clause,[],[f3008,f4377]) ).

thf(f3008,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f1611,f1526]) ).

thf(f1611,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(cnf_transformation,[],[f851]) ).

thf(f851,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X1)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(rectify,[],[f263]) ).

thf(f263,axiom,
    ! [X39: secrecy_KS,X28: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X28)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_rev_Osimps_I2_J) ).

thf(f4375,plain,
    spl303_174,
    inference(avatar_split_clause,[],[f2062,f4373]) ).

thf(f2062,plain,
    ! [X2: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) ),
    inference(equality_resolution,[],[f1813]) ).

thf(f1813,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X2)) )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1050]) ).

thf(f4371,plain,
    spl303_173,
    inference(avatar_split_clause,[],[f1728,f4369]) ).

thf(f1728,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) )
      | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) ) ),
    inference(cnf_transformation,[],[f1256]) ).

thf(f1256,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
      | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) )
      | ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f1253,f1255,f1254]) ).

thf(f1254,plain,
    ! [X0: secrecy_KS > $o] :
      ( ? [X2: secrecy_Secrets] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X2)) )
     => ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Secrets,sK67,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1255,plain,
    ! [X0: secrecy_KS > $o] :
      ( ? [X3: secrecy_Keys] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3)) )
     => ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(sTfun(secrecy_KS,$o),secrecy_Keys,sK68,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1253,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
      | ? [X2: secrecy_Secrets] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X2)) )
      | ? [X3: secrecy_Keys] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3)) ) ),
    inference(rectify,[],[f1009]) ).

thf(f1009,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
      | ? [X3: secrecy_Secrets] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3)) )
      | ? [X2: secrecy_Keys] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) ) ),
    inference(flattening,[],[f1008]) ).

thf(f1008,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ( $true = vAPP(secrecy_KS,$o,X0,X1) )
      | ? [X3: secrecy_Secrets] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3)) )
      | ? [X2: secrecy_Keys] : ( $true != vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) ) ),
    inference(ennf_transformation,[],[f532]) ).

thf(f532,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ! [X2: secrecy_Keys] : ( $true = vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2)) )
     => ( ! [X3: secrecy_Secrets] : ( $true = vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3)) )
       => ( $true = vAPP(secrecy_KS,$o,X0,X1) ) ) ),
    inference(fool_elimination,[],[f531]) ).

thf(f531,plain,
    ! [X0: secrecy_KS > $o,X1: secrecy_KS] :
      ( ! [X2: secrecy_Keys] : vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2))
     => ( ! [X3: secrecy_Secrets] : vAPP(secrecy_KS,$o,X0,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3))
       => vAPP(secrecy_KS,$o,X0,X1) ) ),
    inference(rectify,[],[f17]) ).

thf(f17,axiom,
    ! [X18: secrecy_KS > $o,X19: secrecy_KS] :
      ( ! [X20: secrecy_Keys] : vAPP(secrecy_KS,$o,X18,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X20))
     => ( ! [X20: secrecy_Secrets] : vAPP(secrecy_KS,$o,X18,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X20))
       => vAPP(secrecy_KS,$o,X18,X19) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_KS_Oinduct) ).

thf(f4327,plain,
    spl303_172,
    inference(avatar_split_clause,[],[f2995,f4325]) ).

thf(f2995,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1567,f1527]) ).

thf(f1567,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f951]) ).

thf(f951,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f818]) ).

thf(f818,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),nil_Se901661471ession)) ) ),
    inference(rectify,[],[f285]) ).

thf(f285,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X28) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X28)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X28)),nil_Se901661471ession)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_rotate1__hd__tl) ).

thf(f4323,plain,
    spl303_171,
    inference(avatar_split_clause,[],[f2991,f4321]) ).

thf(f2991,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1557,f1526]) ).

thf(f1557,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f940]) ).

thf(f940,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f808]) ).

thf(f808,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),nil_Secrecy_KS)) ) ),
    inference(rectify,[],[f284]) ).

thf(f284,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X28 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X28)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X28)),nil_Secrecy_KS)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_rotate1__hd__tl) ).

thf(f4319,plain,
    spl303_170,
    inference(avatar_split_clause,[],[f1502,f4316]) ).

thf(f4316,plain,
    ( spl303_170
  <=> ( concat388015140ession = vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),foldr_1531709715ession,append2089414218ession)),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_170])]) ).

thf(f1502,plain,
    concat388015140ession = vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),foldr_1531709715ession,append2089414218ession)),nil_Se901661471ession),
    inference(cnf_transformation,[],[f376]) ).

thf(f376,plain,
    concat388015140ession = vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession),vAPP(sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_S529945141ession,sTfun(list_l425507653ession,list_S529945141ession)),cCOMB,vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),foldr_1531709715ession,append2089414218ession)),nil_Se901661471ession),
    inference(fool_elimination,[],[f375]) ).

thf(f375,plain,
    ( concat388015140ession
    = ( ^ [X0: list_l425507653ession] : vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),foldr_1531709715ession,append2089414218ession),X0),nil_Se901661471ession) ) ),
    inference(rectify,[],[f240]) ).

thf(f240,axiom,
    ( concat388015140ession
    = ( ^ [X93: list_l425507653ession] : vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession),vAPP(sTfun(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession)),sTfun(list_l425507653ession,sTfun(list_S529945141ession,list_S529945141ession)),foldr_1531709715ession,append2089414218ession),X93),nil_Se901661471ession) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_concat__conv__foldr) ).

thf(f4314,plain,
    spl303_169,
    inference(avatar_split_clause,[],[f1496,f4311]) ).

thf(f4311,plain,
    ( spl303_169
  <=> ( concat_Secrecy_KS = vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_Secrecy_KS),vAPP(sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_Secrecy_KS)),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),foldr_1711005747ecy_KS,append_Secrecy_KS)),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_169])]) ).

thf(f1496,plain,
    concat_Secrecy_KS = vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_Secrecy_KS),vAPP(sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_Secrecy_KS)),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),foldr_1711005747ecy_KS,append_Secrecy_KS)),nil_Secrecy_KS),
    inference(cnf_transformation,[],[f364]) ).

thf(f364,plain,
    concat_Secrecy_KS = vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_Secrecy_KS),vAPP(sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_Secrecy_KS)),cCOMB,vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),foldr_1711005747ecy_KS,append_Secrecy_KS)),nil_Secrecy_KS),
    inference(fool_elimination,[],[f363]) ).

thf(f363,plain,
    ( concat_Secrecy_KS
    = ( ^ [X0: list_list_Secrecy_KS] : vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),foldr_1711005747ecy_KS,append_Secrecy_KS),X0),nil_Secrecy_KS) ) ),
    inference(rectify,[],[f241]) ).

thf(f241,axiom,
    ( concat_Secrecy_KS
    = ( ^ [X93: list_list_Secrecy_KS] : vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),vAPP(sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),sTfun(list_list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS)),foldr_1711005747ecy_KS,append_Secrecy_KS),X93),nil_Secrecy_KS) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_concat__conv__foldr) ).

thf(f4274,plain,
    spl303_168,
    inference(avatar_split_clause,[],[f3005,f4272]) ).

thf(f4270,plain,
    spl303_167,
    inference(avatar_split_clause,[],[f3004,f4268]) ).

thf(f4227,plain,
    spl303_166,
    inference(avatar_split_clause,[],[f1907,f4225]) ).

thf(f1907,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1111]) ).

thf(f1111,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f684]) ).

thf(f684,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ) ),
    inference(fool_elimination,[],[f683]) ).

thf(f683,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X1) ),
    inference(rectify,[],[f170]) ).

thf(f170,axiom,
    ! [X2: secrecy_specID,X9: list_S529945141ession,X11: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X9),X11))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_knows2b) ).

thf(f4223,plain,
    spl303_165,
    inference(avatar_split_clause,[],[f1906,f4221]) ).

thf(f1906,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1110]) ).

thf(f1110,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f682]) ).

thf(f682,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) ) ),
    inference(fool_elimination,[],[f681]) ).

thf(f681,plain,
    ! [X0: secrecy_specID,X1: list_S529945141ession,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),X2) ),
    inference(rectify,[],[f171]) ).

thf(f171,axiom,
    ! [X2: secrecy_specID,X11: list_S529945141ession,X9: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X11),X9))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X2),X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_knows2a) ).

thf(f4219,plain,
    spl303_164,
    inference(avatar_split_clause,[],[f1904,f4217]) ).

thf(f1904,plain,
    ! [X2: list_S529945141ession,X0: secrecy_specID,X1: secrecy_Expression] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ),
    inference(cnf_transformation,[],[f1108]) ).

thf(f1108,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) )
      | ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) ) ),
    inference(ennf_transformation,[],[f678]) ).

thf(f678,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)) )
     => ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) ) ),
    inference(fool_elimination,[],[f677]) ).

thf(f677,plain,
    ! [X0: secrecy_specID,X1: secrecy_Expression,X2: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X0),X2) ),
    inference(rectify,[],[f174]) ).

thf(f174,axiom,
    ! [X18: secrecy_specID,X46: secrecy_Expression,X68: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X18),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X46),X68))
     => vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),notSpe1586871396tsExpr,X18),X68) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_notSpecKeysSecretsExpr__L2) ).

thf(f4215,plain,
    spl303_163,
    inference(avatar_split_clause,[],[f1874,f4213]) ).

thf(f1874,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ),
    inference(cnf_transformation,[],[f1098]) ).

thf(f1098,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ),
    inference(ennf_transformation,[],[f662]) ).

thf(f662,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 ) ),
    inference(fool_elimination,[],[f661]) ).

thf(f661,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1)
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X0),X2)) = X2 ) ),
    inference(rectify,[],[f190]) ).

thf(f190,axiom,
    ! [X80: secrecy_Keys,X81: secrecy_Keys,X82: list_S529945141ession] :
      ( vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X80),X81)
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),decr,X81),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),enc,X80),X82)) = X82 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_DecrEnc) ).

thf(f4211,plain,
    spl303_162,
    inference(avatar_split_clause,[],[f1873,f4209]) ).

thf(f1873,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Keys,X1: secrecy_Keys] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ),
    inference(cnf_transformation,[],[f1097]) ).

thf(f1097,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 )
      | ( $true != vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) ) ),
    inference(ennf_transformation,[],[f660]) ).

thf(f660,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( ( $true = vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1) )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 ) ),
    inference(fool_elimination,[],[f659]) ).

thf(f659,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Keys,X2: list_S529945141ession] :
      ( vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X0),X1)
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X1),X2)) = X2 ) ),
    inference(rectify,[],[f189]) ).

thf(f189,axiom,
    ! [X80: secrecy_Keys,X81: secrecy_Keys,X82: list_S529945141ession] :
      ( vAPP(secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(secrecy_Keys,$o),encrDecrKeys,X80),X81)
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),ext,X80),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Keys,sTfun(list_S529945141ession,list_S529945141ession),sign,X81),X82)) = X82 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ExtSign) ).

thf(f4163,plain,
    spl303_161,
    inference(avatar_split_clause,[],[f1956,f4161]) ).

thf(f1956,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(cnf_transformation,[],[f710]) ).

thf(f710,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)) ),
    inference(fool_elimination,[],[f709]) ).

thf(f709,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X2)),
    inference(rectify,[],[f173]) ).

thf(f173,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X77: list_S529945141ession,X78: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),X77),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X77),X78)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_ord_Olexordp__eq__pref) ).

thf(f4159,plain,
    spl303_160,
    inference(avatar_split_clause,[],[f1955,f4157]) ).

thf(f1955,plain,
    ! [X2: list_S529945141ession,X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f917]) ).

thf(f917,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) ),
    inference(flattening,[],[f708]) ).

thf(f708,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: list_S529945141ession] : ( $true != vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f707]) ).

thf(f707,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression,X2: list_S529945141ession] : ~ vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2)),nil_Se901661471ession),
    inference(rectify,[],[f89]) ).

thf(f89,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X39: secrecy_Expression,X28: list_S529945141ession] : ~ vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ord_Olexordp__eq__simps_I3_J) ).

thf(f4155,plain,
    spl303_159,
    inference(avatar_split_clause,[],[f1954,f4153]) ).

thf(f1954,plain,
    ! [X2: list_Secrecy_KS,X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f916]) ).

thf(f916,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS,X2: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) ),
    inference(flattening,[],[f706]) ).

thf(f706,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS,X2: list_Secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f705]) ).

thf(f705,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS,X2: list_Secrecy_KS] : ~ vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2)),nil_Secrecy_KS),
    inference(rectify,[],[f88]) ).

thf(f88,axiom,
    ! [X58: secrecy_KS > secrecy_KS > $o,X39: secrecy_KS,X28: list_Secrecy_KS] : ~ vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)),nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_ord_Olexordp__eq__simps_I3_J) ).

thf(f4151,plain,
    spl303_158,
    inference(avatar_split_clause,[],[f1607,f4149]) ).

thf(f1607,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ),
    inference(cnf_transformation,[],[f847]) ).

thf(f847,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X1)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ),
    inference(rectify,[],[f256]) ).

thf(f256,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X31)),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_rev__append) ).

thf(f4147,plain,
    spl303_157,
    inference(avatar_split_clause,[],[f1606,f4145]) ).

thf(f1606,plain,
    ! [X0: list_l425507653ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ),
    inference(cnf_transformation,[],[f846]) ).

thf(f846,plain,
    ! [X0: list_l425507653ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ),
    inference(rectify,[],[f197]) ).

thf(f197,axiom,
    ! [X28: list_l425507653ession,X31: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_l425507653ession,sTfun(list_l425507653ession,list_l425507653ession),append1105297242ession,X28),X31)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X28)),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_concat__append) ).

thf(f4039,plain,
    spl303_156,
    inference(avatar_split_clause,[],[f2997,f4037]) ).

thf(f2997,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1570,f1527]) ).

thf(f1570,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1218]) ).

thf(f1218,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f955,f1217]) ).

thf(f1217,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X1: list_S529945141ession,X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) = X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,sK40,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK41,X0)),nil_Se901661471ession)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f955,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X1: list_S529945141ession,X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f821]) ).

thf(f821,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ~ ! [X1: list_S529945141ession,X2: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X2),nil_Se901661471ession)) != X0 ) ),
    inference(rectify,[],[f185]) ).

thf(f185,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ~ ! [X34: list_S529945141ession,X33: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X34),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X33),nil_Se901661471ession)) != X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_rev__exhaust) ).

thf(f4035,plain,
    spl303_155,
    inference(avatar_split_clause,[],[f2994,f4033]) ).

thf(f2994,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(forward_demodulation,[],[f1566,f1527]) ).

thf(f1566,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f950]) ).

thf(f950,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f817]) ).

thf(f817,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0)),nil_Se901661471ession)) = X0 ) ),
    inference(rectify,[],[f218]) ).

thf(f218,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X28)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X28)),nil_Se901661471ession)) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_append__butlast__last__id) ).

thf(f4031,plain,
    ( spl303_154
    | ~ spl303_74 ),
    inference(avatar_split_clause,[],[f3986,f3502,f4028]) ).

thf(f4028,plain,
    ( spl303_154
  <=> ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_154])]) ).

thf(f3502,plain,
    ( spl303_74
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_74])]) ).

thf(f3986,plain,
    ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS) )
    | ~ spl303_74 ),
    inference(equality_resolution,[],[f3503]) ).

thf(f3503,plain,
    ( ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) )
    | ~ spl303_74 ),
    inference(avatar_component_clause,[],[f3502]) ).

thf(f4026,plain,
    spl303_153,
    inference(avatar_split_clause,[],[f2993,f4024]) ).

thf(f2993,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1560,f1526]) ).

thf(f1560,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1210]) ).

thf(f1210,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f944,f1209]) ).

thf(f1209,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X1: list_Secrecy_KS,X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) = X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,sK32,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK33,X0)),nil_Secrecy_KS)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f944,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X1: list_Secrecy_KS,X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f811]) ).

thf(f811,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ~ ! [X1: list_Secrecy_KS,X2: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X2),nil_Secrecy_KS)) != X0 ) ),
    inference(rectify,[],[f184]) ).

thf(f184,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X28 )
     => ~ ! [X34: list_Secrecy_KS,X33: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X34),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X33),nil_Secrecy_KS)) != X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_rev__exhaust) ).

thf(f4022,plain,
    spl303_152,
    inference(avatar_split_clause,[],[f2990,f4020]) ).

thf(f2990,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(forward_demodulation,[],[f1556,f1526]) ).

thf(f1556,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f939]) ).

thf(f939,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),nil_Secrecy_KS)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f807]) ).

thf(f807,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0)),nil_Secrecy_KS)) = X0 ) ),
    inference(rectify,[],[f217]) ).

thf(f217,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X28 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X28)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X28)),nil_Secrecy_KS)) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_append__butlast__last__id) ).

thf(f4018,plain,
    spl303_151,
    inference(avatar_split_clause,[],[f1683,f4016]) ).

thf(f1683,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f980]) ).

thf(f980,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f873]) ).

thf(f873,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)),X1) ) ),
    inference(rectify,[],[f289]) ).

thf(f289,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X28)),X31) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_tl__append2) ).

thf(f4014,plain,
    spl303_150,
    inference(avatar_split_clause,[],[f1673,f4012]) ).

thf(f1673,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),X1) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f972]) ).

thf(f972,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),X1) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f869]) ).

thf(f869,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)),X1) ) ),
    inference(rectify,[],[f290]) ).

thf(f290,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X28 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X28)),X31) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_tl__append2) ).

thf(f4010,plain,
    spl303_149,
    inference(avatar_split_clause,[],[f1665,f4008]) ).

thf(f1665,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f966]) ).

thf(f966,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
      & ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) )
        | ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f863]) ).

thf(f863,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != X0 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) ) )
      & ( ( nil_Se901661471ession = X0 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X1) ) ) ),
    inference(rectify,[],[f235]) ).

thf(f235,axiom,
    ! [X31: list_S529945141ession,X28: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != X31 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X31)) ) )
      & ( ( nil_Se901661471ession = X31 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X28) = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_butlast__append) ).

thf(f4006,plain,
    spl303_148,
    inference(avatar_split_clause,[],[f1661,f4004]) ).

thf(f1661,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f964]) ).

thf(f964,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) )
        | ( nil_Se901661471ession = X0 ) )
      & ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) )
        | ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f861]) ).

thf(f861,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( ( nil_Se901661471ession != X0 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X0)) ) )
      & ( ( nil_Se901661471ession = X0 )
       => ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) ) ) ),
    inference(rectify,[],[f234]) ).

thf(f234,axiom,
    ! [X28: list_S529945141ession,X39: secrecy_Expression] :
      ( ( ( nil_Se901661471ession != X28 )
       => ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,X28)) ) )
      & ( ( nil_Se901661471ession = X28 )
       => ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_butlast_Osimps_I2_J) ).

thf(f4002,plain,
    spl303_147,
    inference(avatar_split_clause,[],[f1655,f4000]) ).

thf(f1655,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f961]) ).

thf(f961,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
      & ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f858]) ).

thf(f858,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X0 )
       => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) ) )
      & ( ( nil_Secrecy_KS = X0 )
       => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X1) ) ) ),
    inference(rectify,[],[f236]) ).

thf(f236,axiom,
    ! [X31: list_Secrecy_KS,X28: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X31 )
       => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X31)) ) )
      & ( ( nil_Secrecy_KS = X31 )
       => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_butlast__append) ).

thf(f3998,plain,
    spl303_146,
    inference(avatar_split_clause,[],[f1651,f3996]) ).

thf(f1651,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f959]) ).

thf(f959,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) )
      & ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f856]) ).

thf(f856,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X0 )
       => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X0)) ) )
      & ( ( nil_Secrecy_KS = X0 )
       => ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) ) ) ),
    inference(rectify,[],[f233]) ).

thf(f233,axiom,
    ! [X28: list_Secrecy_KS,X39: secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X28 )
       => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,X28)) ) )
      & ( ( nil_Secrecy_KS = X28 )
       => ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_butlast_Osimps_I2_J) ).

thf(f3969,plain,
    spl303_145,
    inference(avatar_split_clause,[],[f1781,f3967]) ).

thf(f1781,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK114,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X1 ),
    inference(cnf_transformation,[],[f1299]) ).

thf(f3965,plain,
    spl303_144,
    inference(avatar_split_clause,[],[f1780,f3963]) ).

thf(f1780,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK113,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK112,X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f1299]) ).

thf(f3961,plain,
    spl303_143,
    inference(avatar_split_clause,[],[f1778,f3959]) ).

thf(f1778,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK111,X1),X0)) = X1 ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f3957,plain,
    spl303_142,
    inference(avatar_split_clause,[],[f1777,f3955]) ).

thf(f1777,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK109,X1),X0)),vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),sK110,X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f1297]) ).

thf(f3952,plain,
    spl303_141,
    inference(avatar_split_clause,[],[f1775,f3950]) ).

thf(f1775,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK108,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X1 ),
    inference(cnf_transformation,[],[f1295]) ).

thf(f3948,plain,
    spl303_140,
    inference(avatar_split_clause,[],[f1774,f3946]) ).

thf(f1774,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK107,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK106,X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f1295]) ).

thf(f3944,plain,
    spl303_139,
    inference(avatar_split_clause,[],[f1772,f3942]) ).

thf(f1772,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK105,X1),X0)) = X1 ),
    inference(cnf_transformation,[],[f1293]) ).

thf(f3940,plain,
    spl303_138,
    inference(avatar_split_clause,[],[f1771,f3938]) ).

thf(f1771,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK103,X1),X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),sK104,X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f1293]) ).

thf(f3932,plain,
    spl303_137,
    inference(avatar_split_clause,[],[f1605,f3930]) ).

thf(f1605,plain,
    ! [X0: list_S529945141ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ),
    inference(cnf_transformation,[],[f845]) ).

thf(f845,plain,
    ! [X0: list_S529945141ession,X1: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X1)) ),
    inference(rectify,[],[f202]) ).

thf(f202,axiom,
    ! [X39: list_S529945141ession,X28: list_l425507653ession] : ( vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,X39),X28)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X39),vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_concat_Osimps_I2_J) ).

thf(f3925,plain,
    spl303_136,
    inference(avatar_split_clause,[],[f1546,f3923]) ).

thf(f3923,plain,
    ( spl303_136
  <=> ! [X0: set_Secrecy_KS] : ( vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,vAPP(set_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,member_Secrecy_KS2),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_136])]) ).

thf(f1546,plain,
    ! [X0: set_Secrecy_KS] : ( vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,vAPP(set_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,member_Secrecy_KS2),X0)) = X0 ),
    inference(cnf_transformation,[],[f412]) ).

thf(f412,plain,
    ! [X0: set_Secrecy_KS] : ( vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,vAPP(set_Secrecy_KS,sTfun(secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(set_Secrecy_KS,$o)),sTfun(set_Secrecy_KS,sTfun(secrecy_KS,$o)),cCOMB,member_Secrecy_KS2),X0)) = X0 ),
    inference(fool_elimination,[],[f411]) ).

thf(f411,plain,
    ! [X0: set_Secrecy_KS] :
      ( vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,
          ^ [X1: secrecy_KS] : vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X1),X0)) = X0 ),
    inference(rectify,[],[f56]) ).

thf(f56,axiom,
    ! [X2: set_Secrecy_KS] :
      ( vAPP(sTfun(secrecy_KS,$o),set_Secrecy_KS,collect_Secrecy_KS,
          ^ [X47: secrecy_KS] : vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS2,X47),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Collect__mem__eq) ).

thf(f3920,plain,
    spl303_135,
    inference(avatar_split_clause,[],[f1545,f3918]) ).

thf(f3918,plain,
    ( spl303_135
  <=> ! [X0: set_Secrecy_Keys] : ( vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,vAPP(set_Secrecy_Keys,sTfun(secrecy_Keys,$o),vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_Keys,$o)),sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),cCOMB,member_Secrecy_Keys),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_135])]) ).

thf(f1545,plain,
    ! [X0: set_Secrecy_Keys] : ( vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,vAPP(set_Secrecy_Keys,sTfun(secrecy_Keys,$o),vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_Keys,$o)),sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),cCOMB,member_Secrecy_Keys),X0)) = X0 ),
    inference(cnf_transformation,[],[f410]) ).

thf(f410,plain,
    ! [X0: set_Secrecy_Keys] : ( vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,vAPP(set_Secrecy_Keys,sTfun(secrecy_Keys,$o),vAPP(sTfun(secrecy_Keys,sTfun(set_Secrecy_Keys,$o)),sTfun(set_Secrecy_Keys,sTfun(secrecy_Keys,$o)),cCOMB,member_Secrecy_Keys),X0)) = X0 ),
    inference(fool_elimination,[],[f409]) ).

thf(f409,plain,
    ! [X0: set_Secrecy_Keys] :
      ( vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,
          ^ [X1: secrecy_Keys] : vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X1),X0)) = X0 ),
    inference(rectify,[],[f57]) ).

thf(f57,axiom,
    ! [X2: set_Secrecy_Keys] :
      ( vAPP(sTfun(secrecy_Keys,$o),set_Secrecy_Keys,collect_Secrecy_Keys,
          ^ [X47: secrecy_Keys] : vAPP(set_Secrecy_Keys,$o,vAPP(secrecy_Keys,sTfun(set_Secrecy_Keys,$o),member_Secrecy_Keys,X47),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Collect__mem__eq) ).

thf(f3916,plain,
    spl303_134,
    inference(avatar_split_clause,[],[f1544,f3914]) ).

thf(f3914,plain,
    ( spl303_134
  <=> ! [X0: set_Secrecy_Secrets] : ( vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,vAPP(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o),vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o)),sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),cCOMB,member2138796287ecrets),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_134])]) ).

thf(f1544,plain,
    ! [X0: set_Secrecy_Secrets] : ( vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,vAPP(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o),vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o)),sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),cCOMB,member2138796287ecrets),X0)) = X0 ),
    inference(cnf_transformation,[],[f408]) ).

thf(f408,plain,
    ! [X0: set_Secrecy_Secrets] : ( vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,vAPP(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o),vAPP(sTfun(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o)),sTfun(set_Secrecy_Secrets,sTfun(secrecy_Secrets,$o)),cCOMB,member2138796287ecrets),X0)) = X0 ),
    inference(fool_elimination,[],[f407]) ).

thf(f407,plain,
    ! [X0: set_Secrecy_Secrets] :
      ( vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,
          ^ [X1: secrecy_Secrets] : vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X1),X0)) = X0 ),
    inference(rectify,[],[f55]) ).

thf(f55,axiom,
    ! [X2: set_Secrecy_Secrets] :
      ( vAPP(sTfun(secrecy_Secrets,$o),set_Secrecy_Secrets,collec836099393ecrets,
          ^ [X47: secrecy_Secrets] : vAPP(set_Secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(set_Secrecy_Secrets,$o),member2138796287ecrets,X47),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Collect__mem__eq) ).

thf(f3908,plain,
    spl303_133,
    inference(avatar_split_clause,[],[f1549,f3906]) ).

thf(f3906,plain,
    ( spl303_133
  <=> ! [X0: list_l425507653ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0) )
        | ( nil_li311616943ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_133])]) ).

thf(f1549,plain,
    ! [X0: list_l425507653ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0)) )
      | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0) )
      | ( nil_li311616943ession = X0 ) ),
    inference(cnf_transformation,[],[f931]) ).

thf(f931,plain,
    ! [X0: list_l425507653ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0)) )
      | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0) )
      | ( nil_li311616943ession = X0 ) ),
    inference(flattening,[],[f930]) ).

thf(f930,plain,
    ! [X0: list_l425507653ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0)) )
      | ( nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0) )
      | ( nil_li311616943ession = X0 ) ),
    inference(ennf_transformation,[],[f800]) ).

thf(f800,plain,
    ! [X0: list_l425507653ession] :
      ( ( nil_li311616943ession != X0 )
     => ( ( nil_Se901661471ession != vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0) )
       => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X0)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X0)) ) ) ),
    inference(rectify,[],[f281]) ).

thf(f281,axiom,
    ! [X28: list_l425507653ession] :
      ( ( nil_li311616943ession != X28 )
     => ( ( nil_Se901661471ession != vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X28) )
       => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,X28)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_l425507653ession,list_S529945141ession,hd_lis1623417098ession,X28)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_hd__concat) ).

thf(f3904,plain,
    spl303_132,
    inference(avatar_split_clause,[],[f1547,f3902]) ).

thf(f3902,plain,
    ( spl303_132
  <=> ! [X0: list_list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0) )
        | ( nil_list_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_132])]) ).

thf(f1547,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0) )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f927]) ).

thf(f927,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0) )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(flattening,[],[f926]) ).

thf(f926,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0) )
      | ( nil_list_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f798]) ).

thf(f798,plain,
    ! [X0: list_list_Secrecy_KS] :
      ( ( nil_list_Secrecy_KS != X0 )
     => ( ( nil_Secrecy_KS != vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0) )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,X0)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X0)) ) ) ),
    inference(rectify,[],[f282]) ).

thf(f282,axiom,
    ! [X28: list_list_Secrecy_KS] :
      ( ( nil_list_Secrecy_KS != X28 )
     => ( ( nil_Secrecy_KS != vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X28) )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,X28)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_list_Secrecy_KS,list_Secrecy_KS,hd_list_Secrecy_KS,X28)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_hd__concat) ).

thf(f3812,plain,
    spl303_131,
    inference(avatar_split_clause,[],[f3131,f3809]) ).

thf(f3131,plain,
    $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)),
    inference(forward_demodulation,[],[f2023,f1527]) ).

thf(f2023,plain,
    vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)) = $true,
    inference(cnf_transformation,[],[f770]) ).

thf(f770,plain,
    vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)) = $true,
    inference(fool_elimination,[],[f769]) ).

thf(f769,plain,
    vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,a),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,m)),nil_Se901661471ession)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).

thf(f3807,plain,
    spl303_130,
    inference(avatar_split_clause,[],[f3078,f3805]) ).

thf(f3078,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f1788,f1527]) ).

thf(f1788,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) ),
    inference(cnf_transformation,[],[f590]) ).

thf(f590,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) ),
    inference(fool_elimination,[],[f589]) ).

thf(f589,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: secrecy_Expression] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)),
    inference(rectify,[],[f326]) ).

thf(f326,axiom,
    ! [X18: secrecy_Expression > secrecy_Expression > $o,X39: secrecy_Expression] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X18),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_successively_Osimps_I2_J) ).

thf(f3803,plain,
    spl303_129,
    inference(avatar_split_clause,[],[f3077,f3801]) ).

thf(f3077,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f1787,f1526]) ).

thf(f1787,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(cnf_transformation,[],[f588]) ).

thf(f588,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(fool_elimination,[],[f587]) ).

thf(f587,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)),
    inference(rectify,[],[f325]) ).

thf(f325,axiom,
    ! [X18: secrecy_KS > secrecy_KS > $o,X39: secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X18),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_successively_Osimps_I2_J) ).

thf(f3796,plain,
    ( spl303_128
    | ~ spl303_127 ),
    inference(avatar_split_clause,[],[f3791,f3788,f3794]) ).

thf(f3788,plain,
    ( spl303_127
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_127])]) ).

thf(f3791,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X0 )
    | ~ spl303_127 ),
    inference(forward_demodulation,[],[f3789,f3005]) ).

thf(f3789,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = X0 )
    | ~ spl303_127 ),
    inference(avatar_component_clause,[],[f3788]) ).

thf(f3790,plain,
    spl303_127,
    inference(avatar_split_clause,[],[f3003,f3788]) ).

thf(f3003,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = X0 ),
    inference(forward_demodulation,[],[f1604,f1527]) ).

thf(f1604,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))) = X0 ),
    inference(cnf_transformation,[],[f844]) ).

thf(f844,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))) = X0 ),
    inference(rectify,[],[f209]) ).

thf(f209,axiom,
    ! [X28: list_S529945141ession,X39: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession))) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_butlast__snoc) ).

thf(f3783,plain,
    ( spl303_126
    | ~ spl303_125 ),
    inference(avatar_split_clause,[],[f3779,f3776,f3781]) ).

thf(f3776,plain,
    ( spl303_125
  <=> ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_125])]) ).

thf(f3779,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0))) = X1 )
    | ~ spl303_125 ),
    inference(forward_demodulation,[],[f3777,f3005]) ).

thf(f3777,plain,
    ( ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = X1 )
    | ~ spl303_125 ),
    inference(avatar_component_clause,[],[f3776]) ).

thf(f3778,plain,
    spl303_125,
    inference(avatar_split_clause,[],[f3002,f3776]) ).

thf(f3002,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession))) = X1 ),
    inference(forward_demodulation,[],[f1603,f1527]) ).

thf(f1603,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))) = X1 ),
    inference(cnf_transformation,[],[f843]) ).

thf(f843,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession))) = X1 ),
    inference(rectify,[],[f211]) ).

thf(f211,axiom,
    ! [X28: list_S529945141ession,X39: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession))) = X39 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_last__snoc) ).

thf(f3771,plain,
    ( spl303_124
    | ~ spl303_123 ),
    inference(avatar_split_clause,[],[f3767,f3764,f3769]) ).

thf(f3764,plain,
    ( spl303_123
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_123])]) ).

thf(f3767,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X0 )
    | ~ spl303_123 ),
    inference(forward_demodulation,[],[f3765,f3004]) ).

thf(f3765,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = X0 )
    | ~ spl303_123 ),
    inference(avatar_component_clause,[],[f3764]) ).

thf(f3766,plain,
    spl303_123,
    inference(avatar_split_clause,[],[f3001,f3764]) ).

thf(f3001,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = X0 ),
    inference(forward_demodulation,[],[f1602,f1526]) ).

thf(f1602,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))) = X0 ),
    inference(cnf_transformation,[],[f842]) ).

thf(f842,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))) = X0 ),
    inference(rectify,[],[f208]) ).

thf(f208,axiom,
    ! [X28: list_Secrecy_KS,X39: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS))) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_butlast__snoc) ).

thf(f3759,plain,
    ( spl303_122
    | ~ spl303_121 ),
    inference(avatar_split_clause,[],[f3755,f3752,f3757]) ).

thf(f3752,plain,
    ( spl303_121
  <=> ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_121])]) ).

thf(f3755,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0))) = X1 )
    | ~ spl303_121 ),
    inference(forward_demodulation,[],[f3753,f3004]) ).

thf(f3753,plain,
    ( ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = X1 )
    | ~ spl303_121 ),
    inference(avatar_component_clause,[],[f3752]) ).

thf(f3754,plain,
    spl303_121,
    inference(avatar_split_clause,[],[f3000,f3752]) ).

thf(f3000,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS))) = X1 ),
    inference(forward_demodulation,[],[f1601,f1526]) ).

thf(f1601,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))) = X1 ),
    inference(cnf_transformation,[],[f841]) ).

thf(f841,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS))) = X1 ),
    inference(rectify,[],[f210]) ).

thf(f210,axiom,
    ! [X28: list_Secrecy_KS,X39: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS))) = X39 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_last__snoc) ).

thf(f3749,plain,
    spl303_120,
    inference(avatar_split_clause,[],[f2989,f3747]) ).

thf(f2989,plain,
    ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f1529,f1527]) ).

thf(f1529,plain,
    ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) ),
    inference(cnf_transformation,[],[f797]) ).

thf(f797,plain,
    ! [X0: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) ),
    inference(rectify,[],[f349]) ).

thf(f349,axiom,
    ! [X39: secrecy_Expression] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession) = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_remdups__adj_Osimps_I2_J) ).

thf(f3745,plain,
    spl303_119,
    inference(avatar_split_clause,[],[f2988,f3743]) ).

thf(f2988,plain,
    ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f1528,f1526]) ).

thf(f1528,plain,
    ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(cnf_transformation,[],[f796]) ).

thf(f796,plain,
    ! [X0: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(rectify,[],[f348]) ).

thf(f348,axiom,
    ! [X39: secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS) = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_remdups__adj_Osimps_I2_J) ).

thf(f3741,plain,
    spl303_118,
    inference(avatar_split_clause,[],[f1747,f3739]) ).

thf(f1747,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK92,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1280]) ).

thf(f3737,plain,
    spl303_117,
    inference(avatar_split_clause,[],[f1745,f3735]) ).

thf(f1745,plain,
    ! [X0: list_S529945141ession > $o,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,X0,X1) )
      | ( $true = vAPP(list_S529945141ession,$o,X0,vAPP(sTfun(list_S529945141ession,$o),list_S529945141ession,sK90,X0)) )
      | ( $true != vAPP(list_S529945141ession,$o,X0,nil_Se901661471ession) ) ),
    inference(cnf_transformation,[],[f1278]) ).

thf(f3733,plain,
    spl303_116,
    inference(avatar_split_clause,[],[f1737,f3731]) ).

thf(f1737,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK80,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1268]) ).

thf(f3729,plain,
    spl303_115,
    inference(avatar_split_clause,[],[f1735,f3727]) ).

thf(f1735,plain,
    ! [X0: list_Secrecy_KS > $o,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,X0,X1) )
      | ( $true = vAPP(list_Secrecy_KS,$o,X0,vAPP(sTfun(list_Secrecy_KS,$o),list_Secrecy_KS,sK78,X0)) )
      | ( $true != vAPP(list_Secrecy_KS,$o,X0,nil_Secrecy_KS) ) ),
    inference(cnf_transformation,[],[f1266]) ).

thf(f3721,plain,
    spl303_114,
    inference(avatar_split_clause,[],[f3045,f3719]) ).

thf(f3719,plain,
    ( spl303_114
  <=> ! [X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_114])]) ).

thf(f3045,plain,
    ! [X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) ),
    inference(forward_demodulation,[],[f2061,f1511]) ).

thf(f1511,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X0) = X0 ),
    inference(cnf_transformation,[],[f779]) ).

thf(f779,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X0) = X0 ),
    inference(rectify,[],[f166]) ).

thf(f166,axiom,
    ! [X31: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X31) = X31 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_append__Nil) ).

thf(f2061,plain,
    ! [X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,nil_Se901661471ession),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) ),
    inference(equality_resolution,[],[f1721]) ).

thf(f1721,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
      | ( nil_Se901661471ession != X0 ) ),
    inference(cnf_transformation,[],[f1004]) ).

thf(f3716,plain,
    spl303_113,
    inference(avatar_split_clause,[],[f3044,f3714]) ).

thf(f3714,plain,
    ( spl303_113
  <=> ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_113])]) ).

thf(f3044,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f2060,f1514]) ).

thf(f1514,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),nil_Se901661471ession) = X0 ),
    inference(cnf_transformation,[],[f782]) ).

thf(f782,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),nil_Se901661471ession) = X0 ),
    inference(rectify,[],[f152]) ).

thf(f152,axiom,
    ! [X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),nil_Se901661471ession) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_append__Nil2) ).

thf(f2060,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),nil_Se901661471ession)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession)) ),
    inference(equality_resolution,[],[f1722]) ).

thf(f1722,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) = vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X1)) )
      | ( nil_Se901661471ession != X1 ) ),
    inference(cnf_transformation,[],[f1004]) ).

thf(f3712,plain,
    spl303_112,
    inference(avatar_split_clause,[],[f3043,f3710]) ).

thf(f3043,plain,
    ! [X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) ),
    inference(forward_demodulation,[],[f2059,f1505]) ).

thf(f1505,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),X0) = X0 ),
    inference(cnf_transformation,[],[f773]) ).

thf(f773,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),X0) = X0 ),
    inference(rectify,[],[f165]) ).

thf(f165,axiom,
    ! [X46: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),X46) = X46 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_append_Oleft__neutral) ).

thf(f2059,plain,
    ! [X1: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,nil_Secrecy_KS),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) ),
    inference(equality_resolution,[],[f1718]) ).

thf(f1718,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(cnf_transformation,[],[f1003]) ).

thf(f3708,plain,
    spl303_111,
    inference(avatar_split_clause,[],[f3042,f3706]) ).

thf(f3042,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f2058,f1508]) ).

thf(f1508,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),nil_Secrecy_KS) = X0 ),
    inference(cnf_transformation,[],[f776]) ).

thf(f776,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),nil_Secrecy_KS) = X0 ),
    inference(rectify,[],[f139]) ).

thf(f139,axiom,
    ! [X46: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X46),nil_Secrecy_KS) = X46 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_append_Oright__neutral) ).

thf(f2058,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),nil_Secrecy_KS)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,nil_Secrecy_KS)) ),
    inference(equality_resolution,[],[f1719]) ).

thf(f1719,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X1)) )
      | ( nil_Secrecy_KS != X1 ) ),
    inference(cnf_transformation,[],[f1003]) ).

thf(f3704,plain,
    spl303_110,
    inference(avatar_split_clause,[],[f1785,f3702]) ).

thf(f3702,plain,
    ( spl303_110
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),nil_Se901661471ession),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_110])]) ).

thf(f1785,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),nil_Se901661471ession),X1) ),
    inference(cnf_transformation,[],[f584]) ).

thf(f584,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),nil_Se901661471ession),X1) ),
    inference(fool_elimination,[],[f583]) ).

thf(f583,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X0),nil_Se901661471ession),X1),
    inference(rectify,[],[f109]) ).

thf(f109,axiom,
    ! [X58: secrecy_Expression > secrecy_Expression > $o,X31: list_S529945141ession] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),lexord1123423577ession,X58),nil_Se901661471ession),X31),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_ord_Olexordp__eq_ONil) ).

thf(f3700,plain,
    spl303_109,
    inference(avatar_split_clause,[],[f1783,f3698]) ).

thf(f3698,plain,
    ( spl303_109
  <=> ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),nil_Secrecy_KS),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_109])]) ).

thf(f1783,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),nil_Secrecy_KS),X1) ),
    inference(cnf_transformation,[],[f580]) ).

thf(f580,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),nil_Secrecy_KS),X1) ),
    inference(fool_elimination,[],[f579]) ).

thf(f579,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X0),nil_Secrecy_KS),X1),
    inference(rectify,[],[f106]) ).

thf(f106,axiom,
    ! [X58: secrecy_KS > secrecy_KS > $o,X31: list_Secrecy_KS] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),lexord948960489ecy_KS,X58),nil_Secrecy_KS),X31),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_ord_Olexordp__eq__simps_I1_J) ).

thf(f3695,plain,
    spl303_108,
    inference(avatar_split_clause,[],[f1590,f3693]) ).

thf(f3693,plain,
    ( spl303_108
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),nil_Se901661471ession),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_108])]) ).

thf(f1590,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),nil_Se901661471ession),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f442]) ).

thf(f442,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),nil_Se901661471ession),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f441]) ).

thf(f441,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X0),nil_Se901661471ession),nil_Se901661471ession),
    inference(rectify,[],[f112]) ).

thf(f112,axiom,
    ! [X60: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,sTfun(list_S529945141ession,$o)),listre84909707ession,X60),nil_Se901661471ession),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_listrelp_ONil) ).

thf(f3691,plain,
    spl303_107,
    inference(avatar_split_clause,[],[f1589,f3689]) ).

thf(f3689,plain,
    ( spl303_107
  <=> ! [X0: secrecy_KS > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),nil_Secrecy_KS),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_107])]) ).

thf(f1589,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),nil_Secrecy_KS),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f440]) ).

thf(f440,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),nil_Secrecy_KS),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f439]) ).

thf(f439,plain,
    ! [X0: secrecy_KS > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X0),nil_Secrecy_KS),nil_Se901661471ession),
    inference(rectify,[],[f114]) ).

thf(f114,axiom,
    ! [X60: secrecy_KS > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(list_Secrecy_KS,sTfun(list_S529945141ession,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_Expression,$o)),sTfun(list_Secrecy_KS,sTfun(list_S529945141ession,$o)),listre1601064475ession,X60),nil_Secrecy_KS),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_listrelp_ONil) ).

thf(f3687,plain,
    spl303_106,
    inference(avatar_split_clause,[],[f1588,f3685]) ).

thf(f3685,plain,
    ( spl303_106
  <=> ! [X0: secrecy_Expression > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),nil_Se901661471ession),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_106])]) ).

thf(f1588,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),nil_Se901661471ession),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f438]) ).

thf(f438,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),nil_Se901661471ession),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f437]) ).

thf(f437,plain,
    ! [X0: secrecy_Expression > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X0),nil_Se901661471ession),nil_Secrecy_KS),
    inference(rectify,[],[f113]) ).

thf(f113,axiom,
    ! [X60: secrecy_Expression > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(list_S529945141ession,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_Expression,sTfun(secrecy_KS,$o)),sTfun(list_S529945141ession,sTfun(list_Secrecy_KS,$o)),listre565996059ecy_KS,X60),nil_Se901661471ession),nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_listrelp_ONil) ).

thf(f3683,plain,
    spl303_105,
    inference(avatar_split_clause,[],[f1587,f3681]) ).

thf(f3681,plain,
    ( spl303_105
  <=> ! [X0: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),nil_Secrecy_KS),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_105])]) ).

thf(f1587,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),nil_Secrecy_KS),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f436]) ).

thf(f436,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),nil_Secrecy_KS),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f435]) ).

thf(f435,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X0),nil_Secrecy_KS),nil_Secrecy_KS),
    inference(rectify,[],[f115]) ).

thf(f115,axiom,
    ! [X60: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o)),listre788412843ecy_KS,X60),nil_Secrecy_KS),nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_listrelp_ONil) ).

thf(f3640,plain,
    spl303_104,
    inference(avatar_split_clause,[],[f1766,f3638]) ).

thf(f3638,plain,
    ( spl303_104
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
        | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_104])]) ).

thf(f1766,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(cnf_transformation,[],[f1046]) ).

thf(f1046,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) )
      | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(ennf_transformation,[],[f574]) ).

thf(f574,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
     => ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X0) ) ),
    inference(fool_elimination,[],[f573]) ).

thf(f573,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))
     => vAPP(list_S529945141ession,$o,distin1076152135ession,X0) ),
    inference(rectify,[],[f297]) ).

thf(f297,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31))
     => vAPP(list_S529945141ession,$o,distin1076152135ession,X28) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_distinct__adj__appendD1) ).

thf(f3636,plain,
    spl303_103,
    inference(avatar_split_clause,[],[f1765,f3634]) ).

thf(f3634,plain,
    ( spl303_103
  <=> ! [X0: list_S529945141ession,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_103])]) ).

thf(f1765,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(cnf_transformation,[],[f1045]) ).

thf(f1045,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ),
    inference(ennf_transformation,[],[f572]) ).

thf(f572,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
     => ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) ) ),
    inference(fool_elimination,[],[f571]) ).

thf(f571,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1))
     => vAPP(list_S529945141ession,$o,distin1076152135ession,X1) ),
    inference(rectify,[],[f298]) ).

thf(f298,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31))
     => vAPP(list_S529945141ession,$o,distin1076152135ession,X31) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_distinct__adj__appendD2) ).

thf(f3632,plain,
    spl303_102,
    inference(avatar_split_clause,[],[f1764,f3630]) ).

thf(f3630,plain,
    ( spl303_102
  <=> ! [X0: secrecy_Expression,X1: list_S529945141ession] :
        ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) )
        | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_102])]) ).

thf(f1764,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) ) ),
    inference(cnf_transformation,[],[f1044]) ).

thf(f1044,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) )
      | ( $true != vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) ) ),
    inference(ennf_transformation,[],[f570]) ).

thf(f570,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) )
     => ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,X1) ) ),
    inference(fool_elimination,[],[f569]) ).

thf(f569,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1))
     => vAPP(list_S529945141ession,$o,distin1076152135ession,X1) ),
    inference(rectify,[],[f301]) ).

thf(f301,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession] :
      ( vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28))
     => vAPP(list_S529945141ession,$o,distin1076152135ession,X28) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_distinct__adj__ConsD) ).

thf(f3628,plain,
    ( spl303_101
    | ~ spl303_18 ),
    inference(avatar_split_clause,[],[f3583,f3250,f3625]) ).

thf(f3625,plain,
    ( spl303_101
  <=> ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_101])]) ).

thf(f3250,plain,
    ( spl303_18
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_18])]) ).

thf(f3583,plain,
    ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,nil_Se901661471ession) )
    | ~ spl303_18 ),
    inference(equality_resolution,[],[f3251]) ).

thf(f3251,plain,
    ( ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) )
    | ~ spl303_18 ),
    inference(avatar_component_clause,[],[f3250]) ).

thf(f3623,plain,
    spl303_100,
    inference(avatar_split_clause,[],[f1669,f3621]) ).

thf(f1669,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f968]) ).

thf(f968,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) )
        | ( nil_Se901661471ession = X0 ) )
      & ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) )
        | ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f865]) ).

thf(f865,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != X0 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) ) )
      & ( ( nil_Se901661471ession = X0 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X1),X0)) ) ) ),
    inference(rectify,[],[f231]) ).

thf(f231,axiom,
    ! [X31: list_S529945141ession,X28: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != X31 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X31) ) )
      & ( ( nil_Se901661471ession = X31 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_last__append) ).

thf(f3619,plain,
    spl303_99,
    inference(avatar_split_clause,[],[f1667,f3617]) ).

thf(f1667,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f967]) ).

thf(f967,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
        | ( nil_Se901661471ession = X0 ) )
      & ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) )
        | ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f864]) ).

thf(f864,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != X0 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) )
      & ( ( nil_Se901661471ession = X0 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X1) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X0),X1)) ) ) ),
    inference(rectify,[],[f277]) ).

thf(f277,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != X28 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X28) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) ) )
      & ( ( nil_Se901661471ession = X28 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),append2089414218ession,X28),X31)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X31) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_hd__append) ).

thf(f3615,plain,
    spl303_98,
    inference(avatar_split_clause,[],[f1663,f3613]) ).

thf(f1663,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f965]) ).

thf(f965,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) )
        | ( nil_Se901661471ession = X0 ) )
      & ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = X1 )
        | ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f862]) ).

thf(f862,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( ( nil_Se901661471ession != X0 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) ) )
      & ( ( nil_Se901661471ession = X0 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = X1 ) ) ),
    inference(rectify,[],[f228]) ).

thf(f228,axiom,
    ! [X28: list_S529945141ession,X39: secrecy_Expression] :
      ( ( ( nil_Se901661471ession != X28 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X28) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) ) )
      & ( ( nil_Se901661471ession = X28 )
       => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28)) = X39 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_last_Osimps) ).

thf(f3611,plain,
    spl303_97,
    inference(avatar_split_clause,[],[f1659,f3609]) ).

thf(f1659,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f963]) ).

thf(f963,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS = X0 ) )
      & ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f860]) ).

thf(f860,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X0 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) ) )
      & ( ( nil_Secrecy_KS = X0 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X1),X0)) ) ) ),
    inference(rectify,[],[f232]) ).

thf(f232,axiom,
    ! [X31: list_Secrecy_KS,X28: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X31 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X31) ) )
      & ( ( nil_Secrecy_KS = X31 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_last__append) ).

thf(f3607,plain,
    spl303_96,
    inference(avatar_split_clause,[],[f1657,f3605]) ).

thf(f1657,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f962]) ).

thf(f962,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS = X0 ) )
      & ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) )
        | ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f859]) ).

thf(f859,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X0 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) )
      & ( ( nil_Secrecy_KS = X0 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X1) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),X1)) ) ) ),
    inference(rectify,[],[f278]) ).

thf(f278,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X28 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) ) )
      & ( ( nil_Secrecy_KS = X28 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X28),X31)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X31) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_hd__append) ).

thf(f3603,plain,
    spl303_95,
    inference(avatar_split_clause,[],[f1653,f3601]) ).

thf(f1653,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f960]) ).

thf(f960,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) )
        | ( nil_Secrecy_KS = X0 ) )
      & ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = X1 )
        | ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f857]) ).

thf(f857,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X0 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) ) )
      & ( ( nil_Secrecy_KS = X0 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = X1 ) ) ),
    inference(rectify,[],[f227]) ).

thf(f227,axiom,
    ! [X28: list_Secrecy_KS,X39: secrecy_KS] :
      ( ( ( nil_Secrecy_KS != X28 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)) ) )
      & ( ( nil_Secrecy_KS = X28 )
       => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),X28)) = X39 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_last_Osimps) ).

thf(f3599,plain,
    spl303_94,
    inference(avatar_split_clause,[],[f1569,f3597]) ).

thf(f1569,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f1216]) ).

thf(f1216,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f954,f1215]) ).

thf(f1215,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,sK38,X0)),vAPP(list_S529945141ession,list_S529945141ession,sK39,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f954,plain,
    ! [X0: list_S529945141ession] :
      ( ? [X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f820]) ).

thf(f820,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ~ ! [X1: secrecy_Expression,X2: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X2) != X0 ) ),
    inference(rectify,[],[f26]) ).

thf(f26,axiom,
    ! [X15: list_S529945141ession] :
      ( ( nil_Se901661471ession != X15 )
     => ~ ! [X26: secrecy_Expression,X27: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X26),X27) != X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Oexhaust) ).

thf(f3595,plain,
    spl303_93,
    inference(avatar_split_clause,[],[f1563,f3593]) ).

thf(f1563,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f947]) ).

thf(f947,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = X0 )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f814]) ).

thf(f814,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) = X0 ) ),
    inference(rectify,[],[f294]) ).

thf(f294,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X28)),vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X28)) = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_hd__Cons__tl) ).

thf(f3591,plain,
    spl303_92,
    inference(avatar_split_clause,[],[f1559,f3589]) ).

thf(f1559,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f1208]) ).

thf(f1208,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f943,f1207]) ).

thf(f1207,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X1: secrecy_KS,X2: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,sK30,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,sK31,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f943,plain,
    ! [X0: list_Secrecy_KS] :
      ( ? [X1: secrecy_KS,X2: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f810]) ).

thf(f810,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ~ ! [X1: secrecy_KS,X2: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X2) != X0 ) ),
    inference(rectify,[],[f25]) ).

thf(f25,axiom,
    ! [X15: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X15 )
     => ~ ! [X26: secrecy_KS,X27: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X26),X27) != X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_list_Oexhaust) ).

thf(f3587,plain,
    spl303_91,
    inference(avatar_split_clause,[],[f1553,f3585]) ).

thf(f1553,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f936]) ).

thf(f936,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = X0 )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f804]) ).

thf(f804,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) = X0 ) ),
    inference(rectify,[],[f291]) ).

thf(f291,axiom,
    ! [X25: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X25 )
     => ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X25)),vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X25)) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_list_Ocollapse) ).

thf(f3577,plain,
    spl303_90,
    inference(avatar_split_clause,[],[f2045,f3574]) ).

thf(f2045,plain,
    $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,nil_Se901661471ession),nil_Se901661471ession)),
    inference(equality_resolution,[],[f2044]) ).

thf(f2044,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),nil_Se901661471ession)) )
      | ( nil_Se901661471ession != X0 ) ),
    inference(equality_resolution,[],[f1697]) ).

thf(f1697,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
      | ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession != X0 ) ),
    inference(cnf_transformation,[],[f994]) ).

thf(f994,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
      | ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession != X0 ) ),
    inference(flattening,[],[f993]) ).

thf(f993,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) )
      | ( nil_Se901661471ession != X1 )
      | ( nil_Se901661471ession != X0 ) ),
    inference(ennf_transformation,[],[f520]) ).

thf(f520,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
     => ( ( nil_Se901661471ession = X1 )
       => ( $true = vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) ) ) ),
    inference(fool_elimination,[],[f519]) ).

thf(f519,plain,
    ! [X0: list_S529945141ession,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
     => ( ( nil_Se901661471ession = X1 )
       => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X0),X1)) ) ),
    inference(rectify,[],[f335]) ).

thf(f335,axiom,
    ! [X28: list_S529945141ession,X31: list_S529945141ession] :
      ( ( nil_Se901661471ession = X28 )
     => ( ( nil_Se901661471ession = X31 )
       => vAPP(set_li185139947ession,$o,vAPP(list_S529945141ession,sTfun(set_li185139947ession,$o),member249235532ession,nil_Se901661471ession),vAPP(list_S529945141ession,set_li185139947ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,set_li185139947ession),shuffl552897610ession,X28),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Nil__in__shufflesI) ).

thf(f3572,plain,
    spl303_89,
    inference(avatar_split_clause,[],[f2041,f3569]) ).

thf(f3569,plain,
    ( spl303_89
  <=> ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,nil_Secrecy_KS),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_89])]) ).

thf(f2041,plain,
    $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,nil_Secrecy_KS),nil_Secrecy_KS)),
    inference(equality_resolution,[],[f2040]) ).

thf(f2040,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),nil_Secrecy_KS)) )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(equality_resolution,[],[f1694]) ).

thf(f1694,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
      | ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(cnf_transformation,[],[f990]) ).

thf(f990,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
      | ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(flattening,[],[f989]) ).

thf(f989,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) )
      | ( nil_Secrecy_KS != X1 )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(ennf_transformation,[],[f518]) ).

thf(f518,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
     => ( ( nil_Secrecy_KS = X1 )
       => ( $true = vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) ) ) ),
    inference(fool_elimination,[],[f517]) ).

thf(f517,plain,
    ! [X0: list_Secrecy_KS,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
     => ( ( nil_Secrecy_KS = X1 )
       => vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X0),X1)) ) ),
    inference(rectify,[],[f336]) ).

thf(f336,axiom,
    ! [X28: list_Secrecy_KS,X31: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X28 )
     => ( ( nil_Secrecy_KS = X31 )
       => vAPP(set_list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(set_list_Secrecy_KS,$o),member193705948ecy_KS,nil_Secrecy_KS),vAPP(list_Secrecy_KS,set_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,set_list_Secrecy_KS),shuffles_Secrecy_KS,X28),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Nil__in__shufflesI) ).

thf(f3567,plain,
    spl303_88,
    inference(avatar_split_clause,[],[f1527,f3565]) ).

thf(f3563,plain,
    spl303_87,
    inference(avatar_split_clause,[],[f1526,f3561]) ).

thf(f3556,plain,
    spl303_86,
    inference(avatar_split_clause,[],[f2971,f3554]) ).

thf(f3554,plain,
    ( spl303_86
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_86])]) ).

thf(f2971,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) ) ),
    inference(equality_proxy_clausification,[],[f2970]) ).

thf(f2970,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2966]) ).

thf(f2966,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1532]) ).

thf(f1532,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) ),
    inference(cnf_transformation,[],[f384]) ).

thf(f384,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) ),
    inference(fool_elimination,[],[f383]) ).

thf(f383,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) )
      = ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f196]) ).

thf(f196,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X28) )
      = ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rotate1__is__Nil__conv) ).

thf(f3552,plain,
    spl303_85,
    inference(avatar_split_clause,[],[f1575,f3550]) ).

thf(f1575,plain,
    ! [X0: secrecy_KS] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = X0 )
      | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1222]) ).

thf(f1222,plain,
    ! [X0: secrecy_KS] :
      ( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = X0 )
      | ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f1219,f1221,f1220]) ).

thf(f1220,plain,
    ! [X0: secrecy_KS] :
      ( ? [X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) = X0 )
     => ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_KS,secrecy_Secrets,sK42,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1221,plain,
    ! [X0: secrecy_KS] :
      ( ? [X2: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2) = X0 )
     => ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_KS,secrecy_Keys,sK43,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1219,plain,
    ! [X0: secrecy_KS] :
      ( ? [X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) = X0 )
      | ? [X2: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X2) = X0 ) ),
    inference(rectify,[],[f958]) ).

thf(f958,plain,
    ! [X0: secrecy_KS] :
      ( ? [X2: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X2) = X0 )
      | ? [X1: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) = X0 ) ),
    inference(ennf_transformation,[],[f824]) ).

thf(f824,plain,
    ! [X0: secrecy_KS] :
      ( ! [X1: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X1) != X0 )
     => ~ ! [X2: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X2) != X0 ) ),
    inference(rectify,[],[f16]) ).

thf(f16,axiom,
    ! [X15: secrecy_KS] :
      ( ! [X16: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X16) != X15 )
     => ~ ! [X17: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X17) != X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_KS_Oexhaust) ).

thf(f3548,plain,
    spl303_84,
    inference(avatar_split_clause,[],[f1574,f3546]) ).

thf(f3546,plain,
    ( spl303_84
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_84])]) ).

thf(f1574,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) ) ),
    inference(cnf_transformation,[],[f957]) ).

thf(f957,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) )
      | ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        & ( nil_Se901661471ession != X0 ) ) ),
    inference(ennf_transformation,[],[f823]) ).

thf(f823,plain,
    ! [X0: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0) )
        | ( nil_Se901661471ession = X0 ) )
     => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X0)) ) ),
    inference(rectify,[],[f309]) ).

thf(f309,axiom,
    ! [X28: list_S529945141ession] :
      ( ( ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X28) )
        | ( nil_Se901661471ession = X28 ) )
     => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X28) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_last__tl) ).

thf(f3544,plain,
    spl303_83,
    inference(avatar_split_clause,[],[f1572,f3542]) ).

thf(f3542,plain,
    ( spl303_83
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_83])]) ).

thf(f1572,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) ) ),
    inference(cnf_transformation,[],[f956]) ).

thf(f956,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) )
      | ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        & ( nil_Secrecy_KS != X0 ) ) ),
    inference(ennf_transformation,[],[f822]) ).

thf(f822,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0) )
        | ( nil_Secrecy_KS = X0 ) )
     => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X0)) ) ),
    inference(rectify,[],[f310]) ).

thf(f310,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X28) )
        | ( nil_Secrecy_KS = X28 ) )
     => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_last__tl) ).

thf(f3536,plain,
    spl303_82,
    inference(avatar_split_clause,[],[f1562,f3534]) ).

thf(f3534,plain,
    ( spl303_82
  <=> ! [X0: list_S529945141ession] :
        ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
        | ( nil_Se901661471ession = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_82])]) ).

thf(f1562,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f946]) ).

thf(f946,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f813]) ).

thf(f813,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(rectify,[],[f271]) ).

thf(f271,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28)) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,X28) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_last__rev) ).

thf(f3532,plain,
    spl303_81,
    inference(avatar_split_clause,[],[f1561,f3530]) ).

thf(f1561,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(cnf_transformation,[],[f945]) ).

thf(f945,plain,
    ! [X0: list_S529945141ession] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) )
      | ( nil_Se901661471ession = X0 ) ),
    inference(ennf_transformation,[],[f812]) ).

thf(f812,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
     => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X0) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(rectify,[],[f273]) ).

thf(f273,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession != X28 )
     => ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,X28) = vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_hd__rev) ).

thf(f3528,plain,
    spl303_80,
    inference(avatar_split_clause,[],[f2969,f3526]) ).

thf(f3526,plain,
    ( spl303_80
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_80])]) ).

thf(f2969,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0) ) ),
    inference(equality_proxy_clausification,[],[f2968]) ).

thf(f2968,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2967]) ).

thf(f2967,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1532]) ).

thf(f3524,plain,
    spl303_79,
    inference(avatar_split_clause,[],[f1552,f3522]) ).

thf(f3522,plain,
    ( spl303_79
  <=> ! [X0: list_Secrecy_KS] :
        ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
        | ( nil_Secrecy_KS = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_79])]) ).

thf(f1552,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f935]) ).

thf(f935,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f803]) ).

thf(f803,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ) ),
    inference(rectify,[],[f272]) ).

thf(f272,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X28 )
     => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X28)) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,X28) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_last__rev) ).

thf(f3520,plain,
    spl303_78,
    inference(avatar_split_clause,[],[f1551,f3518]) ).

thf(f1551,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(cnf_transformation,[],[f934]) ).

thf(f934,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) )
      | ( nil_Secrecy_KS = X0 ) ),
    inference(ennf_transformation,[],[f802]) ).

thf(f802,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
     => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X0) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ) ),
    inference(rectify,[],[f274]) ).

thf(f274,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X28 )
     => ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,X28) = vAPP(list_Secrecy_KS,secrecy_KS,hd_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_hd__rev) ).

thf(f3516,plain,
    spl303_77,
    inference(avatar_split_clause,[],[f2965,f3514]) ).

thf(f3514,plain,
    ( spl303_77
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_77])]) ).

thf(f2965,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ),
    inference(equality_proxy_clausification,[],[f2964]) ).

thf(f2964,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2960]) ).

thf(f2960,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1533]) ).

thf(f1533,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) ),
    inference(cnf_transformation,[],[f386]) ).

thf(f386,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) ),
    inference(fool_elimination,[],[f385]) ).

thf(f385,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) )
      = ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f346]) ).

thf(f346,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X28) )
      = ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_remdups__adj__Nil__iff) ).

thf(f3512,plain,
    spl303_76,
    inference(avatar_split_clause,[],[f3021,f3510]) ).

thf(f3021,plain,
    ! [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) = X1 ),
    inference(forward_demodulation,[],[f2032,f1527]) ).

thf(f2032,plain,
    ! [X1: secrecy_Expression] : ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) = X1 ),
    inference(equality_resolution,[],[f1662]) ).

thf(f1662,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( vAPP(list_S529945141ession,secrecy_Expression,last_S1532390982ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) = X1 )
      | ( nil_Se901661471ession != X0 ) ),
    inference(cnf_transformation,[],[f965]) ).

thf(f3508,plain,
    spl303_75,
    inference(avatar_split_clause,[],[f3020,f3506]) ).

thf(f3020,plain,
    ! [X1: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X1),nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f2031,f1527]) ).

thf(f2031,plain,
    ! [X1: secrecy_Expression] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),nil_Se901661471ession)) ),
    inference(equality_resolution,[],[f1660]) ).

thf(f1660,plain,
    ! [X0: list_S529945141ession,X1: secrecy_Expression] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X1),X0)) )
      | ( nil_Se901661471ession != X0 ) ),
    inference(cnf_transformation,[],[f964]) ).

thf(f3504,plain,
    spl303_74,
    inference(avatar_split_clause,[],[f2963,f3502]) ).

thf(f2963,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0) ) ),
    inference(equality_proxy_clausification,[],[f2962]) ).

thf(f2962,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2961]) ).

thf(f2961,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,remdup351570169ecy_KS,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1533]) ).

thf(f3500,plain,
    spl303_73,
    inference(avatar_split_clause,[],[f3019,f3498]) ).

thf(f3019,plain,
    ! [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) = X1 ),
    inference(forward_demodulation,[],[f2027,f1526]) ).

thf(f2027,plain,
    ! [X1: secrecy_KS] : ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) = X1 ),
    inference(equality_resolution,[],[f1652]) ).

thf(f1652,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( vAPP(list_Secrecy_KS,secrecy_KS,last_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) = X1 )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(cnf_transformation,[],[f960]) ).

thf(f3496,plain,
    spl303_72,
    inference(avatar_split_clause,[],[f3018,f3494]) ).

thf(f3494,plain,
    ( spl303_72
  <=> ! [X1: secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_72])]) ).

thf(f3018,plain,
    ! [X1: secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f2026,f1526]) ).

thf(f2026,plain,
    ! [X1: secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),nil_Secrecy_KS)) ),
    inference(equality_resolution,[],[f1650]) ).

thf(f1650,plain,
    ! [X0: list_Secrecy_KS,X1: secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X1),X0)) )
      | ( nil_Secrecy_KS != X0 ) ),
    inference(cnf_transformation,[],[f959]) ).

thf(f3492,plain,
    spl303_71,
    inference(avatar_split_clause,[],[f2999,f3490]) ).

thf(f2999,plain,
    ! [X0: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),insert1173886601ession,X0),nil_Se901661471ession)) ),
    inference(forward_demodulation,[],[f1585,f1527]) ).

thf(f1585,plain,
    ! [X0: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) ),
    inference(cnf_transformation,[],[f432]) ).

thf(f432,plain,
    ! [X0: secrecy_Expression] : ( $true = vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)) ),
    inference(fool_elimination,[],[f431]) ).

thf(f431,plain,
    ! [X0: secrecy_Expression] : vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),nil_Se901661471ession)),
    inference(rectify,[],[f312]) ).

thf(f312,axiom,
    ! [X39: secrecy_Expression] : vAPP(list_S529945141ession,$o,distin1076152135ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),nil_Se901661471ession)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_distinct__adj__singleton) ).

thf(f3488,plain,
    spl303_70,
    inference(avatar_split_clause,[],[f2998,f3486]) ).

thf(f2998,plain,
    ! [X0: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),insert_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(forward_demodulation,[],[f1583,f1526]) ).

thf(f1583,plain,
    ! [X0: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(cnf_transformation,[],[f428]) ).

thf(f428,plain,
    ! [X0: secrecy_KS] : ( $true = vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)) ),
    inference(fool_elimination,[],[f427]) ).

thf(f427,plain,
    ! [X0: secrecy_KS] : vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),nil_Secrecy_KS)),
    inference(rectify,[],[f311]) ).

thf(f311,axiom,
    ! [X39: secrecy_KS] : vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X39),nil_Secrecy_KS)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_distinct__adj__singleton) ).

thf(f3484,plain,
    spl303_69,
    inference(avatar_split_clause,[],[f1597,f3482]) ).

thf(f1597,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X1 ),
    inference(cnf_transformation,[],[f837]) ).

thf(f837,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X1 ),
    inference(rectify,[],[f304]) ).

thf(f304,axiom,
    ! [X21: secrecy_Expression,X22: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X21),X22)) = X22 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_list_Osel_I3_J) ).

thf(f3480,plain,
    spl303_68,
    inference(avatar_split_clause,[],[f1596,f3478]) ).

thf(f1596,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X0 ),
    inference(cnf_transformation,[],[f836]) ).

thf(f836,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1)) = X0 ),
    inference(rectify,[],[f283]) ).

thf(f283,axiom,
    ! [X21: secrecy_Expression,X22: list_S529945141ession] : ( vAPP(list_S529945141ession,secrecy_Expression,hd_Sec357328890ession,vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X21),X22)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_list_Osel_I1_J) ).

thf(f3476,plain,
    spl303_67,
    inference(avatar_split_clause,[],[f1586,f3474]) ).

thf(f3474,plain,
    ( spl303_67
  <=> ! [X0: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_67])]) ).

thf(f1586,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f434]) ).

thf(f434,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o] : ( $true = vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f433]) ).

thf(f433,plain,
    ! [X0: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X0),nil_Se901661471ession),
    inference(rectify,[],[f331]) ).

thf(f331,axiom,
    ! [X18: secrecy_Expression > secrecy_Expression > $o] : vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,sTfun(secrecy_Expression,$o)),sTfun(list_S529945141ession,$o),succes1388047762ession,X18),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_successively_Osimps_I1_J) ).

thf(f3472,plain,
    spl303_66,
    inference(avatar_split_clause,[],[f1584,f3470]) ).

thf(f3470,plain,
    ( spl303_66
  <=> ! [X0: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_66])]) ).

thf(f1584,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f430]) ).

thf(f430,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o] : ( $true = vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f429]) ).

thf(f429,plain,
    ! [X0: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X0),nil_Secrecy_KS),
    inference(rectify,[],[f332]) ).

thf(f332,axiom,
    ! [X18: secrecy_KS > secrecy_KS > $o] : vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,sTfun(secrecy_KS,$o)),sTfun(list_Secrecy_KS,$o),succes590251810ecy_KS,X18),nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_successively_Osimps_I1_J) ).

thf(f3468,plain,
    spl303_65,
    inference(avatar_split_clause,[],[f1525,f3466]) ).

thf(f1525,plain,
    ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,nil_Se901661471ession),X0) ),
    inference(cnf_transformation,[],[f793]) ).

thf(f793,plain,
    ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,nil_Se901661471ession),X0) ),
    inference(rectify,[],[f90]) ).

thf(f90,axiom,
    ! [X59: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_S529945141ession),list_S529945141ession),bind_S815874003ession,nil_Se901661471ession),X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_bind__simps_I1_J) ).

thf(f3464,plain,
    spl303_64,
    inference(avatar_split_clause,[],[f1524,f3462]) ).

thf(f3462,plain,
    ( spl303_64
  <=> ! [X0: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession),bind_S711229283ession,nil_Secrecy_KS),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_64])]) ).

thf(f1524,plain,
    ! [X0: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession),bind_S711229283ession,nil_Secrecy_KS),X0) ),
    inference(cnf_transformation,[],[f792]) ).

thf(f792,plain,
    ! [X0: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession),bind_S711229283ession,nil_Secrecy_KS),X0) ),
    inference(rectify,[],[f92]) ).

thf(f92,axiom,
    ! [X59: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_S529945141ession),list_S529945141ession),bind_S711229283ession,nil_Secrecy_KS),X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_bind__simps_I1_J) ).

thf(f3460,plain,
    spl303_63,
    inference(avatar_split_clause,[],[f2959,f3458]) ).

thf(f3458,plain,
    ( spl303_63
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS = X0 )
        | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_63])]) ).

thf(f2959,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ),
    inference(equality_proxy_clausification,[],[f2958]) ).

thf(f2958,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X0 )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2954]) ).

thf(f2954,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1534]) ).

thf(f1534,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ),
    inference(cnf_transformation,[],[f388]) ).

thf(f388,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ),
    inference(fool_elimination,[],[f387]) ).

thf(f387,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) )
      = ( nil_Secrecy_KS = X0 ) ),
    inference(rectify,[],[f253]) ).

thf(f253,axiom,
    ! [X28: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X28) )
      = ( nil_Secrecy_KS = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Nil__is__rev__conv) ).

thf(f3456,plain,
    spl303_62,
    inference(avatar_split_clause,[],[f1523,f3454]) ).

thf(f3454,plain,
    ( spl303_62
  <=> ! [X0: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS),bind_S1823644515ecy_KS,nil_Se901661471ession),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_62])]) ).

thf(f1523,plain,
    ! [X0: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS),bind_S1823644515ecy_KS,nil_Se901661471ession),X0) ),
    inference(cnf_transformation,[],[f791]) ).

thf(f791,plain,
    ! [X0: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS),bind_S1823644515ecy_KS,nil_Se901661471ession),X0) ),
    inference(rectify,[],[f91]) ).

thf(f91,axiom,
    ! [X59: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_S529945141ession,sTfun(sTfun(secrecy_Expression,list_Secrecy_KS),list_Secrecy_KS),bind_S1823644515ecy_KS,nil_Se901661471ession),X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_bind__simps_I1_J) ).

thf(f3452,plain,
    spl303_61,
    inference(avatar_split_clause,[],[f1522,f3450]) ).

thf(f3450,plain,
    ( spl303_61
  <=> ! [X0: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS),bind_S645462771ecy_KS,nil_Secrecy_KS),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_61])]) ).

thf(f1522,plain,
    ! [X0: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS),bind_S645462771ecy_KS,nil_Secrecy_KS),X0) ),
    inference(cnf_transformation,[],[f790]) ).

thf(f790,plain,
    ! [X0: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS),bind_S645462771ecy_KS,nil_Secrecy_KS),X0) ),
    inference(rectify,[],[f93]) ).

thf(f93,axiom,
    ! [X59: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(sTfun(secrecy_KS,list_Secrecy_KS),list_Secrecy_KS),bind_S645462771ecy_KS,nil_Secrecy_KS),X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_bind__simps_I1_J) ).

thf(f3448,plain,
    spl303_60,
    inference(avatar_split_clause,[],[f1493,f3445]) ).

thf(f1493,plain,
    vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession) = vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession),
    inference(cnf_transformation,[],[f81]) ).

thf(f81,axiom,
    vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession) = vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_subseqs_Osimps_I1_J) ).

thf(f3443,plain,
    spl303_59,
    inference(avatar_split_clause,[],[f1492,f3440]) ).

thf(f3440,plain,
    ( spl303_59
  <=> ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS) = vAPP(list_Secrecy_KS,list_list_Secrecy_KS,subseqs_Secrecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_59])]) ).

thf(f1492,plain,
    vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS) = vAPP(list_Secrecy_KS,list_list_Secrecy_KS,subseqs_Secrecy_KS,nil_Secrecy_KS),
    inference(cnf_transformation,[],[f82]) ).

thf(f82,axiom,
    vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS) = vAPP(list_Secrecy_KS,list_list_Secrecy_KS,subseqs_Secrecy_KS,nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_subseqs_Osimps_I1_J) ).

thf(f3438,plain,
    ( spl303_58
    | ~ spl303_57 ),
    inference(avatar_split_clause,[],[f3433,f3429,f3435]) ).

thf(f3435,plain,
    ( spl303_58
  <=> ( vAPP(list_l425507653ession,list_l425507653ession,produc1450295286ession,nil_li311616943ession) = vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_58])]) ).

thf(f3429,plain,
    ( spl303_57
  <=> ( vAPP(list_l425507653ession,list_l425507653ession,produc1450295286ession,nil_li311616943ession) = vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_57])]) ).

thf(f3433,plain,
    ( ( vAPP(list_l425507653ession,list_l425507653ession,produc1450295286ession,nil_li311616943ession) = vAPP(list_S529945141ession,list_l425507653ession,subseq348280080ession,nil_Se901661471ession) )
    | ~ spl303_57 ),
    inference(forward_demodulation,[],[f3431,f1493]) ).

thf(f3431,plain,
    ( ( vAPP(list_l425507653ession,list_l425507653ession,produc1450295286ession,nil_li311616943ession) = vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession) )
    | ~ spl303_57 ),
    inference(avatar_component_clause,[],[f3429]) ).

thf(f3432,plain,
    spl303_57,
    inference(avatar_split_clause,[],[f1491,f3429]) ).

thf(f1491,plain,
    vAPP(list_l425507653ession,list_l425507653ession,produc1450295286ession,nil_li311616943ession) = vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession),
    inference(cnf_transformation,[],[f79]) ).

thf(f79,axiom,
    vAPP(list_l425507653ession,list_l425507653ession,produc1450295286ession,nil_li311616943ession) = vAPP(list_l425507653ession,list_l425507653ession,vAPP(list_S529945141ession,sTfun(list_l425507653ession,list_l425507653ession),cons_l533358079ession,nil_Se901661471ession),nil_li311616943ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_product__lists_Osimps_I1_J) ).

thf(f3427,plain,
    ( spl303_56
    | ~ spl303_55 ),
    inference(avatar_split_clause,[],[f3422,f3418,f3424]) ).

thf(f3424,plain,
    ( spl303_56
  <=> ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,produc713695622ecy_KS,nil_list_Secrecy_KS) = vAPP(list_Secrecy_KS,list_list_Secrecy_KS,subseqs_Secrecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_56])]) ).

thf(f3418,plain,
    ( spl303_55
  <=> ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,produc713695622ecy_KS,nil_list_Secrecy_KS) = vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_55])]) ).

thf(f3422,plain,
    ( ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,produc713695622ecy_KS,nil_list_Secrecy_KS) = vAPP(list_Secrecy_KS,list_list_Secrecy_KS,subseqs_Secrecy_KS,nil_Secrecy_KS) )
    | ~ spl303_55 ),
    inference(forward_demodulation,[],[f3420,f1492]) ).

thf(f3420,plain,
    ( ( vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,produc713695622ecy_KS,nil_list_Secrecy_KS) = vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS) )
    | ~ spl303_55 ),
    inference(avatar_component_clause,[],[f3418]) ).

thf(f3421,plain,
    spl303_55,
    inference(avatar_split_clause,[],[f1490,f3418]) ).

thf(f1490,plain,
    vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,produc713695622ecy_KS,nil_list_Secrecy_KS) = vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS),
    inference(cnf_transformation,[],[f80]) ).

thf(f80,axiom,
    vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,produc713695622ecy_KS,nil_list_Secrecy_KS) = vAPP(list_list_Secrecy_KS,list_list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_list_Secrecy_KS,list_list_Secrecy_KS),cons_list_Secrecy_KS,nil_Secrecy_KS),nil_list_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_product__lists_Osimps_I1_J) ).

thf(f3416,plain,
    spl303_54,
    inference(avatar_split_clause,[],[f2957,f3414]) ).

thf(f3414,plain,
    ( spl303_54
  <=> ! [X0: list_Secrecy_KS] :
        ( ( nil_Secrecy_KS != X0 )
        | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_54])]) ).

thf(f2957,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0) ) ),
    inference(equality_proxy_clausification,[],[f2956]) ).

thf(f2956,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS != X0 )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2955]) ).

thf(f2955,plain,
    ! [X0: list_Secrecy_KS] :
      ( ( $false = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),X0) )
      | ( $true = vAPP(list_Secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,$o),vEQ(list_Secrecy_KS),nil_Secrecy_KS),vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1534]) ).

thf(f3404,plain,
    spl303_53,
    inference(avatar_split_clause,[],[f1835,f3402]) ).

thf(f1835,plain,
    ! [X0: $o,X1: list_S529945141ession] :
      ( ( $true = X0 )
      | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f1313,plain,
    ! [X0: $o,X1: list_S529945141ession] :
      ( ( ( $true = X0 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) ) ),
    inference(rectify,[],[f1312]) ).

thf(f1312,plain,
    ! [X2: $o,X1: list_S529945141ession] :
      ( ( ( $true = X2 )
        & ( nil_Se901661471ession = X1 ) )
      | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X2) ) ),
    inference(nnf_transformation,[],[f1169]) ).

thf(f3400,plain,
    spl303_52,
    inference(avatar_split_clause,[],[f1834,f3398]) ).

thf(f1834,plain,
    ! [X0: $o,X1: list_S529945141ession] :
      ( ( nil_Se901661471ession = X1 )
      | ( $true != vAPP($o,$o,vAPP(list_S529945141ession,sTfun($o,$o),sP3,X1),X0) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f3396,plain,
    spl303_51,
    inference(avatar_split_clause,[],[f1829,f3394]) ).

thf(f1829,plain,
    ! [X0: $o,X1: list_Secrecy_KS] :
      ( ( $true = X0 )
      | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) ) ),
    inference(cnf_transformation,[],[f1307]) ).

thf(f1307,plain,
    ! [X0: $o,X1: list_Secrecy_KS] :
      ( ( ( $true = X0 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) ) ),
    inference(rectify,[],[f1306]) ).

thf(f1306,plain,
    ! [X2: $o,X1: list_Secrecy_KS] :
      ( ( ( $true = X2 )
        & ( nil_Secrecy_KS = X1 ) )
      | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X2) ) ),
    inference(nnf_transformation,[],[f1167]) ).

thf(f3392,plain,
    spl303_50,
    inference(avatar_split_clause,[],[f1828,f3390]) ).

thf(f1828,plain,
    ! [X0: $o,X1: list_Secrecy_KS] :
      ( ( nil_Secrecy_KS = X1 )
      | ( $true != vAPP($o,$o,vAPP(list_Secrecy_KS,sTfun($o,$o),sP2,X1),X0) ) ),
    inference(cnf_transformation,[],[f1307]) ).

thf(f3384,plain,
    spl303_49,
    inference(avatar_split_clause,[],[f2925,f3382]) ).

thf(f3382,plain,
    ( spl303_49
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_49])]) ).

thf(f2925,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2924]) ).

thf(f2924,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2920]) ).

thf(f2920,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1538]) ).

thf(f1538,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) ),
    inference(cnf_transformation,[],[f396]) ).

thf(f396,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) ),
    inference(fool_elimination,[],[f395]) ).

thf(f395,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) )
      = ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f195]) ).

thf(f195,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X28) )
      = ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_rotate1__is__Nil__conv) ).

thf(f3380,plain,
    spl303_48,
    inference(avatar_split_clause,[],[f1581,f3378]) ).

thf(f1581,plain,
    ! [X0: secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f830]) ).

thf(f830,plain,
    ! [X0: secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) ),
    inference(flattening,[],[f424]) ).

thf(f424,plain,
    ! [X0: secrecy_Expression > $o] : ( $true != vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f423]) ).

thf(f423,plain,
    ! [X0: secrecy_Expression > $o] : ~ vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X0),nil_Se901661471ession),
    inference(rectify,[],[f84]) ).

thf(f84,axiom,
    ! [X18: secrecy_Expression > $o] : ~ vAPP(list_S529945141ession,$o,vAPP(sTfun(secrecy_Expression,$o),sTfun(list_S529945141ession,$o),list_e1486860828ession,X18),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_list__ex1__simps_I1_J) ).

thf(f3376,plain,
    spl303_47,
    inference(avatar_split_clause,[],[f1580,f3374]) ).

thf(f1580,plain,
    ! [X0: secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f829]) ).

thf(f829,plain,
    ! [X0: secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(flattening,[],[f422]) ).

thf(f422,plain,
    ! [X0: secrecy_KS > $o] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f421]) ).

thf(f421,plain,
    ! [X0: secrecy_KS > $o] : ~ vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X0),nil_Secrecy_KS),
    inference(rectify,[],[f85]) ).

thf(f85,axiom,
    ! [X18: secrecy_KS > $o] : ~ vAPP(list_Secrecy_KS,$o,vAPP(sTfun(secrecy_KS,$o),sTfun(list_Secrecy_KS,$o),list_ex1_Secrecy_KS,X18),nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_list__ex1__simps_I1_J) ).

thf(f3372,plain,
    spl303_46,
    inference(avatar_split_clause,[],[f1521,f3370]) ).

thf(f3370,plain,
    ( spl303_46
  <=> ! [X0: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_46])]) ).

thf(f1521,plain,
    ! [X0: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)) ),
    inference(cnf_transformation,[],[f789]) ).

thf(f789,plain,
    ! [X0: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0)) ),
    inference(rectify,[],[f74]) ).

thf(f74,axiom,
    ! [X3: secrecy_Keys] : ( vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X3) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_KS2Expression_Osimps_I1_J) ).

thf(f3368,plain,
    spl303_45,
    inference(avatar_split_clause,[],[f1520,f3366]) ).

thf(f3364,plain,
    spl303_44,
    inference(avatar_split_clause,[],[f2923,f3362]) ).

thf(f3362,plain,
    ( spl303_44
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_44])]) ).

thf(f2923,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2922]) ).

thf(f2922,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2921]) ).

thf(f2921,plain,
    ! [X0: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1538]) ).

thf(f3360,plain,
    spl303_43,
    inference(avatar_split_clause,[],[f1519,f3358]) ).

thf(f1519,plain,
    ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f787]) ).

thf(f787,plain,
    ! [X0: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X0),nil_Se901661471ession) ),
    inference(rectify,[],[f203]) ).

thf(f203,axiom,
    ! [X59: secrecy_Expression > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,vAPP(sTfun(secrecy_Expression,list_S529945141ession),sTfun(list_S529945141ession,list_S529945141ession),maps_S599402637ession,X59),nil_Se901661471ession) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_maps__simps_I2_J) ).

thf(f3356,plain,
    spl303_42,
    inference(avatar_split_clause,[],[f1518,f3354]) ).

thf(f3354,plain,
    ( spl303_42
  <=> ! [X0: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_Secrecy_KS,list_S529945141ession,vAPP(sTfun(secrecy_KS,list_S529945141ession),sTfun(list_Secrecy_KS,list_S529945141ession),maps_S1434541085ession,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_42])]) ).

thf(f1518,plain,
    ! [X0: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_Secrecy_KS,list_S529945141ession,vAPP(sTfun(secrecy_KS,list_S529945141ession),sTfun(list_Secrecy_KS,list_S529945141ession),maps_S1434541085ession,X0),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f786]) ).

thf(f786,plain,
    ! [X0: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_Secrecy_KS,list_S529945141ession,vAPP(sTfun(secrecy_KS,list_S529945141ession),sTfun(list_Secrecy_KS,list_S529945141ession),maps_S1434541085ession,X0),nil_Secrecy_KS) ),
    inference(rectify,[],[f205]) ).

thf(f205,axiom,
    ! [X59: secrecy_KS > list_S529945141ession] : ( nil_Se901661471ession = vAPP(list_Secrecy_KS,list_S529945141ession,vAPP(sTfun(secrecy_KS,list_S529945141ession),sTfun(list_Secrecy_KS,list_S529945141ession),maps_S1434541085ession,X59),nil_Secrecy_KS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_maps__simps_I2_J) ).

thf(f3352,plain,
    spl303_41,
    inference(avatar_split_clause,[],[f1517,f3350]) ).

thf(f3350,plain,
    ( spl303_41
  <=> ! [X0: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),sTfun(list_S529945141ession,list_Secrecy_KS),maps_S399472669ecy_KS,X0),nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_41])]) ).

thf(f1517,plain,
    ! [X0: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),sTfun(list_S529945141ession,list_Secrecy_KS),maps_S399472669ecy_KS,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f785]) ).

thf(f785,plain,
    ! [X0: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),sTfun(list_S529945141ession,list_Secrecy_KS),maps_S399472669ecy_KS,X0),nil_Se901661471ession) ),
    inference(rectify,[],[f204]) ).

thf(f204,axiom,
    ! [X59: secrecy_Expression > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,vAPP(sTfun(secrecy_Expression,list_Secrecy_KS),sTfun(list_S529945141ession,list_Secrecy_KS),maps_S399472669ecy_KS,X59),nil_Se901661471ession) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_maps__simps_I2_J) ).

thf(f3348,plain,
    spl303_40,
    inference(avatar_split_clause,[],[f1516,f3346]) ).

thf(f3346,plain,
    ( spl303_40
  <=> ! [X0: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(list_Secrecy_KS,list_Secrecy_KS),maps_S377605037ecy_KS,X0),nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_40])]) ).

thf(f1516,plain,
    ! [X0: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(list_Secrecy_KS,list_Secrecy_KS),maps_S377605037ecy_KS,X0),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f784]) ).

thf(f784,plain,
    ! [X0: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(list_Secrecy_KS,list_Secrecy_KS),maps_S377605037ecy_KS,X0),nil_Secrecy_KS) ),
    inference(rectify,[],[f206]) ).

thf(f206,axiom,
    ! [X59: secrecy_KS > list_Secrecy_KS] : ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(sTfun(secrecy_KS,list_Secrecy_KS),sTfun(list_Secrecy_KS,list_Secrecy_KS),maps_S377605037ecy_KS,X59),nil_Secrecy_KS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_maps__simps_I2_J) ).

thf(f3340,plain,
    spl303_39,
    inference(avatar_split_clause,[],[f2919,f3338]) ).

thf(f3338,plain,
    ( spl303_39
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_39])]) ).

thf(f2919,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2918]) ).

thf(f2918,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2914]) ).

thf(f2914,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1539]) ).

thf(f1539,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ),
    inference(cnf_transformation,[],[f398]) ).

thf(f398,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ),
    inference(fool_elimination,[],[f397]) ).

thf(f397,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) )
      = ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f254]) ).

thf(f254,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X28) )
      = ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_rev__is__Nil__conv) ).

thf(f3332,plain,
    spl303_38,
    inference(avatar_split_clause,[],[f2917,f3330]) ).

thf(f3330,plain,
    ( spl303_38
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession != X0 )
        | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_38])]) ).

thf(f2917,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2916]) ).

thf(f2916,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2915]) ).

thf(f2915,plain,
    ! [X0: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1539]) ).

thf(f3328,plain,
    spl303_37,
    inference(avatar_split_clause,[],[f1595,f3326]) ).

thf(f1595,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) != X1 ),
    inference(cnf_transformation,[],[f835]) ).

thf(f835,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) != X1 ),
    inference(rectify,[],[f39]) ).

thf(f39,axiom,
    ! [X39: secrecy_Expression,X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X39),X28) != X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_not__Cons__self2) ).

thf(f3324,plain,
    spl303_36,
    inference(avatar_split_clause,[],[f1594,f3322]) ).

thf(f1594,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) ),
    inference(cnf_transformation,[],[f834]) ).

thf(f834,plain,
    ! [X0: secrecy_Expression,X1: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X0),X1) ),
    inference(rectify,[],[f22]) ).

thf(f22,axiom,
    ! [X21: secrecy_Expression,X22: list_S529945141ession] : ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,vAPP(secrecy_Expression,sTfun(list_S529945141ession,list_S529945141ession),cons_S112077679ession,X21),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list_Odistinct_I1_J) ).

thf(f3320,plain,
    spl303_35,
    inference(avatar_split_clause,[],[f1593,f3318]) ).

thf(f1593,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1) ),
    inference(cnf_transformation,[],[f833]) ).

thf(f833,plain,
    ! [X0: secrecy_KS,X1: list_Secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X0),X1) ),
    inference(rectify,[],[f21]) ).

thf(f21,axiom,
    ! [X21: secrecy_KS,X22: list_Secrecy_KS] : ( nil_Secrecy_KS != vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),cons_Secrecy_KS,X21),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list_Odistinct_I1_J) ).

thf(f3316,plain,
    spl303_34,
    inference(avatar_split_clause,[],[f1582,f3314]) ).

thf(f1582,plain,
    ! [X0: secrecy_specID] : ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f426]) ).

thf(f426,plain,
    ! [X0: secrecy_specID] : ( $true = vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f425]) ).

thf(f425,plain,
    ! [X0: secrecy_specID] : vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X0),nil_Se901661471ession),
    inference(rectify,[],[f15]) ).

thf(f15,axiom,
    ! [X4: secrecy_specID] : vAPP(list_S529945141ession,$o,vAPP(secrecy_specID,sTfun(list_S529945141ession,$o),knowle731562421_knows,X4),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_knows__emptyexpression) ).

thf(f3312,plain,
    spl303_33,
    inference(avatar_split_clause,[],[f1579,f3310]) ).

thf(f1579,plain,
    ! [X0: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) ),
    inference(cnf_transformation,[],[f828]) ).

thf(f828,plain,
    ! [X0: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) ),
    inference(flattening,[],[f420]) ).

thf(f420,plain,
    ! [X0: secrecy_Expression] : ( $true != vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession) ),
    inference(fool_elimination,[],[f419]) ).

thf(f419,plain,
    ! [X0: secrecy_Expression] : ~ vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X0),nil_Se901661471ession),
    inference(rectify,[],[f238]) ).

thf(f238,axiom,
    ! [X39: secrecy_Expression] : ~ vAPP(list_S529945141ession,$o,vAPP(secrecy_Expression,sTfun(list_S529945141ession,$o),mem_Se1967555118ession,X39),nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mem_Osimps_I1_J) ).

thf(f3308,plain,
    spl303_32,
    inference(avatar_split_clause,[],[f1578,f3306]) ).

thf(f1578,plain,
    ! [X0: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(cnf_transformation,[],[f827]) ).

thf(f827,plain,
    ! [X0: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(flattening,[],[f418]) ).

thf(f418,plain,
    ! [X0: secrecy_KS] : ( $true != vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS) ),
    inference(fool_elimination,[],[f417]) ).

thf(f417,plain,
    ! [X0: secrecy_KS] : ~ vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X0),nil_Secrecy_KS),
    inference(rectify,[],[f237]) ).

thf(f237,axiom,
    ! [X39: secrecy_KS] : ~ vAPP(list_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(list_Secrecy_KS,$o),mem_Secrecy_KS,X39),nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_mem_Osimps_I1_J) ).

thf(f3304,plain,
    spl303_31,
    inference(avatar_split_clause,[],[f1577,f3302]) ).

thf(f1577,plain,
    ! [X0: secrecy_Expression] : ( $true != vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) ),
    inference(cnf_transformation,[],[f826]) ).

thf(f826,plain,
    ! [X0: secrecy_Expression] : ( $true != vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) ),
    inference(flattening,[],[f416]) ).

thf(f416,plain,
    ! [X0: secrecy_Expression] : ( $true != vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0) ),
    inference(fool_elimination,[],[f415]) ).

thf(f415,plain,
    ! [X0: secrecy_Expression] : ~ vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X0),
    inference(rectify,[],[f128]) ).

thf(f128,axiom,
    ! [X15: secrecy_Expression] : ~ vAPP(secrecy_Expression,$o,vAPP(list_S529945141ession,sTfun(secrecy_Expression,$o),member2020590922ession,nil_Se901661471ession),X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_member__rec_I2_J) ).

thf(f3300,plain,
    spl303_30,
    inference(avatar_split_clause,[],[f1576,f3298]) ).

thf(f1576,plain,
    ! [X0: secrecy_KS] : ( $true != vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) ),
    inference(cnf_transformation,[],[f825]) ).

thf(f825,plain,
    ! [X0: secrecy_KS] : ( $true != vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) ),
    inference(flattening,[],[f414]) ).

thf(f414,plain,
    ! [X0: secrecy_KS] : ( $true != vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0) ),
    inference(fool_elimination,[],[f413]) ).

thf(f413,plain,
    ! [X0: secrecy_KS] : ~ vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X0),
    inference(rectify,[],[f129]) ).

thf(f129,axiom,
    ! [X15: secrecy_KS] : ~ vAPP(secrecy_KS,$o,vAPP(list_Secrecy_KS,sTfun(secrecy_KS,$o),member_Secrecy_KS,nil_Secrecy_KS),X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_member__rec_I2_J) ).

thf(f3296,plain,
    spl303_29,
    inference(avatar_split_clause,[],[f1514,f3294]) ).

thf(f3292,plain,
    spl303_28,
    inference(avatar_split_clause,[],[f1513,f3290]) ).

thf(f1513,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),nil_Se901661471ession) = X0 ),
    inference(cnf_transformation,[],[f781]) ).

thf(f781,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X0),nil_Se901661471ession) = X0 ),
    inference(rectify,[],[f156]) ).

thf(f156,axiom,
    ! [X28: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,X28),nil_Se901661471ession) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_splice__Nil2) ).

thf(f3288,plain,
    spl303_27,
    inference(avatar_split_clause,[],[f2907,f3286]) ).

thf(f3286,plain,
    ( spl303_27
  <=> ! [X0: list_S529945141ession] :
        ( ( nil_Se901661471ession = X0 )
        | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_27])]) ).

thf(f2907,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( nil_Se901661471ession != vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2906]) ).

thf(f2906,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = X0 )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2902]) ).

thf(f2902,plain,
    ! [X0: list_S529945141ession] :
      ( ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1541]) ).

thf(f1541,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) ),
    inference(cnf_transformation,[],[f402]) ).

thf(f402,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) ),
    inference(fool_elimination,[],[f401]) ).

thf(f401,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) )
      = ( nil_Se901661471ession = X0 ) ),
    inference(rectify,[],[f345]) ).

thf(f345,axiom,
    ! [X28: list_S529945141ession] :
      ( ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X28) )
      = ( nil_Se901661471ession = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_remdups__adj__Nil__iff) ).

thf(f3284,plain,
    spl303_26,
    inference(avatar_split_clause,[],[f1511,f3282]) ).

thf(f3280,plain,
    spl303_25,
    inference(avatar_split_clause,[],[f1510,f3278]) ).

thf(f3278,plain,
    ( spl303_25
  <=> ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,nil_Se901661471ession),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_25])]) ).

thf(f1510,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,nil_Se901661471ession),X0) = X0 ),
    inference(cnf_transformation,[],[f778]) ).

thf(f778,plain,
    ! [X0: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,nil_Se901661471ession),X0) = X0 ),
    inference(rectify,[],[f176]) ).

thf(f176,axiom,
    ! [X31: list_S529945141ession] : ( vAPP(list_S529945141ession,list_S529945141ession,vAPP(list_S529945141ession,sTfun(list_S529945141ession,list_S529945141ession),splice1390717708ession,nil_Se901661471ession),X31) = X31 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_splice_Osimps_I1_J) ).

thf(f3276,plain,
    spl303_24,
    inference(avatar_split_clause,[],[f1508,f3274]) ).

thf(f3274,plain,
    ( spl303_24
  <=> ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),append_Secrecy_KS,X0),nil_Secrecy_KS) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_24])]) ).

thf(f3272,plain,
    spl303_23,
    inference(avatar_split_clause,[],[f1507,f3270]) ).

thf(f3270,plain,
    ( spl303_23
  <=> ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),nil_Secrecy_KS) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_23])]) ).

thf(f1507,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),nil_Secrecy_KS) = X0 ),
    inference(cnf_transformation,[],[f775]) ).

thf(f775,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X0),nil_Secrecy_KS) = X0 ),
    inference(rectify,[],[f157]) ).

thf(f157,axiom,
    ! [X28: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,X28),nil_Secrecy_KS) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_splice__Nil2) ).

thf(f3268,plain,
    spl303_22,
    inference(avatar_split_clause,[],[f1505,f3266]) ).

thf(f3264,plain,
    spl303_21,
    inference(avatar_split_clause,[],[f1504,f3262]) ).

thf(f3262,plain,
    ( spl303_21
  <=> ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,nil_Secrecy_KS),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_21])]) ).

thf(f1504,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,nil_Secrecy_KS),X0) = X0 ),
    inference(cnf_transformation,[],[f772]) ).

thf(f772,plain,
    ! [X0: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,nil_Secrecy_KS),X0) = X0 ),
    inference(rectify,[],[f177]) ).

thf(f177,axiom,
    ! [X31: list_Secrecy_KS] : ( vAPP(list_Secrecy_KS,list_Secrecy_KS,vAPP(list_Secrecy_KS,sTfun(list_Secrecy_KS,list_Secrecy_KS),splice_Secrecy_KS,nil_Secrecy_KS),X31) = X31 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_splice_Osimps_I1_J) ).

thf(f3260,plain,
    spl303_20,
    inference(avatar_split_clause,[],[f1592,f3258]) ).

thf(f3258,plain,
    ( spl303_20
  <=> ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) != vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_20])]) ).

thf(f1592,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) != vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) ),
    inference(cnf_transformation,[],[f832]) ).

thf(f832,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X1) != vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X0) ),
    inference(rectify,[],[f73]) ).

thf(f73,axiom,
    ! [X12: secrecy_Keys,X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) != vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Expression_Odistinct_I1_J) ).

thf(f3256,plain,
    spl303_19,
    inference(avatar_split_clause,[],[f1591,f3254]) ).

thf(f1591,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) ),
    inference(cnf_transformation,[],[f831]) ).

thf(f831,plain,
    ! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) ),
    inference(rectify,[],[f18]) ).

thf(f18,axiom,
    ! [X12: secrecy_Keys,X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_KS_Odistinct_I1_J) ).

thf(f3252,plain,
    spl303_18,
    inference(avatar_split_clause,[],[f2905,f3250]) ).

thf(f2905,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0) ) ),
    inference(equality_proxy_clausification,[],[f2904]) ).

thf(f2904,plain,
    ! [X0: list_S529945141ession] :
      ( ( nil_Se901661471ession != X0 )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) ) ),
    inference(equality_proxy_clausification,[],[f2903]) ).

thf(f2903,plain,
    ! [X0: list_S529945141ession] :
      ( ( $false = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),X0) )
      | ( $true = vAPP(list_S529945141ession,$o,vAPP(list_S529945141ession,sTfun(list_S529945141ession,$o),vEQ(list_S529945141ession),nil_Se901661471ession),vAPP(list_S529945141ession,list_S529945141ession,remdup484344169ession,X0)) ) ),
    inference(binary_proxy_clausification,[],[f1541]) ).

thf(f3245,plain,
    spl303_17,
    inference(avatar_split_clause,[],[f2022,f3242]) ).

thf(f2022,plain,
    vAPP(list_S529945141ession,$o,distin1076152135ession,nil_Se901661471ession) = $true,
    inference(cnf_transformation,[],[f768]) ).

thf(f768,plain,
    vAPP(list_S529945141ession,$o,distin1076152135ession,nil_Se901661471ession) = $true,
    inference(fool_elimination,[],[f767]) ).

thf(f767,plain,
    vAPP(list_S529945141ession,$o,distin1076152135ession,nil_Se901661471ession),
    inference(rectify,[],[f299]) ).

thf(f299,axiom,
    vAPP(list_S529945141ession,$o,distin1076152135ession,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_distinct__adj__Nil) ).

thf(f3240,plain,
    spl303_16,
    inference(avatar_split_clause,[],[f2021,f3237]) ).

thf(f2021,plain,
    vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,nil_Secrecy_KS) = $true,
    inference(cnf_transformation,[],[f766]) ).

thf(f766,plain,
    vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,nil_Secrecy_KS) = $true,
    inference(fool_elimination,[],[f765]) ).

thf(f765,plain,
    vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,nil_Secrecy_KS),
    inference(rectify,[],[f300]) ).

thf(f300,axiom,
    vAPP(list_Secrecy_KS,$o,distin1495927511ecy_KS,nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_distinct__adj__Nil) ).

thf(f3235,plain,
    spl303_15,
    inference(avatar_split_clause,[],[f1489,f3232]) ).

thf(f3232,plain,
    ( spl303_15
  <=> ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_15])]) ).

thf(f1489,plain,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,nil_Se901661471ession),
    inference(cnf_transformation,[],[f302]) ).

thf(f302,axiom,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,tl_Sec1905266422ession,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_list_Osel_I2_J) ).

thf(f3230,plain,
    spl303_14,
    inference(avatar_split_clause,[],[f1488,f3227]) ).

thf(f1488,plain,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,nil_Se901661471ession),
    inference(cnf_transformation,[],[f261]) ).

thf(f261,axiom,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rev_Se1073238207ession,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_rev_Osimps_I1_J) ).

thf(f3225,plain,
    spl303_13,
    inference(avatar_split_clause,[],[f1487,f3222]) ).

thf(f3222,plain,
    ( spl303_13
  <=> ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_13])]) ).

thf(f1487,plain,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,nil_Se901661471ession),
    inference(cnf_transformation,[],[f219]) ).

thf(f219,axiom,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,butlas171474643ession,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_butlast_Osimps_I1_J) ).

thf(f3220,plain,
    spl303_12,
    inference(avatar_split_clause,[],[f1486,f3217]) ).

thf(f3217,plain,
    ( spl303_12
  <=> ( nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_12])]) ).

thf(f1486,plain,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,nil_Se901661471ession),
    inference(cnf_transformation,[],[f198]) ).

thf(f198,axiom,
    nil_Se901661471ession = vAPP(list_S529945141ession,list_S529945141ession,rotate1237234450ession,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_rotate1_Osimps_I1_J) ).

thf(f3215,plain,
    spl303_11,
    inference(avatar_split_clause,[],[f1485,f3212]) ).

thf(f1485,plain,
    nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,nil_li311616943ession),
    inference(cnf_transformation,[],[f200]) ).

thf(f200,axiom,
    nil_Se901661471ession = vAPP(list_l425507653ession,list_S529945141ession,concat388015140ession,nil_li311616943ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_concat_Osimps_I1_J) ).

thf(f3210,plain,
    ( spl303_10
    | spl303_2
    | ~ spl303_3 ),
    inference(avatar_split_clause,[],[f3157,f3143,f3138,f3207]) ).

thf(f3138,plain,
    ( spl303_2
  <=> ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_2])]) ).

thf(f3157,plain,
    ( ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $false )
    | spl303_2
    | ~ spl303_3 ),
    inference(trivial_inequality_removal,[],[f3155]) ).

thf(f3155,plain,
    ( ( $true != $true )
    | ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) = $false )
    | spl303_2
    | ~ spl303_3 ),
    inference(superposition,[],[f3140,f3144]) ).

thf(f3140,plain,
    ( ( vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) != $true )
    | spl303_2 ),
    inference(avatar_component_clause,[],[f3138]) ).

thf(f3205,plain,
    spl303_9,
    inference(avatar_split_clause,[],[f1484,f3202]) ).

thf(f3202,plain,
    ( spl303_9
  <=> ( nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,secrec1371625429on2KSL,nil_Se901661471ession) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_9])]) ).

thf(f1484,plain,
    nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,secrec1371625429on2KSL,nil_Se901661471ession),
    inference(cnf_transformation,[],[f83]) ).

thf(f83,axiom,
    nil_Secrecy_KS = vAPP(list_S529945141ession,list_Secrecy_KS,secrec1371625429on2KSL,nil_Se901661471ession),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Expression2KSL_Osimps_I1_J) ).

thf(f3200,plain,
    spl303_8,
    inference(avatar_split_clause,[],[f1483,f3197]) ).

thf(f3197,plain,
    ( spl303_8
  <=> ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_8])]) ).

thf(f1483,plain,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,nil_Secrecy_KS),
    inference(cnf_transformation,[],[f303]) ).

thf(f303,axiom,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,tl_Secrecy_KS,nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_list_Osel_I2_J) ).

thf(f3195,plain,
    spl303_7,
    inference(avatar_split_clause,[],[f1482,f3192]) ).

thf(f3192,plain,
    ( spl303_7
  <=> ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_7])]) ).

thf(f1482,plain,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,nil_Secrecy_KS),
    inference(cnf_transformation,[],[f220]) ).

thf(f220,axiom,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,butlast_Secrecy_KS,nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_butlast_Osimps_I1_J) ).

thf(f3190,plain,
    spl303_6,
    inference(avatar_split_clause,[],[f1481,f3187]) ).

thf(f1481,plain,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,nil_Secrecy_KS),
    inference(cnf_transformation,[],[f262]) ).

thf(f262,axiom,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rev_Secrecy_KS,nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_rev_Osimps_I1_J) ).

thf(f3185,plain,
    spl303_5,
    inference(avatar_split_clause,[],[f1480,f3182]) ).

thf(f3182,plain,
    ( spl303_5
  <=> ( nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,nil_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_5])]) ).

thf(f1480,plain,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,nil_Secrecy_KS),
    inference(cnf_transformation,[],[f199]) ).

thf(f199,axiom,
    nil_Secrecy_KS = vAPP(list_Secrecy_KS,list_Secrecy_KS,rotate1_Secrecy_KS,nil_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_rotate1_Osimps_I1_J) ).

thf(f3180,plain,
    spl303_4,
    inference(avatar_split_clause,[],[f1479,f3177]) ).

thf(f3177,plain,
    ( spl303_4
  <=> ( nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,nil_list_Secrecy_KS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_4])]) ).

thf(f1479,plain,
    nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,nil_list_Secrecy_KS),
    inference(cnf_transformation,[],[f201]) ).

thf(f201,axiom,
    nil_Secrecy_KS = vAPP(list_list_Secrecy_KS,list_Secrecy_KS,concat_Secrecy_KS,nil_list_Secrecy_KS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_concat_Osimps_I1_J) ).

thf(f3145,plain,
    spl303_3,
    inference(avatar_split_clause,[],[f356,f3143]) ).

thf(f356,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f3141,plain,
    ~ spl303_2,
    inference(avatar_split_clause,[],[f1478,f3138]) ).

thf(f1478,plain,
    vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) != $true,
    inference(cnf_transformation,[],[f771]) ).

thf(f771,plain,
    vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) != $true,
    inference(flattening,[],[f358]) ).

thf(f358,plain,
    vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)) != $true,
    inference(fool_elimination,[],[f357]) ).

thf(f357,plain,
    ~ vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)),
    inference(rectify,[],[f354]) ).

thf(f354,negated_conjecture,
    ~ vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)),
    inference(negated_conjecture,[],[f353]) ).

thf(f353,conjecture,
    vAPP(secrecy_KS,$o,vAPP(secrecy_specID,sTfun(secrecy_KS,$o),knowle945212990e_know,a),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,m)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f3136,plain,
    ~ spl303_1,
    inference(avatar_split_clause,[],[f355,f3133]) ).

thf(f3133,plain,
    ( spl303_1
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl303_1])]) ).

thf(f355,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ITP085^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat May 18 17:01:37 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (14873)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40  % (14876)WARNING: value z3 for option sas not known
% 0.15/0.40  % (14880)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)
% 0.15/0.40  % (14876)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)
% 0.15/0.40  % (14875)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.42  % (14874)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.42  % (14879)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)
% 0.22/0.42  % (14877)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.42  % (14878)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)
% 0.22/0.48  % (14880)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.50  % Exception at run slice level
% 0.22/0.50  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.51  % (14881)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.52  % Exception at run slice level
% 0.22/0.52  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.53  % Exception at run slice level
% 0.22/0.53  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.53  % (14882)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)
% 0.22/0.55  % (14883)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)
% 0.22/0.55  % (14881)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.56  % Exception at run slice level
% 0.22/0.56  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.41/0.58  % (14884)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)
% 1.41/0.58  % (14882)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 12.14/2.14  % (14878)First to succeed.
% 13.44/2.35  % (14878)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14873"
% 13.44/2.36  % (14878)Refutation found. Thanks to Tanya!
% 13.44/2.36  % SZS status Theorem for theBenchmark
% 13.44/2.36  % SZS output start Proof for theBenchmark
% See solution above
% 13.89/2.41  % (14878)------------------------------
% 13.89/2.41  % (14878)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 13.89/2.41  % (14878)Termination reason: Refutation
% 13.89/2.41  
% 13.89/2.41  % (14878)Memory used [KB]: 14114
% 13.89/2.41  % (14878)Time elapsed: 1.931 s
% 13.89/2.41  % (14878)Instructions burned: 5521 (million)
% 13.89/2.41  % (14873)Success in time 2.039 s
%------------------------------------------------------------------------------